2016/2017
1st Quarter Elementary Mathematics
Curriculum Guide
Grade 4 Page 1 of 72 4th Grade Year at a Glance Math Florida Standards Modules Duration Quarter 1 8/15/16 ‐ 9/15/16 23 Days Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction Operations and Algebraic Thinking 4.OA.1.3 4.OA.1.1 Number and Operations in Base Ten 4.NBT.1.1 4.NBT.1.2 4.NBT.1.3 4.NBT.2.4 9/16/16 ‐ 9/23/16 6 Days Module 2: Unit Conversions and Problem Solving Measurement and Data 4.MD.1.1 4.MD1.2 Quarter 2 9/26/16 ‐ 10/17/16 ‐
10/14/16 11/17/16 15 Days 22 Days Module 3:
Multi‐Digit Multiplication and Division Operations and Algebraic Thinking 4.OA.1.1 4.OA.1.2 4.OA.1.3 4.OA.2.4 4.OA.3.5 4.OA.1.a* 4.OA.1.b* Number and Operations in Base Ten 4.NBT.2.5 4.NBT.2.6 4.NBT.1.1 Measurement and Data 4.MD.1.3 11/18/16 ‐
1/9/17 ‐
12/22/16 2/3/17 22 Days 18 Days Module 5:
Fraction Equivalence, Ordering, and Operations Number and Operations ‐
Fractions 4.NF.1.1 4.NF.1.2 4.NF.2.3 4.NF.2.4 Measurement and Data 4.MD.2.4 4.MD.1.2 Quarter 3
Quarter 4
2/6/17 ‐
3/2/17 18 Days Module 6: Decimal Fractions 3/3/17 ‐ 3/27/17‐
3/16/17
4/4/17 10 Days 6 Days Module 4:
Angle Measure and Plane Figures Number and Operations in Base Ten 4.NBT.1.1 Number and Operations ‐ Fractions 4.NF.3.5 4.NF.3.6 4.NF.3.7 4.NF.1.1 4.NF.2.3 Measurement and Data 4.MD.1.1 4.MD.1.2 Measurement and Data 4.MD.3.5 4.MD.3.6 4.MD.3.7 Geometry 4.G.1.1 4.G.1.2 4.G.1.3 4/5/17 –
5/1/17 17 Days Module 7:
Exploring Measurement with Multiplication Operations and Algebraic Thinking 4.OA.1.1 4.OA.1.2 4.OA.1.3 Number and Operations in Base Ten 4.NBT.2.5 4.NBT.2.6 Measurement and Data 4.MD.1.1 4.MD.1.2 5/2/17 – 6/2/17 23 Days Deepening Understanding: Reteach/ Enrich 4th Grade Major Work Operations and Algebraic Thinking 4.OA.1.3 4.OA.1.a* 4.OA.1.b* 4.OA.3.5 4.OA.1.2 4.OA.2.4 Number and Operations ‐ Fractions 4.NF.1.1 4.NF.2.3 4.NF.2.4 Measurement and Data 4.MD.2.4 4.MD.1.3 Page 2 of 72 Elementary Mathematics 4th Grade Testing Calendar Required (The following assessments have been scheduled for you in your grade level curriculum guides. Please note: these assessments are required to be administered within the testing window provided. Please refer to the Optional Testing calendar for additional assessments that have been developed for you to administer should you choose to. Required assessments are subject to change. Please refer to the district testing calendar for testing window and details.) Quarter Assessment Approximate Testing Dates Duration 1 i‐Ready Fall 8/17 ‐ 8/31 2 days 2 Mid‐Year Scrimmage 12/1 ‐ 12/18 2 days i‐Ready WInter 12/5 ‐ 12/16 2 days 3 FSA 4/10 ‐ 5/5 2 days 4 i‐Ready Spring 5/1 ‐ 5/12 2 days Page 3 of 72 Elementary Mathematics 4th Grade Testing Calendar Optional (The following assessments have been developed and scheduled in your grade level Curriculum Guides. Please note: these assessments are optional, should you choose to administer them. Please refer to the required assessment calendar for required testing for your grade level.) Quarter Assessment 1 Assess/Performance Task 4.NBT.1.3 Mid‐Module 1 2 3 Approximate Testing Dates 8/29 Duration 9/1 1 day Assess/Performance Task 4.NBT.2.4 End of Module 1 9/9 9/14 1 day End of Module 2 9/23 1 day Assess/Performance Task 4.NBT.2.5 Mid‐Module 3 10/7 10/12 1 day Assess/Performance Task 4.NBT.2.6 Assess/Performance Task 4.NBT.2.5 End of Module 3 10/31 11/10 11/16 1 day Assess/Performance Task 4.NF.1.1 Mid‐Module 5 12/9 12/22 1 day Performance Task 4.NF.2.3 End of Module 5 1/25 2/2 1 day Mid‐Module 6 2/15 1 day Performance Task 4.NF.3.7 End of Module 6 2/17 3/1 1 day Performance Task 3/7 Page 4 of 72 4.G.1.1 4 Mid‐Module 4 3/14 1 day Performance Task 4.MD.3.7 Performance Task 4.G.1.2 End of Module 4 3/27 3/30 4/3 Performance Task 4.MD.1.1 Performance Task 4.MD.1.2 End of Module 7 4/6 4/24 5/1 1 day 5/4 5/12 Performance Task: 4.OA.3.5 Performance Task 4.OA.1.3 Page 5 of 72 August
Notes
Mon
Tues
4th Grade
Wed
Thu
Fri
1
2
3
4
5
8
9
10
11
12
Notes
PRE‐PLANNING WEEK 15
Day 1
16
Day 2
Mod 1
Lesson 1
17
Day 3
Mod 1
Lesson 2
18
Day 4
Mod 1
Lesson 3
19
Day 5
Mod 1
Lesson 4
25
Day 9
Mod 1
Lesson 6
26
Day 10
Mod 1
Lesson 7
i-Ready testing
window begins on this
day. There are two
days allotted as “flex”
for accommodating
testing days.
22
Day 6
Mod 1
Lesson 5
29
Day 11
Mod 1
Lesson 8
23
Day 7
i-Ready
Diagnostic
30
Day 12
Mod 1
Lesson 9
24
Day 8
i-Ready
Diagnostic
31
ERD
Day 13
Mod 1
Lesson 10
*Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class
needs.
Page 6 of 72 September
Notes
Mon
Tues
4th Grade Wed
5
6
Schools Closed Day 16
Mod 1
Lesson 12
7
Day 17
Mod 1
Lesson 13
12
Day 20
Mod 1
Lesson 16
13
Day 21
Mod 1
Lesson 18
14
ERD
Day 22
End of Module
1 Assessment
19
Day 25
Mod 2
Lesson 2
26
Day 30
Mod 3
Lesson 1
20
Day 26
Mod 2
Lesson 3
27
Day 31
Mod 3
Lesson 2
Thu
1
Day 14
Mid-Module 1
Assessment,
Topic A-C
8
Day 18
Mod 1
Lesson 14
15
Day 23
Review and
Remediate
previous
taught
standards
21
22
Day 27
Day 28
Mod 2
Mod 2
Lesson 4
Lesson 5
28
ERD 29
Day 32
Day 33
Mod 3
Mod 3
Lesson 3
Lesson 4
Fri
Notes
2
Day 15
Mod 1
Lesson 11
9
Day 19
Mod 1
Lesson 15
16
Day 24
Mod 2
Lesson 1
23
Day 29
End of Module
2 Assessment
30
Day 34
Mod 3
Lesson 5
*Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class
needs.
Page 7 of 72 October
Notes
Mon
Tues
4th Grade
Wed
Thu
Fri
3
Day 35
Mod 3
Lesson 6
4
Day 36
Mod 3
Lesson 7
5
Day 37
Mod 3
Lesson 8
6
Day 38
Mod 3
Lesson 9
7
Day 39
Mod 3
Lesson 11
10
Day 40
Mod 3
Lesson 12
11
Day 41
Mod 3
Lesson 13
13
Day 43
Mod 3
Lesson 14
14
Day 44
Mod 3
Lesson 15
17
Day 45
Mod 3
Lesson 16
18
Day 46
Mod 3
Lesson 17
12
ERD
Day 42
Mid-Module
Assessment
Topics A-D
19
Day 47
Mod 3
Lesson 18
20
Day 48
Mod 3
Lesson 20
21
Planning Day
25
Day 50
Mod 3
Lesson 23
26
ERD
Day 51
Mod 3
Lesson 24
27
Day 52
Mod 3
Lesson 25
28
Day 53
Mod 3
Lesson 26
Notes
Quarter 1 Ends
Quarter 2 Begins
24
Day 49
Mod 3
Lesson 22
31
Day 54
Mod 3
Lesson 27
*Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class
needs. Page 8 of 72 Quarter 1 Module 1 Course: DUVAL COUNTY PUBLIC SCHOOLS
Math Curriculum Lesson Guide
Unit # Dates/Pacing: Grade 4 Math Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction 08/15/16 ‐‐ 09/15/16, 23 days Operations and Algebraic Thinking 4.OA.1.3: Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.OA.1.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Cognitive Complexity: Level 1 Recall Numbers and Operations in Base Ten 4.NBT.1.1: Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. For MAFS example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Cognitive Complexity: Level 1 Recall 4.NBT.1.2: Read and write multi‐digit whole numbers using base‐ten numerals, number names, and expanded form. Compare two multi‐digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.NBT.1.3: Use place value understanding to round multi‐digit whole numbers to any place. Cognitive Complexity: Level 1 Recall 4.NBT.2.4: Fluently add and subtract multi‐digit whole numbers using the standard algorithm. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Cognitive Complexity: Level 1 Recall Page 9 of 72 Standards for Mathematical Practices
Mathematically proficient students in grade 4 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may 1. Make sense of problems and use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking persevere in solving them. themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers. Mathematically proficient fourth grade students should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate 2. Reason abstractly and units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with quantitatively. fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts. In fourth grade mathematically proficient students may construct arguments using concrete referents, such as objects, 3. Construct viable arguments pictures, and drawings. They explain their thinking and make connections between models and equations. They refine their and critique the reasoning of mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get others. that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. Mathematically proficient fourth grade students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, 4. Model with mathematics. etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense. Mathematically proficient fourth grader students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper or a number 5. Use appropriate tools line to represent and compare decimals and protractors to measure angles. They use other measurement tools to strategically. understand the relative size of units within a system and express measurements given in larger units in terms of smaller units. As fourth grader students develop their mathematical communication skills, they try to use clear and precise language in 6. Attend to precision. their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot. In fourth grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use 7. Look for and make use of properties of operations to explain calculations (partial products model). They relate representations of counting problems structure. such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns that follow a given rule. Students in fourth grade should notice repetitive actions in computation to make generalizations. Students use models to 8. Look for and express explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own regularity in repeated reasoning. algorithms. For example, students use visual fraction models to write equivalent fractions. Page 10 of 72 Test Item Specifications Content Standard MAFS.4.OA.1.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Items requiring precise or exact solutions are limited to: Assessment Limits  addition and subtraction within 1,000.  multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit.  division of 2‐digit by 1‐digit. Items may contain a maximum of 3 steps. Items involving remainders must require the student to interpret and/or use the remainder with respect to the context. Variables must be represented by a letter, and variables must be defined or described in the context. Equation Editor Multiselect Item Types Multiple Choice Open Response Required
Context Level: 2 Basic Application of Skills & Concepts Complexity Level Achievement Level Descriptions Level 2 solves one‐step word problems (which do not include remainders) using the four operations with simple context and scaffolding where the sum, difference, product, or quotient is always the unknown Level 3 Level 4 Level 5 solves two‐step word problems (including interpreting remainders) using the four operations, where the unknown is in a variety of positions, and can be represented by a symbol/letter solves three‐step word problems using the four operations; recognizes the reasonableness of answers using mental computation and estimation strategies solves multistep word problems with multiple possible solutions and determines which would be the most reasonable based upon given criteria Page 11 of 72 Content Standard MAFS.4.OA.1.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Items may not require students to solve for unknown factors that exceed 10 x 10 multiplication facts. Assessment Limits Item must include a verbal description of an equation or a multiplication equation. Multiplication situations must be a comparison (e.g., times as many). Equation Editor Multiple Choice Item Types GRID Multiselect Matching Item Open Response Allowable Context Level: 1 Recall Complexity Level Achievement Level Descriptions Level 2 [intentionally left blank] Level 3 recognizes that any two factors and their product can be read as a comparison; represents those comparisons as equations Level 4 creates a context for a multiplicative comparison problem given an equation Level 5 [intentionally left blank] Page 12 of 72 Content Standard MAFS.4.NBT.1.1 Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Items may contain whole numbers within 1,000,000. Assessment Limits Items may not compare digits across more than 1 place value. Editing Task Choice Multiple Choice Item Types Equation Editor Multiselect Hot Text Open Response No context Context Complexity Level Level 1: Recall Level 2 recognizes that a digit in one place represents 10 times as much as it represents in the place to its right (for numbers up to and including 10,000), with visual representations Achievement Level Descriptions Level 3 Level 4 Level 5 [intentionally left blank] recognizes that a digit in one place recognizes that a digit in one place represents 10 times as much as it represents 10 times as much as it represents in the place to its right (for represents in the place to its right (for numbers up to and including 100,000) numbers up to and including 1,000,000) Content Standard MAFS.4.NBT.1.2 Read and write multi‐digit whole numbers using base‐ten numerals, number names, and expanded form. Compare two multi‐digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Given values and item solutions may only be whole numbers between 1 and 1,000,000. Assessment Limits Item Types Context Complexity Level Level 2 reads and writes multi‐digit whole numbers to the thousands place Equation Editor Multiple Choice GRID Multiselect Matching Item Allowable Level: 2 Basic Application of Skills & Concepts Achievement Level Descriptions Level 4 Level 3 recognizes that a digit in one place reads, writes, and compares whole numbers to the hundred‐thousandths represents 10 times as much as it represents in the place to its right (for place, using base‐ten numerals, number names, and expanded form numbers up to and including 1,000,000) Level 5 [intentionally left blank] Page 13 of 72 Content Standard MAFS.4.NBT.1.3 Use place value understanding to round multi‐digit whole numbers to any place. Given values and item solutions may only be whole numbers between 1,000 and Assessment Limits 1,000,000. Equation Editor Matching Item Item Types Multiselect Table Item Multiple Choice Allowable Context Level: 1 Recall Complexity Level Achievement Level Descriptions Level 2 uses place value understanding to round multi‐digit whole numbers to any place within 1,000 Level 3 uses place value understanding to round multi‐digit whole numbers to any place within 1,000,000 Level 4 uses place value understanding to round whole numbers up to any place where the digit to the left is also affected (e.g., round 199 to the nearest ten) Level 5 determines a number that falls between two numbers of different place values Content Standard MAFS.4.NBT.2.4 Fluently add and subtract multi‐digit whole numbers using the standard algorithm. Items may only contain whole number factors and solutions greater than 1,000 and within 1,000,000. Assessment Limits Addition expressions may contain up to three addends. Equation Editor Multiple Choice Item Types GRID Multiselect No Context Context Complexity Level Level: 1 Recall Achievement Level Descriptions Level 2 adds and subtracts two multi‐digit whole numbers using the standard algorithm (not including subtraction across zeros) Level 3 fluently adds up to three and subtracts two multi‐digit whole numbers using the standard algorithm Level 4 determines the missing digit(s) within the addend in an addition or subtraction problem Level 5 analyzes and describes an error in a strategy and shows the correct solution Page 14 of 72 Teacher Academic Language New or Recently Introduced Terms  Ten thousands, hundred thousands (as places on the place value chart)  Millions, ten millions, hundred millions (as places on the place value chart)  Variable (letters that stand for numbers and can be added, subtracted, multiplied, and divided as numbers are) Familiar Terms and Symbols  =, <, > (equal to, less than, greater than)  Addend (e.g., in 4 + 5, the numbers 4 and 5 are the addends)  Algorithm (a step‐by‐step procedure to solve a particular type of problem)  Bundling, making, renaming, changing, exchanging, regrouping, trading (e.g., exchanging 10 ones for 1 ten)  Compose (e.g., to make 1 larger unit from 10 smaller units)  Decompose (e.g., to break 1 larger unit into 10 smaller units)  Difference (answer to a subtraction problem)  Digit (any of the numbers 0 to 9; e.g., What is the value of the digit in the tens place?)  Endpoint (used with rounding on the number line; the numbers that mark the beginning and end of a given interval)  Equation (e.g., 2,389 + 80,601 = _____)  Estimate (an approximation of a quantity or number)  Expanded form (e.g., 100 + 30 + 5 = 135)  Expression (e.g., 2 thousands × 10)  Halfway (with reference to a number line, the midpoint between two numbers, e.g., 5 is halfway between 0 and 10)  Number line (a line marked with numbers at evenly spaced intervals)  Number sentence (e.g., 4 + 3 = 7)  Place value (the numerical value that a digit has by virtue of its position in a number)  Rounding (approximating the value of a given number)  Standard form (a number written in the format 135)  Sum (answer to an addition problem)  Tape diagram (bar diagram)  Unbundling, breaking, renaming, changing, regrouping, trading (e.g., exchanging 1 ten for 10 ones)  Word form (e.g., one hundred thirty‐five) Page 15 of 72 Place Value, Rounding, and Algorithms for Addition and Subtraction OVERVIEW In this 22‐day module of Grade 4, students extend their work with whole numbers. They begin with large numbers using familiar units (hundreds and thousands) and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1.1). They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion).1 The place value chart will be fundamental in Topic A. Building upon their previous knowledge of bundling, students learn that 10 hundreds can be composed into 1 thousand and, therefore, 30 hundreds can be composed into 3 thousands because a digit’s value is ten times what it would be one place to its right (4.NBT.1.1). Conversely, students learn to recognize that in a number such as 7,777 each 7 has a value that is 10 times the value of its neighbor to the immediate right. 1 thousand can be decomposed into 10 hundreds, therefore 7 thousands can be decomposed into 70 hundreds. Similarly, multiplying by 10 will shift digits one place to the left, and dividing by 10 will shift digits one place to the right. 3,000 = 300 x 10 3,000 ÷ 10 = 300 In Topic B, students use place value as a basis for comparison of whole numbers. Although this is not a new topic, it becomes more complex because the numbers are larger. For example, it becomes clear that 34,156 is 3 thousand greater than 31,156. 34,156>31,156 Comparison leads directly into rounding, where their skill with isolating units is applied and extended. Rounding to the nearest ten and hundred was mastered with 3 digit numbers in Grade 3. Now Grade 4 students moving into Topic C learn to round to any place value (4.NBT.1.3) initially using the vertical number line though ultimately moving away from the visual model altogether. Topic C also includes word problems where students apply rounding to real life situations. In Grade 4, students become fluent with the standard algorithms for addition and subtraction. In Topics D and E students focus on single like‐unit calculations (ones with ones, thousands with thousands, etc.) at times requiring the composition of greater units when adding (10 hundreds are composed into 1 thousand) and decomposition into smaller units when subtracting (1 thousand is decomposed into 10 hundreds) (4.NBT.2.4). Throughout these topics, students will apply their algorithmic knowledge to solve word problems. Also, students use a variable to represent the unknown quantity. The module culminates with multi‐step word problems in Topic F (4.OA.1.3). Tape diagrams are used throughout the topic to model additive compare problems like the one exemplified below. These diagrams facilitate deeper comprehension and serve as a way to support the reasonableness of an answer. 1 Grade 4 expectations in the NBT standards domain, however, are limited to whole numbers less than or equal to 1,000,000. Page 16 of 72 A goat produces 5,212 gallons of milk a year. The cow produces 17,279 gallons a year. How much more milk does the goat need to produce to make the same amount of milk as a cow? 17,279
5,212
______ The goat needs to produce _______ more gallons of milk a year. The mid‐module assessment will follow Topic C. The end‐of‐module assessment follows Topic F. Suggested Methods of Instructional Delivery Directions for Administration of Sprints Sprints are designed to develop fluency. They should be fun, adrenaline‐rich activities that intentionally build energy and excitement. A fast pace is essential. During Sprint administration, teachers assume the role of athletic coaches. A rousing routine fuels students’ motivation to do their personal best. Student recognition of increasing success is critical, and so every improvement is celebrated. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. With practice, the following routine takes about 9 minutes. Sprint A Pass Sprint A out quickly, face down on student desks with instructions to not look at the problems until the signal is given. (Some Sprints include words. If necessary, prior to starting the Sprint, quickly review the words so that reading difficulty does not slow students down.) T: You will have 60 seconds to do as many problems as you can. I do not expect you to finish all of them. Just do as many as you can, your personal best. (If some students are likely to finish before time is up, assign a number to count by on the back.) T: Take your mark! Get set! THINK! Page 17 of 72 Students immediately turn papers over and work furiously to finish as many problems as they can in 60 seconds. Time precisely. T: T: S: T: S: Stop! Circle the last problem you did. I will read just the answers. If you got it right, call out “Yes!” If you made a mistake, circle it. Ready? (Energetically, rapid‐fire call the first answer.) Yes! (Energetically, rapid‐fire call the second answer.) Yes! Repeat to the end of Sprint A or until no student has a correct answer. If needed, read the count‐by answers in the same way you read Sprint answers. Each number counted‐by on the back is considered a correct answer. T: Fantastic! Now, write the number you got correct at the top of your page. This is your personal goal for Sprint B. T: How many of you got one right? (All hands should go up.) T: Keep your hand up until I say the number that is one more than the number you got correct. So, if you got 14 correct, when I say 15, your hand goes down. Ready? T: (Continue quickly.) How many got two correct? Three? Four? Five? (Continue until all hands are down.) If the class needs more practice with Sprint A, continue with the optional routine presented below. T: I’ll give you one minute to do more problems on this half of the Sprint. If you finish, stand behind your chair. As students work, the student who scored highest on Sprint A might pass out Sprint B. T: Stop! I will read just the answers. If you got it right, call out “Yes!” If you made a mistake, circle it. Ready? (Read the answers to the first half again as students stand.) Movement To keep the energy and fun going, always do a stretch or a movement game in between Sprints A and B. For example, the class might do jumping jacks while skip‐counting by 5 for about 1 minute. Feeling invigorated, students take their seats for Sprint B, ready to make every effort to complete more problems this time. Sprint B Pass Sprint B out quickly, face down on student desks with instructions to not look at the problems until the signal is given. (Repeat the procedure for Sprint A up through the show of hands for how many right.) T: Stand up if you got more correct on the second Sprint than on the first. S: (Stand.) T: Keep standing until I say the number that tells how many more you got right on Sprint B. If you got three more right on Sprint B than you did on Sprint A, when I say three, you sit down. Ready? (Call out numbers starting with one. Students sit as the number by which they improved is called. Celebrate the students who improved most with a cheer.) T: Well done! Now, take a moment to go back and correct your mistakes. Think about what patterns you noticed in today’s Sprint. Page 18 of 72 T: How did the patterns help you get better at solving the problems?
T: Rally Robin your thinking with your partner for 1 minute. Go! Rally Robin is a style of sharing in which partners trade information back and forth, one statement at a time per person, for about 1 minute. This is an especially valuable part of the routine for students who benefit from their friends’ support to identify patterns and try new strategies. Students may take Sprints home. RDW or Read, Draw, Write (an Equation and a Statement) Mathematicians and teachers suggest a simple process applicable to all grades: 1) Read. 2) Draw and Label. 3) Write an equation. 4) Write a word sentence (statement). The more students participate in reasoning through problems with a systematic approach, the more they internalize those behaviors and thought processes. 
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What do I see? Can I draw something? What conclusions can I make from my drawing? Page 19 of 72 Module Specific Notes: 
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The game Close to 1,000 can be modified to meet the content limits of the standard. According to the Item Specifications students work with numbers to 1,000,000. Changes on the 10,000 chart can be adapted as an aligned activity. The 10,000 charts may need to be made before hand. Resources Math Studio Talk: Common Core for Grade 4.NBT https://www.engageny.org/resource/math‐studio‐
talk‐common‐core‐instruction‐4nbt Common Core Instruction: Solving Addition and Subtraction Word Problems with Tape Diagrams https://www.engageny.org/resource/common‐core‐
instruction‐solving‐addition‐and‐subtraction‐word‐
problems‐with‐tape‐diagrams Module Materials 
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Number lines (vertical to represent rounding up and rounding down) Personal white boards (one per student) Place value cards (one large set per classroom including 7 units to model place value) Place value disks (can be concrete manipulatives or pictorial drawings, such as the chip model, to represent numbers; one set per student or per pair) Tape diagrams (drawn to model a word problem) Additional Aligned Activities Investigations in Numbers, Data & Space Unit 5 Session 2.5 Close to 1,000 Unit 5 Session 3.3 Changing Places on the 10,000. enVision Math Common Core Topic 3 ‐ 3.2** Toss and Talk Topic 3 ‐ 3.3** Clip and Cover Topic 3 ‐ 3.5** Toss and Talk Topic 4 ‐ 4.3* Toss and Talk Topic 4 ‐ 4.3**Toss and Talk Topic 4 – 4.4* Display the Digits Topic 4 – 4.4** Display the Digits Page 20 of 72 Standards 4.NBT.1.1 4.NBT.1.2 4.OA.1.1 4.NBT.1.2 Topics and Objectives A B Place Value of Multi‐Digit Whole Numbers Lesson 1: Interpret a multiplication equation as a comparison. Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its right. Lesson 3: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units. Lesson 4: Read and write multi‐digit numbers using base ten numerals, number names, and expanded form. Comparing Multi‐Digit Whole Numbers Lesson 5: Compare numbers based on meanings of the digits using >, <, or = to record the comparison. Lesson 6: 4.NBT.1.3 C 4.OA.1.3 4.NBT.2.4 4.NBT.1.1 4.NBT.1.2 D 4.OA.1.3 4.NBT.2.4 4.NBT.1.1 4.NBT.1.2 E Find 1, 10, and 100 thousand more and less than a given number. Rounding Multi‐Digit Whole Numbers Lesson 7: Round multi‐digit numbers to the thousands place using the vertical number line. Lesson 8: Round multi‐digit numbers to any place using the vertical number line. Lesson 9: Use place value understanding to round multi‐digit numbers to any place value. Lesson 10: Use place value understanding to round multi‐digit numbers to any place value using real world applications. Mid‐Module Assessment: Topics A–C Multi‐Digit Whole Number Addition Lesson 11: Use place value understanding to fluently add multi‐digit whole numbers using the standard addition algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 12: Solve multi‐step word problems using the standard addition algorithm modeled with tape diagrams, and assess the reasonableness of answers using rounding. Multi‐Digit Whole Number Subtraction Lesson 13: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 14: Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 15: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard Page 21 of 72 Standards Topics and Objectives subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.
Lesson 16: 4.OA.1.3 4.NBT.1.1 4.NBT.1.2 4.NBT.2.4 F Solve two‐step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding. Addition and Subtraction Word Problems Lesson 17: Solve additive compare word problems modeled with tape diagrams. Omitted in Duval County Curriculum Guide. Lesson is outside of test item specifications. Lesson 18: Solve multi‐step word problems modeled with tape diagrams, and assess the reasonableness of answers using rounding. Lesson 19: Create and solve multi‐step word problems from given tape diagrams and equations. Omitted in Duval County Curriculum Guide. Lesson is outside of test item specifications. End‐of‐Module Assessment: Topics A–F Page 22 of 72 Topic A: Place Value of Multi‐Digit Whole Numbers
In Topic A, students build the place value chart to 1 million and learn the relationship between each place value as 10 times the value of the place to the right. Students manipulate numbers to see this relationship, such as 30 hundreds composed as 3 thousands. They decompose numbers to see that 7 thousands is the same as 70 hundreds. As students build the place value chart into thousands and up to 1 million, the sequence of three digits is emphasized. They become familiar with the base thousand unit names up to 1 billion. Students fluently write numbers in multiple formats: as digits, in unit form, as words, and in expanded form up to 1 million. Date/ Day of the school year Approx. Date: 08/15/2016 Day: 1 Objective/ Essential Question OBJ: Students will become familiar with math rituals and routines. EQ: How can I become familiar with math rituals and routines? Math Florida Standards/ Mathematical Practice Target Embedded Fluency Mathematical Practices Academic Language Lesson Assessment / Performance Tasks journals centers manipulatives core instruction GRRM *common board configuration expectations home learning CHAMPs transitions Rituals and Routines  Interactive Journals  Centers  Introduce Sprints  Accountable Talk  Manipulatives During Centers Block: Rituals and Routines Lesson During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. place value
disks place value chart ones tens hundreds thousands multiply equation model digit Module 1
Topic A Lesson 1: Interpret a multiplication equation as a comparison. During Centers Block: Rituals and Routines Lesson Lesson Materials: Multiply and Divide by 10 Sprint (T) Place value disks: ones, tens, hundreds, and thousands; unlabeled thousands place value chart (Template) (S) Personal white board, unlabeled thousands place value chart (Template) During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Notes: Approx. Date: 8/16/2016 Day: 2 OBJ: Students will recognize a digit represents 10 times the value of what it represents in the place to its right. EQ: How can I interpret a multiplication equation as a comparison? Target 4.NBT.1.1 Embedded 4.OA.1.1 4.NBT.1.2 Fluency 3.MD.3.7 Mathematical Practices MP6 Page 23 of 72 Notes: MAFS.OA.1.1 will be addressed again in Module 3 to the depth of the standard. Approx. Date: 8/17/2016 Day: 3 OBJ: Students will recognize a digit represents 10 times the value of what it represents in the place to its right. EQ: How can I recognize a digit that represents 10 times the value of what is represents in the place to its right? Target 4.NBT.1.1 Embedded 4.OA.1.1 4.NBT.1.2 Fluency 3.OA.3.7 Mathematical Practices MP1 Module 1
Topic A Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its right. During Centers: Rituals and Routines Lesson Lesson Materials: (S) Personal white board, unlabeled thousands place value chart (Lesson 1 Template) (S) Unlabeled millions place value chart (Template) During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Module 1
Topic A Lesson 3: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units. During Centers Block: Rituals and Routines Lesson Lesson Materials: (S) Multiply by 3 Sprint (T) Unlabeled millions place value chart (Lesson 2 Template) (S) Personal white board During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Notes: Approx. Date: 8/18/2016 Day: 4 OBJ: Students will name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units. EQ: How can I name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units? Approx. Date: OBJ: 8/19/2016 Students will read and write multi‐digit Day: 5 numbers using base ten numerals, number Target 4.NBT.1.2 Embedded 4.NBT.1.1 Fluency 3.OA.3.7 Mathematical Practices MP2 expression
addend composition sum commas/periods standard form written form expanded form Notes: 

Within the Concept Development piece the teacher conversation extends past the content limits into the billions, we only need to go into the millions. Lesson 3‐4 only address representing numbers in all form (standard, expanded, and written). Target 4.NBT.1.2 Embedded 4.NBT.1.1 value
word form expanded form zero represent Module 1
Topic A Lesson 4: Read and write multi‐digit numbers using base ten numerals, number names, and expanded form. During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons Page 24 of 72 names, and expanded form. EQ: How can I read and write multi‐digit numbers using base ten numerals, number names, and expanded forms? Fluency 3.OA.1.4—3.7 Mathematical Practices MP3 During Centers Block: Rituals and Routines Lesson
Lesson Materials: (S) Personal white board, unlabeled millions place value chart (Lesson 2 Template) using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Notes: • Expose students to multiple ways of expressing the expanded form of a number (see 5.NBT.1.3) • For example, 65,203 could be expressed in all of the following expanded forms: 65,203 = 60,000 + 5,000 + 200 +3 65,203 = (6 x 10,000) + (5 x 1,000) + (2 x 100) + (3 x 1) 65,203 = (6 x 10,000) + (52 x 100) + (3 x 1) Topic B: Comparing Multi‐Digit Whole Numbers
In Topic B, students use place value to compare whole numbers. Initially using the place value chart, students compare the value of each digit to surmise which number is of greater value. Moving away from dependency on models and toward fluency with numbers, students compare numbers by observing across the entire number and noticing value differences. For example, in comparing 12,566 to 19,534, it is evident 19 thousands is greater than 12 thousands because of the value of the digits in the thousands unit. Additionally, students continue with number fluency by finding what is 1, 10, or 100 thousand more or less than a given number. Date/ Day of the school year Approx. Date: 08/22/2016 Day: 6
Objective/ Essential Question OBJ: Students will compare numbers based on meanings of the digits using >, <, or = to record the comparison. EQ: How can I compare numbers based on
meanings of the digit using >,<, or = to record the comparison? Math Florida Standards/ Mathematical Practice Target 4. NBT.1.2 Embedded 4. NBT.1.1 Fluency 3.OA.3.7 Mathematical Practices MP1 Academic Language compare
greater than less than symbols equal
Lesson Module 1
Topic B Lesson 5: Compare numbers based on meanings of the digits using >, <, or = to record the comparison. During Centers Block: Rituals and Routines Lesson Lesson Materials: (S) Multiply by 4 Sprint (S) Personal white board, unlabeled hundred thousands place value chart (Template)
Assessment / Performance Tasks During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Page 25 of 72 Notes: Lesson 5‐6 continues to address MAFS.4.NBT.1.2 by comparing numbers.
Approx. Date: 8/23/2016 Day: 7 OBJ: Approx. Date: 8/24/2016 Day: 8 OBJ: Approx. Date: 08/25/2016 Day: 9 OBJ: Students will find 1, 10, and 100 thousand more and less than a given number. EQ: How can I find 1, 10, and 100 thousands more and less than a given number? Students will complete I‐
ready Diagnostic. Students will complete I‐
ready Diagnostic. Target 4. NBT.1.2 Embedded 4.NBT.1.1 Fluency Mathematical Practices MP5 Continue use of academic language from lesson 1‐5. Flex Day: I‐Ready Diagnostic Testing. This day is added as a flex day to accommodate for I‐Ready testing. Please move this date to accommodate for the testing window and continue to move forward with the pacing of the curriculum guide as necessary. Recommendation: Curriculum Associates recommends 4th grade administer in 40 minute sessions for completion, not a continuous 80‐90 minutes. Flex Day: I‐Ready Diagnostic Testing. This day is added as a flex day to accommodate for I‐Ready testing. Please move this date to accommodate for the testing window and continue to move forward with the pacing of the curriculum guide as necessary. Recommendation: Curriculum Associates recommends 4th grade administer in 40 minute sessions for completion, not a continuous 80‐90 minutes. I‐Ready Diagnostic
Module 1
Topic B Lesson 6: Find 1, 10, and 100 thousand more and less than a given number. During Centers: Rituals and Routines Lesson Lesson Materials: (T) Unlabeled hundred thousands place value chart (Lesson 5 Template) (S) Personal white board, unlabeled hundred thousands place value chart (Lesson 5 Template) During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. I‐Ready Diagnostic
Notes: Page 26 of 72 Topic C: Rounding Multi‐Digit Whole Numbers
In Topic C, students round to any place using the vertical number line and approximation. The vertical number line allows students to line up place values of the numbers they are comparing. In Grade 3, students rounded to the nearest 10 or 100 using place value understanding. Now, they extend this understanding rounding to the nearest thousand, ten thousand, and hundred thousand. Uniformity in the base ten system easily transfers understanding from the Grade 3 (3.NBT.1.1) to Grade 4 (4.NBT.1.3) standard. Rounding to the leftmost unit is easiest for students, but Grade 4 students learn the advantages to rounding to any place value, which increases accuracy. Students move from dependency on the number line and learn to round a number to a particular unit. To round 34,108 to the nearest thousand, students find the nearest multiple, 34,000 or 35,000, by seeing if 34,108 is more than or less than halfway between the multiples. The final lesson of Topic C presents complex and real world examples of rounding, including instances where the number requires rounding down, but the context requires rounding up. Math Florida Standards/ Mathematical Practice Approx. Date: OBJ: Target 08/26/2016 Round multi‐digit 4.NBT.1.3 numbers to the Day: 10 thousands place using Embedded the vertical number line. 4.NBT.1.1 EQ: Fluency How can I round multi‐
digit numbers to the Mathematical thousands place using Practices the vertical number MP2 line? Date/ Day of the school year Approx. Date: 08/29/2016 Day: 11 Objective/ Essential Question OBJ: Students will round multi‐digit numbers to any place using the vertical number line. EQ: How can I round multi‐
digit numbers to any Academic Language vertical number line end point halfway about explain model differ greatest least possible marker estimation nearest Lesson Module 1
Topic C Lesson 7: Round multi‐digit numbers to the thousands place using the vertical number line. During Centers: Rituals and Routines Lesson Lesson Materials: (S) Personal white board, unlabeled hundred thousands place value chart (Lesson 5 Template) Assessment / Performance Tasks During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8 Mathematical Practices. They are designed to be short 30 minute activities that introduce students to the Standards for Mathematical Practices and effective modeling of strategies. Notes: Lessons 7‐10 do not fully address the item specifications for this standard. The focus of the lesson is only rounding and students need to be able to identify the original number from an already rounded number. MAFS.4.NBT.1.3
Target midpoint Module 1
Rounding Numbers 4. NBT.1.3 exact answer Topic C estimate Lesson 8: Round multi‐digit numbers to any place using the Embedded difference vertical number line. 4.NBT.1.2 During Centers: Rituals and Routines Lesson Fluency Lesson Materials: (S) Find the midpoint Sprint Page 27 of 72 place using the vertical number line? Approx. Date: 08/30/2016 Day: 12 OBJ: Students will use place value understanding to round multi‐digit numbers to any place value. EQ: How can I use place value to round multi‐
digit numbers? OBJ: Students will use place value understanding to round multi‐digit numbers to any place value using real world applications. EQ: How can I use place value understanding to round multi‐digit numbers to any place using real world application? Approx. Date: OBJ: 09/01/2016 Students will show mastery of standards Day: 14 introduced in Module 1 Topics A‐C. Approx. Date: 08/31/2016 Day: 13 Mathematical (S) Personal white board
Practices MP2 Notes: Target between Module 1
4. NBT.1.3 halfway Topic C less than Lesson 9: Use place value understanding to round multi‐
Embedded more than digit numbers to any place value. 4.NBT.1.1 accurate periods Fluency Lesson Materials: (S) Personal white board Mathematical Practices MP3 Notes: Academic Language will include sentence starters:  Between what two ______ [place value] is ______ [given number]?  For example: Between what two thousands is 3,642? 3,642 is between 3,000 and 4,000. Target best estimate
Module 1
4.NBT.1.3 advantage Topic C Lesson 10: Use place value understanding to round multi‐
Embedded digit numbers to any place value using real world 4.NBT.1.1 applications. Fluency Lesson Materials: (S) Round to the nearest 10,000 Sprint Mathematical (S) Personal white board Practices MP3 Notes: Target 4.NBT.1.1 4.NBT.1.2 4.NBT.1.3 Embedded 4.OA.1.1 Module 1
Mid‐Module Assessment: Topics A‐C Module 1
Mid‐Module Assessment: Topics A‐C Page 28 of 72 EQ: How can I use strategies I’ve learned to help me as a mathematician? Notes: Remediate this assessment in centers. Topic D: Multi‐Digit Whole Number Addition
Moving away from special strategies for addition, students develop fluency with the standard addition algorithm (4.NBT.2.4). Students compose larger units to add like base ten units, such as composing 10 hundreds to make 1 thousand and working across the numbers unit by unit (ones with ones, thousands with thousands). Recording of regrouping occurs on the line under the addends as shown to the right. For example, in the ones column, students do not record the 0 in the ones column and the 1 above the tens column, instead students record 10, writing the 1 under the tens column and then a 0 in the ones column. They practice and apply the algorithm within the context of word problems and assess the reasonableness of their answers using rounding (4.OA.1.3). When using tape diagrams to model word problems, students use a variable to represent the unknown quantity. Date/ Day of the school year Approx. Date: 09/02/2016 Day: 15 Objective/ Essential Question OBJ: Students will use place value understanding to fluently add multi‐digit whole numbers using the standard addition algorithm, and apply the algorithm to solve word problems using tape diagrams. EQ: How can I use my knowledge of place value to add multi‐digit numbers? Math Florida Standards/ Mathematical Practice Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.NBT.1.3 Fluency Mathematical Practices MP1 Academic Language tape diagram bundling brackets variables unknown quantity standard algorithm add addition Lesson Assessment / Performance Tasks Module 1
Topic D Lesson 11: Use place value understanding to fluently add multi‐digit whole numbers using the standard addition algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson Materials: (T) Millions place value chart (Template) (S) Personal white board, millions place value chart (Template) Notes: Page 29 of 72 Approx. Date: 09/06/2016 Day: 16 OBJ: Students will solve multi‐step word problems using the standard addition algorithm modeled with tape diagrams, and assess the reasonableness of answers using rounding. EQ: How can I use my knowledge of place value and the standard algorithm to solve addition word problems? Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.NBT.1.3 4.OA.1.3 Fluency Mathematical Practices MP2 precise
exact reasonableness Module 1
Topic D Lesson 12: Solve multi‐step word problems using the standard addition algorithm modeled with tape diagrams, and assess the reasonableness of answers using rounding. Lesson Materials: (S) Personal white board Notes: Topic E: Multi‐Digit Whole Number Subtraction
Following the introduction of the standard algorithm for addition in Topic D, the standard algorithm for subtraction replaces special strategies for subtraction in Topic E. Moving slowly from smaller to larger minuends, students practice decomposing larger units into smaller units. First, only one decomposition is introduced, where one zero may appear in the minuend. As in Grades 2 and 3, students continue to decompose all necessary digits before performing the algorithm, allowing subtraction from left to right, or, as taught in the lessons, from right to left. Students use the algorithm to subtract numbers from 1 million allowing for multiple decompositions (4.NBT.2.4). The topic concludes with practicing the standard algorithm for subtraction in the context of two‐step word problems where students have to assess the reasonableness of their answers by rounding (4.OA.1.3). When using tape diagrams to model word problems, students use a variable to represent the unknown quantity. Date/ Day of the school year Approx. Date: 09/07/2016 Day: 17 Objective/ Essential Question OBJ: Students will use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Math Florida Standards/ Mathematical Practice Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.OA.1.3 Fluency Academic Language subtract
ungroup/unbundle difference regroup decompose result in a sum Lesson Assessment / Performance Tasks Module 1
Topic E Lesson 13: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson Materials: (T) Millions place value chart (Lesson 11 Template) (S) Personal white board, millions place value chart template (Lesson 11 Template) Page 30 of 72 EQ: How can I use my knowledge of place value to subtract multi‐
digit numbers? Mathematical Practices MP6 Notes: Approx. Date: 09/08/2016 Day: 18 OBJ: Students will use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. EQ: How can I use my knowledge of place value and the standard algorithm to solve subtraction word problems? Approx. Date: OBJ: 09/09/2016 Students will use place value understanding to Day: 19 fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. EQ: How can I use my knowledge of place value and the standard Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.OA.1.3 Fluency Mathematical Practices MP5 Continue use of academic language from lessons 11‐13. Module 1
Topic E Lesson 14: Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson Materials: (S) Personal white board Continue use of academic language from lessons 11‐13. Module 1
Topic E Lesson 15: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson Materials: (T) Personal white board (T) Millions place value chart (Lesson 11) (S) Personal white board, millions place value chart (Lesson 11 Template) Notes: Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.OA.1.3 Fluency 4.MD.1.1 Mathematical Practices MP6 MAFS.4.NBT.2.4
To Regroup or Not to Regroup Page 31 of 72 algorithm to solve subtraction word problems? Approx. Date: OBJ: 09/12/2016 Students will solve two‐
step word problems Day: 20 using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding. EQ: How can I use my knowledge of place value and the standard algorithm to solve subtraction word problems? Notes: Target 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 4.OA.1.3 Fluency 4.MD.1.1 Mathematical Practices MP6 precise/exact
Continue use of academic language from lessons 11‐13. Module 1
Topic E Lesson 16: Solve two‐step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding. Lesson Materials: (S) Convert Meters and Centimeters to Centimeters Sprint (S) Personal white board Notes: Topic F: Addition and Subtraction Word Problems
Module 1 culminates with multi‐step addition and subtraction word problems in Topic F (4.OA.1.3). In these lessons, the format for the Concept Development is different from the traditional vignette. Instead of following instruction, the Problem Set facilitates the problems and discussion of the Concept Development. Throughout the module, tape diagrams are used to model word problems, and students continue to use tape diagrams to solve additive comparative word problems. Students also continue using a variable to represent an unknown quantity. To culminate the module, students are given tape diagrams or equations and are encouraged to use creativity and the mathematics learned during this module to write their own word problems to solve using place value understanding and the algorithms for addition and subtraction. The module facilitates deeper comprehension and supports determining the reasonableness of an answer. Solving multi‐step word problems using multiplication and division is addressed in later modules. Date/ Day of the school year Approx. Date: 09/13/2016 Day: 21 Objective/ Essential Question OBJ: Students will solve multi‐step word problems modeled with tape diagrams, and assess the Math Florida Standards/ Mathematical Practice Target 4.OA.1.3 4. NBT.2.4 Embedded 4.NBT.1.1 4.NBT.1.2 Academic Language Continue use of academic language from lessons 11‐13. Lesson Assessment / Performance Tasks Module 1
Topic F Lesson 18: Solve multi‐step word problems modeled with tape diagrams, and assess the reasonableness of answers using rounding. Lesson Materials: Page 32 of 72 reasonableness of answers using rounding. EQ: How can I solve multi‐
step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding? Approx. Date: 09/14/2016 Day: 22 Approx. Date: 09/15/2016 Day: 23 4.NBT.1.3
(S) Personal white board (S) Problem Set Fluency 4.MD.1.1 Mathematical Practices MP3 Notes: Lesson 17 and 19 have been omitted. The lessons are outside of the test item specifications. OBJ: Target
Module 1
Students will show 4.NBT.1.1 End of Module Assessment: Topics A‐F mastery of standards 4.NBT.1.2 introduced in Module 1 4.NBT.1.3 Topics A‐F. 4.NBT.2.4 4.OA.1.3 EQ: How can I use strategies Embedded I’ve learned to help me 4.OA.1.1 as a mathematician? Notes:
OBJ: Students will show mastery of standards introduced in Module 1 Topics A‐F. EQ: How can I use strategies I’ve learned to help me as a mathematician? Target
4.NBT.1.1 4.NBT.1.2 4.NBT.1.3 4.NBT.2.4 4.OA.1.3 Embedded 4.OA.1.1 Notes:
Module 1
FLEX DAY Use this time to review and remediate previously taught standards based on data. The recommendation is to use district supported materials. End of Module Assessment: Topics A‐F Review End of Module Assessment: Topics A‐F Page 33 of 72 Quarter 1 Module 2 Course: DUVAL COUNTY PUBLIC SCHOOLS Math Curriculum Lesson Guide Unit # Dates/Pacing: Grade 4 Math Module 2: Unit Conversions and Problem Solving with Metric Measurement 9/16/16 ‐ 9/23/16, 6 days Measurement and Data 4.MD.1.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two‐column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... MAFS Cognitive Complexity: Level 1 Recall 4.MD.1.2 Use the four operations to solve word problems1 involving distances, intervals of time, and money, including problems involving simple fractions or decimals2. Represent fractional quantities of distance and intervals of time using linear models. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts Page 34 of 72 Test Item Specifications Content Standard MAFS.4.MD.1.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two‐column table. For example, know
that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number
pairs (1, 12), (2, 24), (3, 36), ... Measurements may only be whole numbers. Assessment Limits For non‐metric conversions, multiplication is limited to 2‐digit numbers by 1‐digit numbers or a multiple of 10 by a 1‐
digit number. Allowable units of measurement include: kilometer, meter, centimeter, millimeter, liter, milliliter, kilogram, gram, milligram, mile, yard, foot, inch, gallon, quart, pint, cup, ton, pound, and ounce. Equation Editor Multiple Choice Item Types GRID Multiselect Matching Item Table Item Allowable
Context Level: 1 Recall Complexity Level Achievement Level Descriptions Level 2 Level 3 knows relative size of measurement units, within one system of units expresses measurements in a larger unit in terms of a smaller unit, within a single system, records that data in a two‐column table Level 4 expresses measurements in a larger unit in terms of a variety of smaller units, within a single system Level 5 given a context, determines the appropriate unit needed and expresses the measurement to the level of accuracy needed Page 35 of 72 Content Standard MAFS.4.MD.1.2 Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models (Computational fluency with fractions and decimals is not the goal for students at this grade level.) Measurement conversions are from larger units to smaller units. Assessment Limits Calculations are limited to simple fractions or decimals. Operations may include addition, subtraction, multiplication, and division. Item contexts are not limited to distances, intervals of time, and money. Equation Editor Multiple Choice Item Types GRID Multiselect Required
Context Level: 2 Basic Application of Skills and Concepts Complexity Level Achievement Level Descriptions Level 2 Level 3 Level 4 uses the four operations to solve word problems (involving distance, intervals of time, and money) with context, including problems involving whole numbers uses the four operations to solve word problems (involving distance, intervals of time, and money) including problems involving simple fractions or decimals; represents measurement quantities using linear models uses the four operations to solve word problems including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit Level 5 uses the four operations to solve multistep word problems, including problems involving fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit Page 36 of 72 Teacher Academic Language New or Recently Introduced Terms • Convert (express a measurement in a different unit; rename units) • Kilometer (km, a unit of measure for length) • Mass (the measure of the amount of matter in an object) • Milliliter (mL, a unit of measure for liquid volume) • Mixed units (e.g., 3 m 43 cm) Familiar Terms and Symbols • =, <, > (equal to, less than, greater than) • Algorithm ( a step‐by‐step procedure to solve a particular type of problem) • Capacity (the maximum amount that something can contain) • Distance (the length of the line segment joining two points) • Equivalent (equal) • Kilogram (kg), gram (g) (units of measure for mass) • Larger or smaller unit (used in a comparison of units) • Length (the measurement of something from end to end) • Liter (L) (unit of measure for liquid volume) • Measurement (dimensions, quantity, or capacity as determined by comparison with a standard) • Meter (m), centimeter (cm) (units of measure for length) • Mixed units (e.g., 2 tens 4 ones, 2 kilometers 34 meters) • Simplifying strategy (a mental math or recorded method for making a problem easier to solve) • Table (used to represent data) • Times as much as (e.g., 1 hundred is 10 times as much as 1 ten) • Weight (the measurement of how heavy something is) Page 37 of 72 Unit Conversions and Problem Solving with Metric Measurement OVERVIEW The idea of a mixed unit shows up in varied contexts. For instance, students have become accustomed to thinking of 250 as the mixed units of 2 hundreds 5 tens. Mixed units are also used in the context of 2 hr 5 min, $2.50, 2 km 5 m, 2′ 5″, and 2 (hours and minutes, dollars and cents, kilometers and meters, feet and inches, ones and eighths). While the context and the units may vary greatly, there are many common threads present in any mixed unit calculation. Consider the connections and similarities between the following equalities: In order to explore the process of working with mixed units, Module 2 focuses on length, mass, and capacity in the metric system2 where place value serves as a natural guide for moving between larger and smaller units. In Topic A, students review place value concepts while building fluency with decomposing, or converting from larger to smaller units (4.MD.1.1). They learn the relative sizes of measurement units, building off prior knowledge of grams and kilograms from Grade 3 (3.MD.1.2) and meters and centimeters from Grade 2 (2.MD.1.3). Conversions between the units are recorded in a two‐column table. Single‐step problems involving addition and subtraction of metric units provide an opportunity to practice mental math calculations as well as the addition and subtraction algorithms established in Module 1. Students reason by choosing to convert between mixed and single units before or after the computation (4.MD.1.2). Connecting their familiarity with both metric units and place value, the module moves swiftly through each unit of conversion, spending only one day on each type. This initial understanding of unit conversions allows for further application and practice, such as multiplying and dividing metric units, throughout subsequent modules. In Topic B, students continue to build off of their measurement work from previous grade levels. They solidify their understanding of the relationship between metric units and the place value chart and apply unit conversions to solve and reason about multi‐step word problems (4.MD.1.2). Applying the skills learned in Module 1, students discover and explore the relationship between place value and conversions. The beauty of both the place value and measurement systems is the efficiency and precision permitted by the use of different size units to express a given quantity. As students solve word problems by adding and subtracting metric units, their ability to reason in parts and wholes is taken to the next level. This is important preparation for multi‐digit operations and for manipulating fractional units in future modules. Tape diagrams and number lines serve as models throughout the module to support the application of the standard algorithm to word problems. 2 thousands
2 kilometers
2 kilograms
2 liters
437 ones
437 meters
437 grams
437 milliliters
=
=
=
=
2,437 ones 2,437 meters
2,437 grams
2,437 milliliters
2
Pounds, ounces, time, and money are covered in Module 7. Page 38 of 72 Module Specific Notes: Customary Units of Measure will not be taught until 4th quarter (THE WEEK BEFORE FSA TESTING WINDOW OPENS). Consider using kinesthetic activities to support conversions between 2 metric units (example: roll a ball, measure distance using centimeters and meters to compare and help students see relationship between two units. Resources Long Island 4th Grader: Converting Metric Units Is 'Easy' https://www.engageny.org/resource/long‐island‐
4th‐grader‐converting‐metric‐units‐easy Module Materials 
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Balance scale Weights (gram, kilogram,) Centimeter ruler, meter stick Liter containers with milliliter scale 1,000 small paper clips dollar bill dictionary 3‐liter graduated beaker, marked with liters and milliliters (one per student/pair) Additional Aligned Activities enVision Math Common Core Topic 14‐ 14.6* Teamwork Topic 14‐ 14.6** Teamwork Topic 14‐ 14.7 * Teamwork Topic 14‐ 14.7** Teamwork Topic 14‐ 14.8* Display the Digits Topic 14‐ 14.8** Display the Digits Topic 14‐ 14.9* Quick Questions Topic 14‐ 14.9** Quick Questions Page 39 of 72 Standards 4.MD.1.1 4.MD.1.2 Topics and Objectives
A Metric Unit Conversions Lesson 1: Express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length. Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass. Lesson 3: Express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity. 4.MD.1.1 4.MD.1.2 B Application of Metric Unit Conversions Lesson 4: Know and relate metric units to place value units in order to express measurements in different units. Lesson 5: Use addition and subtraction to solve multi‐step word problems involving length, mass, and capacity. End‐of‐Module Assessment: Topics A–B Page 40 of 72 Topic A: Metric Unit Conversions In order to explore the process of working with mixed units, Module 2 focuses on length, mass, and capacity in the metric system, 3 where place value serves as a natural guide for moving between larger and smaller units. In Topic A, students review place value concepts while building fluency with decomposing, or converting from larger to smaller units (4.MD.1.1). They learn the relative sizes of measurement units, building off prior knowledge of grams and kilograms from Grade 3 (3.MD.1.2) and meters and centimeters from Grade 2 (2.MD.1.3). Conversions between the units are recorded in a two‐column table, beginning in Lesson 1. Recording the unit conversions in a table allows students to notice patterns when converting from a smaller unit to a larger unit (e.g., 200 centimeters is the same as 2 meters because 1 meter is equal to 100 centimeters). Single‐step problems involving addition and subtraction of metric units provide an opportunity to practice simplifying strategies (e.g., mental math strategies) as well as the addition and subtraction algorithm established in Module 1 (4.NBT.2.4). Students practice reasoning by choosing to convert mixed units to a single unit before or after the computation (4.MD.1.2). Word problems provide a context in which to apply the conversions and include the addition and subtraction of mixed units. Connecting students’ familiarity with both metric units and place value, the module moves swiftly through each unit of conversion, spending only one day on each type of measurement. This initial understanding of unit conversions allows for further application and practice, such as when multiplying and dividing metric units, throughout subsequent modules. Date/ Day of the school year Approx. Date: 09/16/2016 Day: 24 Objective/ Essential Question OBJ: Students will express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length. EQ: How can I express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length? Math Florida Standards/ Mathematical Practice Target 4.MD.1.1 4.MD.1.2 Embedded 4.NBT.2.4 Fluency Mathematical Practices MP7 Academic Language Lesson centimeter
meter kilometer metric system length unit model conversion table conversion simplifying‐ strategy Module 2
Topic A Lesson 1: Express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length. Lesson Materials: (T) Staples, ruler, meter stick, teacher‐made poster with metric units (shown in lesson plan) (S) Personal white board Assessment / Performance Tasks Notes: Page 41 of 72 OBJ: Students will express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass. EQ: How can I express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass? Approx. Date: OBJ: 09/20/2016 Students will express metric capacity Day: 26 measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity. EQ: How can I express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity? Approx. Date: 09/19/2016 Day: 25 Target 4.MD.1.1 4.MD.1.2 Embedded Fluency Mathematical Practices MP8 mass weight gram kilogram converting rename scale Module 2
Topic A Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass. Lesson Materials: (T) 1‐liter water bottle, 1,000 small paper clips, dollar bill, dictionary, balance scale, weights (1 kg and 1 g) (S) Personal white board liters measure scale milliliters equivalence metric capacity liquid smaller unit container Module 2
Topic A Lesson 3: Express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity. Lesson Materials: (T) 3‐liter beaker, bucket of water (S) 3‐liter graduated beaker (marked with liters and milliliters), bucket of water, personal white board Notes: Target 4.MD.1.1 4.MD.1.2 Embedded 4.NBT.2.4 Fluency Mathematical Practices MP1 Notes: Page 42 of 72 Topic B: Application of Metric Unit Conversions In Topic B, students continue to build off their measurement work from previous grade levels. They solidify their understanding of the relationship between metric units and the place value chart and apply unit conversions to solve and reason about multi‐step word problems (4.MD.1.2). Applying the skills learned in Module 1, students discover and explore the relationship between place value and conversions. The beauty of both the place value and measurement systems is the efficiency and precision permitted by the use of different size units to express a given quantity. Lesson 4 connects metric measurement conversions and place value by comparing mixed units of measure and verifying statements such as 1 kilometer is 1,000 times as much as 1 meter. In Lesson 5, as students solve two‐ and three‐step word problems by adding and subtracting metric units, their ability to reason in parts and wholes is taken to the next level. This is important preparation for multi‐digit operations and manipulating fractional units in future modules. Throughout Topic B, tape diagrams and number lines serve as models to support application of the standard algorithm to word problems. Students solve problems by converting between units and using simplifying strategies or algorithms (4.MD.1.1). Date/ Day of the school year Objective/ Essential Question OBJ: Students will know and relate metric units to place value units in order to express measurements in different units. EQ: How can I use my prior knowledge to relate metric units to place value units in order to express measurements in different units? Approx. Date: OBJ: Students will use 09/22/2016 addition and subtraction to solve multi‐step word Day: 28 problems involving length, mass, and capacity. EQ: How can I use addition and subtraction to solve Approx. Date: 9/21/2016 Day: 27 Math Florida Standards/ Mathematical Practice Target 4.MD.1.1 4.MD.1.2 Embedded 4.NBT.2.4 Fluency 4.MD.1.3 Mathematical Practices MP7 Notes: Target 4.MD.1.1 4.MD.1.2 Embedded Fluency Mathematical Practices MP7 Academic Language Lesson place value units
meters centimeters smaller unit larger unit word form unknown number Module 2
Topic B Lesson 4: Know and relate metric units to place value units in order to express measurements in different units. Lesson Materials: (T) Unlabeled hundred thousands place value chart (Template) (S) Add Meters and Centimeters Pattern Sheet, Unlabeled hundred thousands place value chart (Template), personal white board Continue academic language from Lessons 1‐4. tape diagram weighs less than greater than difference sum Module 2
Topic B Lesson 5: Use addition and subtraction to solve multi‐step word problems involving length, mass, and capacity. Lesson Materials: (S) Convert to Kilograms and Grams Sprint, personal white board, Problem Set Assessment / Performance Tasks Page 43 of 72 multi‐step word problems involving length, mass, and capacity? Approx. Date: 09/23/2016 Day: 29 OBJ: Students will show mastery of standards introduced in Module 2 Topics A‐B. EQ: How can I use strategies I’ve learned to help me as a mathematician? Notes: Target Module 2
4.MD.1.1 End‐of‐Module Assessment: Topic A‐B 4.MD.1.2 Embedded Fluency Mathematical Practices Notes: A remediation day is not provided for this module. Remediate during centers block. Module 2
End‐of‐Module Assessment: Topic A‐B Page 44 of 72 Quarter 1 Module 3 (Part 1) DUVAL COUNTY PUBLIC SCHOOLS
Math Curriculum Lesson Guide
Course: Unit # Dates/Pacing: Grade 4 Math Module 3: Multi‐Digit Multiplication and Division 9/26/16 ‐ 10/14/16, 15 days Operations and Algebraic Thinking 4.OA.1.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Cognitive Complexity: Level 1 Recall 4.OA.1.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.OA.1.3: Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.OA.2.4: Investigate factors and multiples. a. Find all factor pairs for a whole number in the range 1–100.
b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a
MAFS multiple of a given one-digit number.
c. Determine whether a given whole number in the range 1–100 is prime or composite.
Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.OA.3.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the
terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this
way. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.OA.1.a: Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning 4.OA.1.b: Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example,
solve 76 + 9 = n + 5 for n arguing that nine is four more than five, so the unknown number must be four greater than 76. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning Page 45 of 72 Number and Operations in Base Ten 4.NBT.2.5: Multiply a whole number of up to four digits by a one‐digit whole number, and multiply two two‐digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.NBT.2.6: Find whole‐number quotients and remainders with up to four‐digit dividends and one‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 4.NBT.1.1: Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Cognitive Complexity: Level 1 Recall Measurement and Data 4.MD.1.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts Page 46 of 72 Test Item Specifications Content Standard MAFS.4.OA.1.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Items may not require students to solve for unknown factors that exceed 10 x 10 multiplication facts. Assessment Limits Item must include a verbal description of an equation or a multiplication equation. Multiplication situations must be a comparison (e.g., times as many). Equation Editor Multiple Choice Item Types GRID Multiselect Matching Item Open Response Allowable Context Level 1: Recall Complexity Level Achievement Level Descriptions Level 2 [intentionally left blank] Level 3 recognizes that any two factors and their product can be read as a comparison; represents those comparisons as equations Level 4 creates a context for a multiplicative comparison problem given an equation Level 5 [intentionally left blank] Page 47 of 72 Content Standard MAFS.4.OA.1.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiplication situation must be a comparison (e.g., times as many). Assessment Limits Operations are limited to multiplication and division. Limit multiplication and division to 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit. Equation Editor Multiple Choice Item Types GRID Required Context Level 2: Basic Application of Skills & Concepts Complexity Level Level 2 multiplies or divides to solve word problems involving multiplicative comparison (where the unknown is the product or quotient) Achievement Level Descriptions Level 3 Level 4 Level 5 creates and solves a multiplication multiplies or divides to solve word [intentionally left blank] equation with a symbol for the problems involving multiplicative comparison (where the unknown is in unknown number to represent a word a variety of positions) problem involving multiplicative comparison Page 48 of 72 Content Standard MAFS.4.OA.1.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Items requiring precise or exact solutions are limited to: Assessment Limits  addition and subtraction within 1,000  multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit  division of 2‐digit by 1‐digit Items may contain a maximum of 3 steps. Items involving remainders must require the students to interpret and/or use the remainder with respect to the context. Variables must be represented by a letter, and variables must be defined or described in the context. Equation Editor Multiselect Item Types Multiple Choice Open Response Required Context Level 2: Basic Application of Skills & Concepts Complexity Level Achievement Level Descriptions Level 2 solves one‐step word problems (which do not include remainders) using the four operations with simple context and scaffolding where the sum, difference, product, or quotient is always the unknown Level 3 solves two‐step word problems (including interpreting remainders) using the four operations, where the unknown is in a variety of positions, and can be represented by a symbol/letter Level 4 Level 5 solves three‐step word problems using the four operations; recognizes the reasonableness of answers using mental computation and estimation strategies solves multistep word problems with multiple possible solutions and determines which would be the most reasonable based upon given criteria Page 49 of 72 Content Standard MAFS.4.OA.1a (assessed with MAFS.OA.1b) Determine whether an equation is true or false using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false. Whole number equations are limited to: Assessment Limits  addition and subtraction within 1,000  multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit  division of 2‐digit by 1‐digit Variables represented by a letter are allowable. Editing Task Choice Multiple Choice Item Types Equation Editor Multiselect GRID Open Response Hot Text Allowable Context Level 3: Strategic Thinking & Complex Reasoning Complexity Level Achievement Level Descriptions Level 2 determines whether an equation is true or false; identifies true and false equations that use comparative relational thinking Level 3
determines whether an equation is true or false, where addition or subtraction is used on both sides of the equal sign, and justifies by using comparative relational thinking Level 4
determines whether an equation is true or false, where multiplication or division is used on both sides of the equal sign, and justifies by using comparative relational thinking Level 5
determines whether an equation is true or false, where different operations are used on either side of the equal sign, and justifies by using comparative relational thinking Page 50 of 72 Content Standard MAFS.4.OA.1b (Also assesses MAFS.OA.1a) Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = n + 5 for n arguing that nine is four more than five, so the unknown number must be four greater than 76. Whole number equations are limited to: Assessment Limits  addition and subtraction within 1,000  multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit  division of 2‐digit by 1‐digit Variables represented by a letter are allowable. Editing Task Choice Multiple Choice Item Types Equation Editor Multiselect GRID Open Response Hot Text Allowable Context Level 3: Strategic Thinking & Complex Reasoning
Complexity Level Achievement Level Descriptions Level 2 [intentionally left blank] Level 3
determines the unknown number in an equation relating four whole numbers, where addition or subtraction is used on both sides of the equal sign, and justifies using comparative relational thinking Level 4
determines the unknown number in an equation relating four whole numbers, where multiplication or division is used on both sides of the equal sign, and justifies using comparative relational thinking Level 5
determines the unknown number in an equation relating four whole numbers, where different operations are used on either side of the equal sign, and justifies using comparative relational thinking Page 51 of 72 Content Standard MAFS.4.OA.2.4 Investigate factors and multiples. a. Find all factor pairs for a whole number in the range 1–100. b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one‐digit number. c. Determine whether a given whole number in the range 1–100 is prime or composite. Items may only contain whole numbers between 1‐100. Assessment Limits Vocabulary may include prime, composite, factor, or multiple. Equation Editor Multiple Choice Item Types GRID Multiselect Matching Item Table Item Allowable Context Level 2: Basic Application of Skills & Concepts Complexity Level Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 finds factor pairs for numbers in the range of 1 to 100, and determines whether a whole number in the range of 1 to 100 is prime or composite, given visual representations finds all factor pairs for whole numbers in the range of 1 to 100; recognizes that a whole number is a multiple of each of its factors; determines whether a whole number in the range of 1 to 100 is prime or composite determines common factors and multiples of numbers in the range of 1 to 100 applies the concepts of both factors, multiples, and prime and composite numbers in problem‐solving contexts Page 52 of 72 Content Standard MAFS.4.OA.3.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Items may only contain whole numbers from 1 to 1,000. Assessment Limits Operations in rules are limited to addition, subtraction, multiplication, and division. Items may not contain rules that exceed two procedural operations. Division rules may not require fractional responses. Rules may not be provided algebraically (e.g. x + 5). Items must provide the rule. Editing Task Choice Multiple Choice Item Types Equation Editor Multiselect GRID Open Response Hot Text Table Item Matching Item Allowable Context Level 2: Basic Application of Skills & Concepts Complexity Level Achievement Level Descriptions Level 2 extends a number or shape pattern that follows a given one‐step rule Level 3 Level 4 generates a number or shape pattern that follows a given one‐step rule generates a number or shape pattern that follows a given two‐step rule Level 5 identifies and/or explains apparent features that are not explicit in the rule from an observed pattern Page 53 of 72 Content Standard MAFS.4.NBT.2.5 Multiply a whole number of up to four digits by a one‐digit whole number, and multiply two two‐digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Items may require multiplying: four digit by one digit, three digits by one‐digit, two digits by one digit, or two digits by Assessment Limits two digits. Equation Editor Multiselect Item Types GRID Open Response Multiple Choice No context Context Level 2: Basic Application of Skills & Concepts Complexity Level Achievement Level Descriptions Level 2 Level 3 multiplies a whole number (of up to three digits) by a single‐digit whole number, including the use of strategies based on place value and visual models multiplies a whole number up to four digits by a single‐digit whole number and two two‐digit whole numbers, using strategies based on place value; illustrates and explains calculations by using equations, rectangular arrays, and/or area models Level 4 determines the equation that represents a base‐ten model; makes connections between different multiplication strategies Level 5 analyzes and describes an error in a strategy and shows the correct solution Page 54 of 72 Content Standard MAFS.4.NBT.2.6 Find whole‐number quotients and remainders with up to four‐digit dividends and one‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Items may not require finding a quotient within the factor pairs of 10 x 10. Assessment Limits Equation Editor Multiple Choice GRID Multiselect No context Item Types Context Complexity Level Level 2: Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 Level 3 divides a whole number (of up to three digits) by a single‐digit whole number, using strategies based on place value divides a whole number up to four digits by a single‐digit whole number (including remainders), using strategies based on place value, properties of operations, and/or the relationship between multiplication and division; illustrates and explains calculations by using equations, rectangular arrays, and/or area models Level 4 determines the equation that represents a base‐ten model; makes connections between different division strategies Level 5 analyzes and describes an error in a strategy and shows the correct solution Page 55 of 72 Content Standard MAFS.4.NBT.1.1 Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Items may contain whole numbers within 1,000,000. Assessment Limits Items may not compare digits across more than 1 place value. Editing Task Choice Multiple Choice Item Types Equation Editor Multiselect Hot Text Open Response No context Context Complexity Level Level 1: Recall Achievement Level Descriptions Level 2 Level 3 recognizes that a digit in one place represents 10 times as much as it represents in the place to its right (for numbers up to and including 10,000), with visual representations recognizes that a digit in one place represents 10 times as much as it represents in the place to its right (for numbers up to and including 100,000) Level 4 Level 5 [intentionally left blank] recognizes that a digit in one place represents 10 times as much as it represents in the place to its right (for numbers up to and including 1,000,000) Page 56 of 72 Content Standard MAFS.4.MD.1.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Figures are limited to rectangles or composite figures composed of rectangles. Assessment Limits Fractions are limited to like denominators. Limit multiplication and division to 2‐digit by 1‐digit or a multiple of 10 by 1‐digit. Quotients may only be whole numbers. Limit addition and subtraction to solutions within 1,000. When constructing rectangles, one grid must be labeled with the appropriate dimension. That dimension must be “1 ____,” as items at this standard may not assess scale. Equation Editor Multiple Choice Item Types GRID Multiselect Allowable Context Complexity Level Level 2: Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 uses place value understanding to round multi‐digit whole numbers to any place within 1,000 Level 3 Level 4 Level 5 uses place value understanding to uses place value understanding to round determines a number that falls between two numbers of different round multi‐digit whole numbers to whole numbers up to any place where any place within 1,000,000 the digit to the left is also affected (e.g., place values round 199 to the nearest ten) Page 57 of 72 Teacher Academic Language New or Recently Introduced Terms  Associative property [96 = 3 × (4 × 8) = (3 × 4) × 8]  Composite number (positive integer having three or more whole number factors)  Distributive Property [64 × 27 = (60 × 20) + (60 × 7) + (4 × 20) + (4 × 7)]  Divisor (the number by which another number is divided)  Partial product (e.g. 24 × 6 = (20 × 6) + (4 × 6) = 120 + 24)  Prime number (positive integer only having whole number factors of one and itself)  Remainder (the number left over when one integer is divided by another) Familiar Terms and Symbols  Algorithm (steps for base ten computations with the four operations)  Area (the amount of two‐dimensional space in a bounded region)  Area model (a model for multiplication problems, in which the length and width of a rectangle represent the factors)  Bundling, grouping, renaming, changing  Compare (to find the similarity or dissimilarity between)  Distribute (decompose an unknown product in terms of two known products to solve)  Divide/Division (e.g., 15 ÷ 5 = 3)  Equation (a statement that the values of two mathematical expressions are equal using the = sign)  Factors (numbers that can be multiplied together to get other numbers)  Mixed units (e.g., 1 ft 3 in, 4 lb 13 oz)  Multiple (product of a given number and any other whole number)  Multiply/Multiplication (e.g., 5 × 3 =15)  Perimeter (length of a continuous line forming the boundary of a closed geometric figure)  Place value (the numerical value that a digit has by virtue of its position in a number)  Product (the result of multiplication)  Quotient (the result of division)  Rectangular array (an arrangement of a set of objects into rows and columns)  ___ times as many ___ as ___ (sentence frame) Page 58 of 72 Multi‐Digit Multiplication and Division OVERVIEW In this 41‐day module, students use place value understanding and visual representations to solve multiplication and division problems with multi‐digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi‐digit factors and dividends. Students begin in Topic A by investigating the formulas for area and perimeter. They then solve multiplicative comparison problems including the language of times as much as with a focus on problems using area and perimeter as a context (e.g., “A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?”). Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities (4.OA.1.1). This is foundational for understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. This Grade 4 module, beginning with area and perimeter, allows for new and interesting word problems as students learn to calculate with larger numbers and interpret more complex problems (4.OA.1.2, 4.OA.1.3, 4.MD.1.3). In Topic B, students use place value disks to multiply single‐digit numbers by multiples of 10, 100, and 1,000 and two‐digit multiples of 10 by two‐digit multiples of 10 (4.NBT.2.5). Reasoning between arrays and written numerical work allows students to see the role of place value units in multiplication (as pictured below). Students also practice the language of units to prepare them for multiplication of a single‐digit factor by a factor with up to four digits and multiplication of two two‐digit factors. In preparation for two‐digit by two‐digit multiplication, students practice the new complexity of multiplying two two‐digit multiples of 10. For example, students have multiplied 20 by 10 on the place value chart and know that it shifts the value one place to the left, 10 × 20 = 200. To multiply 20 by 30, the associative property allows for simply tripling the product, 3 × (10 × 20), or multiplying the units, 3 tens × 2 tens = 6 hundreds (alternatively, (3 × 10) × (2 × 10) = (3 × 2) × (10 × 10)). Introducing this early in the module allows students to practice during fluency so that, by the time it is embedded within the two‐digit by two‐digit multiplication in Topic H, understanding and skill are in place. Page 59 of 72 Building on their work in Topic B, students begin in Topic C decomposing numbers into base ten units in order to find products of single‐digit by multi‐digit numbers. Students use the distributive property and multiply using place value disks to model. Practice with place value disks is used for two‐, three‐, and four‐digit by one‐digit multiplication problems with recordings as partial products. Students bridge partial products to the recording of multiplication via the standard algorithm.3 Finally, the partial products method, the standard algorithm, and the area model are compared and connected by the distributive property (4.NBT.2.5). 1,423 x 3 Topic D gives students the opportunity to apply their new multiplication skills to solve multi‐step word problems (4.OA.1.3, 4.NBT.2.5) and multiplicative comparison problems (4.OA.1.2). Students write equations from statements within the problems (4.OA.1.1) and use a combination of addition, subtraction, and multiplication to solve. In Topic E, students synthesize their Grade 3 knowledge of division types (group size unknown and number of groups unknown) with their new, deeper understanding of place value. 3 Students become fluent with the standard algorithm for multiplication in Grade 5 (5.NBT.5). Grade 4 students are introduced to the standard algorithm in preparation for fluency and as a general method for solving multiplication problems based on place value strategies, alongside place value disks, partial products, and the area model. Students are not assessed on the standard algorithm in Grade 4. Page 60 of 72 Students focus on interpreting the remainder within division problems, both in word problems and long division (4.OA.1.3). A remainder of 1, as exemplified below, represents a leftover flower in the first situation and a remainder of 1 ten in the second situation.4 While we have no reason to subdivide a remaining flower, there are good reasons to subdivide a remaining ten. Students apply this simple idea to divide two‐
digit numbers unit by unit: dividing the tens units first, finding the remainder (the number of tens unable to be divided), and decomposing remaining tens into ones to then be divided. Students represent division with single‐digit divisors using arrays and the area model before practicing with place value disks. The standard division algorithm5 is practiced using place value knowledge, decomposing unit by unit. Finally, students use the area model to solve division problems, first with and then without remainders (4.NBT.2.6).
In Topic F, armed with an understanding of remainders, students explore factors, multiples, and prime and composite numbers within 100 (4.OA.2.4), gaining valuable insights into patterns of divisibility as they test for primes and find factors and multiples. This prepares them for Topic G’s work with multi‐digit dividends. Topic G extends the practice of division with three‐ and four‐digit dividends using place value understanding. A connection to Topic B is made initially with dividing multiples of 10, 100, and 1,000 by single‐digit numbers. Place value disks support students visually as they decompose each unit before dividing. Students then practice using the standard algorithm to record long division. They solve word problems and make connections to the area model as was done with two‐digit dividends (4.NBT.2.6, 4.OA.1.3). The module closes as students multiply two‐digit by two‐digit numbers. Students use their place value understanding and understanding of the area model to empower them to multiply by larger numbers (as pictured to the right). Topic H culminates at the most abstract level by explicitly connecting the partial products 4 Note that care must be taken in the interpretation of remainders. Consider
the fact that 7 ÷ 3 is not equal to 5 ÷ 2 because the remainder of 1 is in reference to a different whole amount (2 is not
equal to 2 ). 5 Students become fluent with the standard division algorithm in Grade 6 (6.NS.2). For adequate practice in reaching fluency, students are introduced to, but not assessed on, the division algorithm in Grade 4 as a general method for solving division problems. Page 61 of 72 appearing in the area model to the distributive property and recording the calculation vertically (4.NBT.2.5). Students see that partial products written vertically are the same as those obtained via the distributive property: 4 twenty‐sixes + 30 twenty‐sixes = 104 + 780 = 884. As students progress through this module, they are able to apply the multiplication and division algorithms because of their in‐depth experience with the place value system and multiple conceptual models. This helps to prepare them for fluency with the multiplication algorithm in Grade 5 and the division algorithm in Grade 6. Students are encouraged in Grade 4 to continue using models to solve when appropriate. Page 62 of 72 Module Specific Notes: Resources Module Materials Math Studio Talk: Common Core Instruction for 4.OA https://www.engageny.org/resource/math‐studio‐
talk‐common‐core‐instruction‐4oa Grade 4 Math: Represent and solve division problems with up to a three‐digit dividend 4.NBT.6 https://www.engageny.org/resource/grade‐4‐math‐
represent‐and‐solve‐division‐problems‐a‐three‐digit‐
dividend‐4nbt6 
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Place value disks: 18 ones, 18 tens, 18 hundreds, 18 thousands, 1 ten thousand (1 set per student/pair) Square inch tiles (about 30 per student/pair) Personal white boards (class set) Grid paper Crayons: red, green, blue, orange (1 per student/pair) Additional Aligned Activities
Investigations in Numbers, Data, and Space Unit 1 Session 1.4 Factor Pairs Unit 1 Session 2.3 Multiple Turn Over Unit 1 Session 3.1 Finding Factor of 100 enVision Math Common Core Topic 7‐ 7.2** Clip and Cover Topic 8‐8.1** Teamwork Topic 8‐ 8.2* Toss and Talk Topic 8‐ 8.2** Toss and Talk CPALMS Searching for Primes http://www.cpalms.org/Public/PreviewResour
ceLesson/Preview/46825 Using Rectangles to Find Prime and Composite Numbers http://www.cpalms.org/Public/PreviewResour
ceLesson/Preview/73111 Page 63 of 72 Standards 4.OA.1.1 4.OA.1.2 4.MD.1.3 4.OA.1.3 4.NBT.2.5 4.OA.1.1 4.OA.1.2 4.NBT.1.1 4.NBT.2.5 4.OA.1.2 4.NBT.1.1 Topics and Objectives A B C Multiplicative Comparison Word Problems Lesson 1: Investigate and use the formulas for area and perimeter of rectangles. Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas. Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi‐step real world problems. Multiplication by 10, 100, and 1,000 Lesson 4: Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. Lesson 6: Multiply two‐digit multiples of 10 by two‐digit multiples of 10 with the area model. Multiplication of up to Four Digits by Single‐Digit Numbers Lesson 7: Use place value disks to represent two‐digit by one‐digit multiplication. Lesson 8: Extend the use of place value disks to represent three‐ and four‐digit by one‐digit multiplication. Lessons 9 Multiply three‐ and four‐digit numbers by one‐digit numbers applying the standard algorithm. Lesson 10: Multiply three‐ and four‐digit numbers by one‐digit numbers applying the standard algorithm. Lesson 10 omitted from Duval County Curriculum Guide. Lesson is outside of test item specifications. Lesson 11: 4.OA.1.1 4.OA.1.2 4.OA.1.3 4.NBT.5 D Connect the area model and the partial products method to the standard algorithm. Multiplication Word Problems Lesson 12: Solve two‐step word problems, including multiplicative comparison. Lesson 13: Use multiplication, addition, or subtraction to solve multi‐step word problems. Mid‐Module Assessment: Topics A‐D 4.NBT.2.6 4.OA.1.3 E Division of Tens and Ones with Successive Remainders Lesson 14: Solve division word problems with remainders. Lesson 15: Understand and solve division problems with a remainder using the array and area models. *End of Quarter 1. Module 3 is continued in Quarter 2. Page 64 of 72 Topic A: Multiplicative Comparison Word Problems Students begin Topic A by investigating the formulas for area and perimeter. In Lesson 1, they use those formulas to solve for area and perimeter and to find the measurements of unknown lengths and widths. In Lessons 2 and 3, students use their understanding of the area and perimeter formulas to solve multiplicative comparison problems including the language of times as much as with a focus on problems using area and perimeter as a context (e.g., A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?) (4.OA.1.2, 4.MD.1.3). Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities. Multiplicative comparison is foundational for understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. Students determine, using times as much as, the length of one side of a rectangle as compared to its width. Beginning this Grade 4 module with area and perimeter allows students to review their multiplication facts, apply them to new and interesting word problems, and develop a deeper understanding of the area model as a method for calculating with larger numbers. Date/ Day of the school year Approx. Date: 09/26/2016 Day: 30 Math Florida Standards/ Mathematical Practice OBJ: Target
Students will investigate 4.MD.1.3 and use the formulas for area and perimeter Embedded of rectangles. 4.OA.2.4 EQ: Fluency How can I investigate and use the formulas Mathematical for area and perimeter Practices of rectangles? Objective/ Essential Question Academic Language area perimeter rectangle unit vertices parallel angles measurement distance around length width square unit formula square array centimeter unknown square centimeter square meter Lesson Assessment / Performance Tasks Module 3
Topic A Lesson 1: Investigate and use the formulas for area and perimeter of rectangles. Lesson Materials: (T) Grid paper (with ability to project or enlarge grid paper), chart paper (S) Personal white boar, grid paper Notes:  If students struggle with content, consider using i‐Ready Teacher Toolbox lesson to supplement instruction in core or in centers.  The area and perimeter chart from this lesson will be needed again in Lesson 2. Page 65 of 72 Approx. Date: 09/27/2016 Day: 31 OBJ: Students will solve multiplicative comparison word problems by applying the area and perimeter formulas. EQ: How can I solve multiplicative comparison word problems by applying the area and perimeter formulas? Target
4.OA.1.1 4.OA.1.2 4.MD.1.3 Embedded 4.OA.1.3 Fluency 4.NBT.1.1 Mathematical Practices MP7 Notes: Approx. Date: 09/28/2016 Day: 32 OBJ: Students will demonstrate understanding of area and perimeter formulas by solving multi‐step real world problems. EQ: How can I demonstrate my understanding of area and perimeter formulas by solving multi‐step real world problems? length Module 3
Target
width Topic A 4.OA.1.1 area Lesson 3: Demonstrate understanding of area and 4.OA.1.2 perimeter perimeter formulas by solving multi‐step real world 4.MD.1.3 problems. Embedded Lesson Materials: 4.OA.2.4 (S) Squares and Unknown Factors Sprint 4.OA.1.3 (S) Problem Set Fluency Mathematical Practices MP1 Notes: If students struggle with multiplicative comparison in the context of area and perimeter, consider using i‐Ready Teacher Toolbox lessons to supplement instruction in core or in centers. On FSA, MA.4.OA.1.2 will be assess in additional contexts, not only area and perimeter. formula inch meter dimensions diagram area perimeter Module 3
Topic A Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas. Lesson Materials: (T) Chart of formulas for perimeter and area from Lesson 1 (S) Personal white board, square‐inch tiles Page 66 of 72 Topic B: Multiplication by 10, 100, 1,000 In Topic B, students examine multiplication patterns when multiplying by 10, 100, and 1,000. Reasoning between arrays and written numerical work allows students to see the role of place value units in multiplication (as pictured below). Students also practice the language of units to prepare them for multiplication of a single‐digit factor by a factor with up to four digits. Teachers also continue using the phrase “____ is ____ times as much as ____” (e.g., 120 is 3 times as much as 40). This carries forward multiplicative comparison from Topic A, in the context of area, to Topic B, in the context of both calculations and word problems. In preparation for two‐digit by two‐digit multiplication, students practice the new complexity of multiplying two two‐digit multiples of 10. For example, students have multiplied 20 by 10 on the place value chart and know that it shifts the value one place to the left, 10 × 20 = 200. To multiply 20 by 30, the associative property allows for simply tripling the product, 3 × (10 × 20), or multiplying the units, 3 tens × 2 tens = 6 hundreds (alternatively, (3 × 10) × (2 × 10) = (3 × 2) × (10 × 10)). Date/ Day of the school year Objective/ Essential Question Approx. Date: 09/29/2016 Day: 33 OBJ: Students will interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. EQ: How can I interpret and represent patterns when multiplying by 10 100, and 1,000 in arrays and numerically? Approx. Date: 09/30/2016 Day: 34 OBJ: Students will multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. EQ: How can I multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns? Math Florida Standards/ Mathematical Practice Target
4.NBT.2.5 Embedded 4.NBT.1.1 4.OA.1.1 4.OA.1.2 4.MD.1.3 Fluency Mathematical Practices MP4 Notes: Target
4.NBT.2.5 Embedded 4.NBT.1.1 4.OA.1.1 4.OA.1.2 Fluency Mathematical Practices MP4 Academic Language Lesson groups of multiply equation number disks simplifying strategy expression product decompose Module 3
Topic B Lesson 4: Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. Lesson Materials: (T) Thousands place value chart (Template) (S) Personal white board, thousands place value chart (Template) place value chart unit form horizontally zero Module 3
Topic B Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. Lesson Materials: (T) Thousands place value chart (Lesson 4 Template) (S) Personal white board, thousands place value chart (Lesson 4 Template) Assessment / Performance Tasks Page 67 of 72 Approx. Date: 10/03/2016 Day: 35 Notes: OBJ: Students will multiply two‐digit multiples of 10 by two‐digit multiples of 10 with the area model. EQ: How can I multiply two‐
digit multiples of 10 by two digit multiples of 10 with the area model? Target
4.NBT.2.5 Embedded 4.NBT.1.1 4.OA.1.1 4.OA.1.2 Fluency Mathematical Practices Notes: two‐digit number
express equivalent model multiplication‐ sentence area model unit form Module 3
Topic B Lesson 6: Multiply two‐digit multiples of 10 by two‐digit multiples of 10 with the area model. Lesson Materials: (T) Thousands place value chart (Lesson 4 Template) (S) Personal white board, thousands place value chart (Lesson 4 Template) Topic C: Multiplication of up to Four Digits by Single‐Digit Numbers Building on their work in Topic B, students begin in Topic C decomposing numbers into base ten units in order to find products of single‐digit by multi‐digit numbers. Students practice multiplying by using models before being introduced to the standard algorithm. Throughout the topic, students practice multiplication in the context of word problems, including multiplicative comparison problems. In Lessons 7 and 8, students use place value disks to represent the multiplication of two‐, three‐, and four‐digit numbers by a one‐digit whole number. Lessons 9 move students to the abstract level as they multiply three‐ and four‐digit numbers by one‐digit numbers using the standard algorithm. Finally, in Lesson 11, partial products, the standard algorithm, and the area model are compared and connected via the distributive property (4.NBT.2.5). Date/ Day of the school year Approx. Date: 10/04/2016 Day: 36 Objective/ Essential Question OBJ: Students will use place value disks to represent two‐digit by one‐digit multiplication. EQ: How can I use place value disks to represent two‐digit by one digit multiplication? Math Florida Standards/ Mathematical Practice Target
4.NBT.2.5 Embedded 4.OA.1.2 4.NBT.1.1 Fluency Mathematical Practices MP4 Notes: Academic Language total value partial products pattern expression regrouping Lesson Assessment / Performance Tasks Module 3
Topic C Lesson 7: Use place value disks to represent two‐digit by one‐digit multiplication. Lesson Materials: (T) Ten thousands place value chart (Template) (S) Multiply Multiples of 10, 100, and 1,000 Sprint, Personal white board, ten thousands place value chart (Template) Page 68 of 72 Approx. Date: 10/05/2016 Day: 37 OBJ: Students will use place value disks to represent three and four‐digit by one‐digit multiplication. EQ: How can I use place value disks to represent three and four‐digit by one digit multiplication? Approx. Date: 10/06/2016 Day: 38 OBJ: Students will multiply three‐ and four‐digit numbers by one‐digit numbers applying the standard algorithm. EQ: How can I multiply three and four‐digit numbers by one digit numbers applying the standard algorithm? Approx. Date: 10/07/2016 Day: 39 OBJ: Students will connect the area model and the partial products method to the standard algorithm. EQ: How can I connect the area model and the total value Module 3
Target
partial products Topic C 4.NBT.2.5 pattern Lesson 8: Extend the use of place value disks to represent expression three and four digit by one digit multiplication. Embedded regrouping 4.OA.1.2 Lesson Materials: 4.NBT.1.1 (S) Personal white board, ten thousands place value chart (Template) Fluency 2.NBT.1.3 4.NBT.2.4 4.NBT.2.5 Mathematical Practices MP4 Notes: repeated addition Module 3
Target
tape diagram Topic C 4.NBT.2.5 standard algorithm Lesson 9: Multiply three‐ and four‐digit numbers by one‐
digit numbers applying the standard algorithm. Embedded 4.OA.1.2 Lesson Materials: 4.NBT.1.1 (T) Ten thousands place value chart (Lesson 7 Template) 2.NBT.1.2 (S) Personal white board, ten thousands place value chart Fluency (Lesson 7 Template) Mathematical Practices MP2 Notes: Consider introducing area model with this lesson. If students need additional practice, use problems from Lesson 10 Problem Set. Target
4.NBT.2.5 Embedded 4.OA.1.2 4.NBT.1.1 4.MD.1.3 Fluency partial products
distributive‐ property area model standard algorithm statement Module 3
Topic C Lesson 11: Connect the area model and the partial products method to the standard algorithm. Lesson Materials: (S) Place value disks MAFS.4.NBT.2.5
Multiplying Using An Array or Area Model Page 69 of 72 partial products method Mathematical to the standard Practices algorithm? MP5 Notes: Lesson 10 has been omitted. Lesson 10 is outside test item specifications. Topic D: Multiplication Word Problems Topic D gives students the opportunity to apply their new multiplication skills (4.NBT.2.5). In Lesson 12, students extend their work with multiplicative comparison from Topic A to solve real‐world problems (4.OA.1.2). As shown on the next page, students use a combination of addition, subtraction, and multiplication to solve multi‐step problems in Lesson 13 (4.OA.1.3). Date/ Day of the school year Objective/ Essential Question Approx. Date: 10/10/2016 Day: 40 OBJ: Students will solve two‐
step word problems, including multiplicative comparison. EQ: How can I solve two –
step problems, including multiplicative comparison? Approx. Date: 10/11/2016 Day: 41 OBJ: Students will use multiplication, addition, or subtraction to solve multi‐step word problems. EQ: How can I use multiplication, addition, or subtraction to solve Math Florida Standards/ Academic Language Lesson Mathematical Practice Module 3
Target
assess the solution Topic D 4.OA.1.1 equation Lesson 12: Solve two‐step word problems, including 4.OA.1.2 unknown multiplicative comparison. 4.OA.1.3 value 4.NBT.2.5 tape diagram Lesson Materials: RDW process (S) Personal white board, Place value disks, Problem Set Embedded Fluency Mathematical Practices MP1 Notes: Continue the use of the area model as a strategy. Module 3
Target
Utilize vocabulary Topic D 4.OA.1.1 from previous Lesson 13: Use multiplication, addition, or subtraction to 4.OA.1.2 lessons in this solve multi‐step word problems. 4.OA.1.3 module. 4.NBT.2.5 Lesson Materials: (S) Mental Multiplication Sprint, Personal white board, Embedded Problem Set Fluency Mathematical Practices Assessment / Performance Tasks Page 70 of 72 Approx. Date: 10/12/2016 Day: 42 multi‐step word problems? MP1 OBJ: Students will show mastery of standards introduced in Module 3 Topics A‐D. EQ: How can I use strategies I’ve learned to help me as a mathematician? Target
Embedded Fluency Mathematical Practices Notes: Notes: Continue the use of the area model as a strategy. Module 3
Mid‐Module‐Assessment: Topics A‐D Module 3
Mid‐Module‐
Assessment: Topics A‐D Topic E: Division of Tens and Ones with Successive Remainders In Topic E, students synthesize their Grade 3 knowledge of division types (group size unknown and number of groups unknown) with their new, deeper understanding of place value. Students focus on interpreting the remainder within division problems both in word problems and long division (4.OA.1.3). A remainder of 1, as exemplified below, represents a leftover flower in the first situation and a remainder of 1 ten in the second situation.1 1 (Note that care must be taken in the interpretation of remainders. Consider the fact that 7 ÷ 3 is not equal to 5 ÷ 2 because the remainder of 1 is in reference to a different whole amount (2 is not equal to 2 ). While we have no reason to subdivide a remaining flower, there are good reasons to subdivide a remaining ten. Students apply this simple idea to divide two‐digit numbers unit by unit: dividing the tens units first, finding the remainder (the number of tens unable to be divided), and decomposing remaining tens into ones to then be divided. Lesson 14 begins Topic E by having students solve division word problems involving remainders. In Lesson 15, students deepen their understanding of division by solving problems with remainders using both arrays and the area model. Students practice dividing two‐digit dividends with a remainder in the ones place using place value disks in Lesson 16 and continue that modeling in Lesson 17 where the remainder in the tens place is decomposed into ones. The long division algorithm2 is introduced in Lesson 16 by directly relating the steps of the algorithm to the steps involved when dividing using place value disks. Introducing the algorithm in this manner helps students to understand how place value plays a role in the steps of the algorithm. The same process of relating the standard algorithm to the concrete representation of division continues in Lesson 17. Lesson 18 moves students to the abstract level by requiring them to solve division problems numerically without drawing. In Lesson 19, students explain the successive remainders of the algorithm by using place value understanding and place value disks. Finally, in Lessons 20 and 21, students use the area model to solve division problems and then compare the standard algorithm to the area model (4.NBT.2.6). Lesson 20 focuses on division problems without remainders, while Lesson 21 involves remainders. Quotients and remainders are independent of each other but must both be included to give a complete response. A quotient and a remainder cannot be recorded after an equal sign because the symbol R or the words with a remainder of are invalid in an equation. Therefore, a quotient and a remainder can be written as a statement such as seven divided by two is three with a remainder of one, or the quotient is three and the remainder is one. It is mathematically correct to record the quotient and the remainder together at the top of the long division algorithm. Page 71 of 72 Date/ Day of the school year Objective/ Essential Question Approx. Date: 10/13/2016 Day: 43 OBJ: Students will solve division word problems with remainders. EQ: How can I solve division and word problems with remainders? Approx. Date: 10/14/2016 Day: 44 OBJ: Students will understand and solve division problems with a remainder using the array and area models. EQ: How can I understand and solve division problems with a remainder using array and area models? Math Florida Standards/ Mathematical Practice Target
4.NBT.2.6 Embedded 4.OA.1.3 4.NBT.2.5 Fluency Mathematical Practices MP4 Notes: Target
4.NBT.2.6 Embedded 4.OA.1.3 Fluency 4.NBT.1.1 Mathematical Practices MP4 Notes: Academic Language Lesson division quotient division expression remainder array interpretation Module 3
Topic E Lesson 14: Solve division word problems with remainders. Lesson Materials: (S) Personal white board square centimeters array area model Module 3
Topic E Lesson 15: Understand and solve division problems with a remainder using the array and area models. Lesson Materials: (T) Thousands place value chart (Lesson 4 Template) (S) Personal white board, thousands place value chart (Lesson 4 Template), Square grid paper (S) Personal white board, square grid paper Assessment / Performance Tasks Page 72 of 72