2016/2017
1st Quarter Elementary Mathematics
Curriculum Guide
Grade 3 Page 1 of 64 3rd Grade Year at a Glance Math Florida Standards Modules Duration Quarter 1 8/15/16‐ 9/20/16 9/21/16‐
10/14/16 Quarter 2 10/17/16‐
10/19/16 26 Days 3 days 18 Days Module 1: Module 2: Properties of Place Value and Problem Multiplication and Solving with Units of Division and Measure Solving Problems with Units of 2–5 and 10 Operations and Measurement and Data
Algebraic 3.MD.1.1 Thinking 3.MD.1.2 3.OA.1.1 3.OA.1.2 Number & Operations 3.OA.1.3 in Base Ten 3.OA.1.4 3.NBT.1.1 3.OA.2.5 3.NBT.1.2 3.OA.2.6 3.OA.3.7 3.OA.4.8 Quarter 3
10/20/16‐
11/18/16 11/21/16‐
12/22/16 20 Days 21 Days Module 3:
Multi‐Digit Multiplication and Division Operations and Algebraic Thinking 3.OA.1.1 3.OA.1.2 3.OA.1.3 3.OA.1.4 3.OA.2.5 3.OA.2.6 3.OA.3.7 3.OA.4.8 3.OA.4.9 1/9/17‐ 2/15/17 2/16/17‐
3/10/17 26 Days 16 Days Module 4:
Multiplication and Area Module 5: Fractions as Numbers on the Number Line Module 7:
Geometry and Measurement Word Problems Number & Operations in Base Ten 3.NBT.1.3 Measurement and Data 3.MD.3.5 3.MD.3.6 3.MD.3.7a 3.MD.3.7b 3.MD.3.7c 3.MD.3.7d Number and Operations ‐ Fractions 3.NF.1.1 3.NF.1.2a 3.NF.1.2b 3.NF.1.3a 3.NF.1.3b 3.NF.1.3c 3.NF.1.3d Geometry 3.G.1.2 Measurement and Data 3.MD.2.4 Geometry
3.G.1.1 Measurement and Data 3.MD.4.8 Quarter 4
3/13/17‐
3/16/17 3/27/17‐
3/30/17 4/3/17‐ 6/2/17 42 Days 4 Days 4 Days Module 6:
Collecting and Displaying Data Deepening Understanding: Multiplication, Division, and Fractions Measurement and Data 3.MD.2.3 3.MD.2.4 Operations and Algebraic Thinking 3.OA.1.3 3.OA.2.5 3.OA.4.8 Numbers & Operations‐
Fractions 3.NF.1.1 3.NF.1.2 3.NF.1.3 Geometry 3.G.1.2 Page 2 of 64 Elementary Mathematics 3rd 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 64 Elementary Mathematics 3rd 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 Approximate Testing Dates Duration 1 Mid‐Module 1 9/2 1 day End of Module 1 9/19 1 day Assess/Performance Task 3.MD.1.1 Mid‐Module 2 9/26 10/6 1 day End of Module 2 10/18 1 day Mid‐Module 3 11/1 1 day End of Module 3 11/17 1 day Mid‐Module 4 12/9 1 day End of Module 4 12/21 1 day Mid‐Module 5 1/26 1 day End of Module 5 2/14 1 day End of Module 6 3/9 1 day End of Module 7 3/30 1 day Assess/Performance Task 3.NF.1.3 Assess/Performance Task Culminating Activity 4/24 5/23 **Please consider using this culminating activity as an assessment or performance task** 2 3 4 Page 4 of 64 August
Notes
Mon
Tues
3rd Grade
Wed
Thu
Fri
1
2
3
4
5
8
9
10
11
12
Notes
PRE‐PLANNING WEEK
15
Day 1
Rituals and
Routines
16
Day 2
Mod 1
Lesson 1
17
Day 3
Mod 1
Lesson 2
18
Day 4
CG Baseline
19
Day 5
CG Baseline
22
Day 6
Mod 1
Lesson 3
23
Day 7
I-Ready
Diagnostic
24
Day 8
I-Ready
Diagnostic
25
Day 9
Mod 1
Lesson 4
26
Day 10
Mod 1
Lesson 5
29
Day 11
Mod 1
Lesson 6
30
Day 12
Mod 1
Lesson 7
31
ERD
Day 13
Mod 1
Lesson 9
*Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class needs. Page 5 of 64 September
Notes
Mon
Tues
3rd Grade
Wed
Thu
Fri
1
Day 14
Mod 1
Lesson 10
2
Day 15
Mid-Module 1
Assessment
5
6
Schools Closed Day 16
Mod 1
Lesson 11
7
Day 17
Mod 1
Lesson 12/13
8
Day 18
Mod 1
Lesson 14
9
Day 19
Mod 1
Lesson 15
12
Day 20
Mod 1
Lesson 16
13
Day 21
Mod 1
Lessons 18
14
ERD
Day 22
Mod 1
Lesson 19
15
Day 23
Mod 1
Lesson 20
16
Day 24
Mod 1
Lesson 21
19
Day 25
End of Module
1 Assessment
20
Day 26
Review and
Remediate
previous
taught
standards
27
Day 31
Envision 12-5
21
Day 27
Mod 2
Lesson 2
22
Day 28
Mod 2
Lesson 3
23
Day 29
Mod 2
Lesson 4
28
ERD
Day 32
Mod 2
Lesson 6
29
Day 33
Mod 2
Lesson 7
30
Day 34
Mod 2
Lesson 8
26
Day 30
Mod 2
Lesson 5
Notes
*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 64 October
Notes
Mon
Tues
3rd Grade
Wed
Thu
Fri
3
Day 35
Mod 2
Lesson 9
4
Day 36
Mod 2
Lesson 10
5
Day 37
Mod 2
Lesson 11
6
Day 38
Mid Module 2
Assessment
7
Day 39
Mod 2
Lesson 12
10
Day 40
Mod 2
Lesson 13
11
Day 41
Mod 2
Lesson 14
12
ERD
Day 42
Mod 2
Lesson 15/16
13
Day 43
Mod 2
Lesson 18
14
Day 44
Mod 2
Lesson 19
Notes
Quarter 1 Ends
17
Day 45
Mod 2
Lesson 21
18
Day 46
End of Module
2 Assessment
Quarter 2 Begins
24
Day 49
Mod 3
Lesson 2
25
Day 50
Mod 3
Lesson 3
19
Day 47
Review and
Remediate
previous
taught
standards
26
ERD
Day 51
Mod 3
Lesson 4/5
20
Day 48
Mod 3
Lesson 1
21
Employee
Planning
27
Day 52
Mod 3
Lesson 7
28
Day 53
Mod 3
Lesson 8
31
Day 54
Mod 3
Lesson 9
*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 64 Quarter 1 Module 1 Course: DUVAL COUNTY PUBLIC SCHOOLS
Math Curriculum Lesson Guide
Grade 3 Math Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10 Unit # Dates/Pacing: 8/15/16 ‐9/20/16, 26 days 1
Represent and solve problems involving multiplication and division. 3.OA.1.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. Cognitive Complexity: Level: 1 Recall 3.OA.1.2 Interpret whole‐number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Cognitive Complexity: Level: 1 Recall 3.OA.1.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Glossary, Table 2.) Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts 3.OA.1.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? MAFS Cognitive Complexity: Level: 1 Recall Understand properties of multiplication and the relationship between multiplication and division.2 3.OA.2.5 Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 ×10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)3 Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts 3.OA.2.6 Understand division as an unknown‐factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts Multiply and divide within 100.4 3.OA.3.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one‐digit numbers. Page 8 of 64 Cognitive Complexity: Level: 1 Recall Solve problems involving the four operations, and identify and explain patterns in arithmetic.5 3.OA.4.8 Solve two‐step word problems using the four operations. 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. (This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations.) Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts 1
Limited to factors of 2–5 and 10 and the corresponding dividends in this module. Limited to factors of 2–5 and 10 and the corresponding dividends in this module. 3
The associative property is addressed in Module 3. 4
Limited to factors of 2–5 and 10 and the corresponding dividends in this module. 5
In this module, problem solving is limited to factors of 2–5 and 10 and the corresponding dividends. 3.OA.4.9 is addressed in Module 3. 2
Page 9 of 64 Standards for Mathematical Practices 3rd Grade
In third grade, mathematically proficient students 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. Third grade students 1. Make sense of problems may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking and persevere in solving them. themselves, “Does this make sense?” Students listen to other students’ strategies and are able to make connections between various methods for a given problem. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically 6. Attend to precision. Mathematically proficient third 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 units involved and the meaning of quantities. In third grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilities by asking questions such as “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. Mathematically proficient students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students require extensive opportunities to generate various mathematical representations and to both equations and story problems, and explain connections between representations as well as between representations and equations. Students should be able to use all of these representations as needed. They should evaluate their results in the context of the situation and reflect on whether the results make sense. Mathematically proficient third 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 to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles. Mathematically proficient third grader students develop their mathematical communication skills, they try to use clear and precise language in 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, when figuring out the area of a rectangle they record their answers in square units. 7. Look for and make use of structure. In third grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties). 8. Look for and express regularity in repeated reasoning. Mathematically proficient students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?” Page 10 of 64 Test Item Specifications Content Standard MAFS.3.OA.1.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in
which a total number of objects can be expressed as 5 × 7.
Whole number factors may not exceed 10 x 10. Students may not be required to write an equation to represent a Assessment Limits product of whole numbers. Equation Editor Multiple Choice Item Types Multiselect Open Response Table Item
Context Allowable Complexity Level Level: 1 Recall Achievement Levels Level 2 Level 3 interprets products of single‐digit whole numbers (using factors of 1, 2, or 5) using equal groups of objects and arrays of objects interprets products of single‐digit whole numbers (using factors up to 10) Level 4 interprets products of whole numbers within 100, representing context with numbers and words Level 5 [intentionally left blank] Page 11 of 64 Content Standard MAFS.3.OA.1.2 Interpret whole‐number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Whole number quotients and divisors may not exceed 10. Items may not require students to write an equation to Assessment Limits represent a quotient of whole numbers. Equation Editor Item Types GRID Multiple Choice Multiselect Open Response Allowable Context Level: 1 Recall Complexity Level Achievement Levels Level 2 Level 3 interprets whole‐number quotients of whole numbers (with a divisor of 1, 2, or 5) using equal groups of objects and arrays of objects interprets whole‐number quotients of whole numbers (with factors up to 10) using partitive division; interprets whole number quotients of whole numbers (with factors up to 10) using measurement division Level 4 interprets quotients of whole‐
number division problems within 100, representing context using numbers and words Level 5 [intentionally left blank] Page 12 of 64 Content Standard MAFS.3.OA.1.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Assessment Limits Items may not contain more than one unknown per equation. Items may not contain the words “times as much/many.” Equation Editor Item Types GRID Multiple Choice Multiselect Required Context Level: 2 Basic Application of Skills & Concepts Complexity Level Achievement Levels Level 2 Level 3 multiplies and divides with factors and divisors of 1, 2, or 5 to solve word problems involving equal groups and arrays multiplies and divides with factors and divisors that are less than or equal to 10 to solve word problems involving equal groups, arrays, and measurement quantities; writes an equation with a symbol to represent the unknown Level 4 multiplies and divides within 100 using a variety of strategies to solve two‐step word problems Level 5 [intentionally left blank] Page 13 of 64 Content Standard MAFS.3.OA.1.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Assessment Limits Items must provide the equation. Students may not be required to create the equation. Context Equation Editor Multiple Choice Multiselect No Context Complexity Level Level: 1 Recall Item Types Achievement Levels Level 2 Level 3 determines the unknown whole number in a multiplication or division equation, when the unknown number is the product or quotient (with factors and divisors of 1, 2, or 5) determines the unknown whole number in a multiplication or division equation, in any position, with factors and divisors up to 10 Level 4 [intentionally left blank] Level 5
[intentionally left blank] Page 14 of 64 Content Standard MAFS.3.OA.2.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Assessment Limits Context Equation Editor GRID Matching Item Multiple Choice Multiselect
No context
Complexity Level Level: 2 Basic Application of Skills & Concepts Item Types Achievement Levels Level 2 Level 3 applies commutative property of multiplication applies commutative, associative, and distributive properties of operations as strategies to multiply and divide Level 4 determines an appropriate strategy or multiple strategies for a given situation Level 4
determines the error in the steps of a distributive property strategy Page 15 of 64 Content Standard MAFS.3.OA.2.6 Understand division as an unknown‐factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Assessment Limits Context Equation Editor GRID Multiple Choice Multiselect No context Complexity Level Level: 2 Basic Application of Skills & Concepts Item Types Achievement Levels Level 2 Level 3 writes multiplication equations to solve division problems with unknown factors where the factors are 1, 2, or 5 writes multiplication equations to solve division problems with unknown factors where the factors are less than or equal to 10 Level 4 [intentionally left blank] Level 5 [intentionally left blank] Page 16 of 64 Content Standard MAFS.3.OA.3.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one‐digit numbers. All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Assessment Limits Context Equation Editor Multiple Choice Multiselect Table Item No context Complexity Level Level: 1 Recall Item Types Achievement Levels Level 2 Level 3 fluently multiplies and divides factors of 1, 2, or 5 fluently multiplies and divides numbers with factors up to and including 10, using a variety of strategies Level 4 fluently retrieves factor pairs of a product Level 5
[intentionally left blank] Page 17 of 64 Content Standard MAFS.3.OA.4.8 Solve two‐step word problems using the four operations. 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. Adding and subtracting is limited to whole numbers within 1,000. All values in multiplication or division situations Assessment Limits may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Students may not be required to perform rounding in isolation. Equations may be provided in items. Editing Task Choice Item Types Equation Editor Hot Text Multiple Choice Multiselect Open Response Required Context Level: 2 Basic Application of Skills & Concepts Complexity Level Achievement Levels Level 2 Level 3 solves two‐step problems using addition and subtraction within 100 and multiplication and division using factors of 1, 2, or 5 solves two‐step word problems using the four operations and using equations with a letter for the unknown quantity Level 4 assesses the reasonableness of answers using mental computation and estimation strategies including rounding Level 5
creates a two‐step word problem from an equation with a variable Page 18 of 64 Standards for Mathematical Practices 3rd Grade
In third grade, mathematically proficient students 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. Third grade students 1. Make sense of problems may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking and persevere in solving them. themselves, “Does this make sense?” Students listen to other students’ strategies and are able to make connections between various methods for a given problem. Mathematically proficient third 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 units involved and the meaning of quantities. In third grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilities by asking questions such as “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. Mathematically proficient students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students require extensive opportunities to generate various mathematical representations and to both equations and story problems, and explain connections between representations as well as between representations and equations. Students should be able to use all of these representations as needed. They should evaluate their results in the context of the situation and reflect on whether the results make sense. Mathematically proficient third 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 to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles. Mathematically proficient third grader students develop their mathematical communication skills, they try to use clear and precise language in 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, when figuring out the area of a rectangle they record their answers in square units. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically 6. Attend to precision. 7. Look for and make use of structure. In third grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties). 8. Look for and express regularity in repeated reasoning. Mathematically proficient students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?” Page 19 of 64 New or Recently Introduced Terms 
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Array6 (arrangement of objects in rows and columns) Commutative property/commutative (e.g., rotate a rectangular array 90 degrees to demonstrate that factors in a multiplication sentence can switch places) Equal groups (with reference to multiplication and division; one factor is the number of objects in a group and the other is a multiplier that indicates the number of groups) Distribute (with reference to the distributive property, e.g., in 12 × 3 = (10 × 3) + (2 × 3) the 3 is the multiplier for each part of the decomposition) Divide/division (partitioning a total into equal groups to show how many equal groups add up to a specific number, e.g., 15 ÷ 5 = 3) Factors (numbers that are multiplied to obtain a product) Multiplication/multiply (an operation showing how many times a number is added to itself, e.g., 5 × 3 =15) Number of groups (factor in a multiplication problem that refers to the total equal groups) Parentheses (symbols ( ) used around an expression or numbers within an equation) Quotient (the answer when one number is divided by another) Rotate (turn, used with reference to turning arrays 90 degrees) Row/column7 (in reference to rectangular arrays) Size of groups (factor in a multiplication problem that refers to how many in a group) Unit (one segment of a partitioned tape diagram) Unknown (the missing factor or quantity in multiplication or division) !! Please note the descriptions for the following terms, which are frequently misused!! 
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Expression: A number, or any combination of sums, differences, products, or divisions of numbers that evaluates to a number (e.g., 3 + 4, 8 × 3, 15 ÷ 3 as distinct from an equation or number sentence). Equation: A statement that two expressions are equal (e.g., 3 × ___ = 12, 5 × b = 20, 3 + 2 = 5). Number sentence (also addition, subtraction, multiplication, or division sentence): An equation or inequality for which both expressions are numerical and can be evaluated to a single number (e.g., 4 + 3 = 6 + 1, 2 = 2, 21 > 7 × 2, 5 ÷ 5 =1). Number sentences are either true or false (e.g., 4 + 4 < 6 × 2 and 21 ÷ 7 = 4) and contain no unknowns. Familiar Terms and Symbols8 
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Add 1 unit, subtract 1 unit (add or subtract a single unit of two, ten, etc.) Expression (see expanded description in box above) Number bond (illustrates part–part–whole relationship, shown at right) Ones, twos, threes, etc. (units of one, two, or three) Repeated addition (adding equal groups together, e.g., 2 + 2 + 2 + 2) Page 20 of 64 
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Tape diagram (a method for modeling problems)
Value (how much) Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10 OVERVIEW This 25‐day module begins the year by building on students’ fluency with addition and their knowledge of arrays. In Topic A, students initially use repeated addition to find the total from a number of equal groups (2.OA.1.4). As students notice patterns, they let go of longer addition sentences in favor of more efficient multiplication facts (3.OA.1.1). Lessons in Topic A move students' Grade 2 work with arrays and repeated addition a step further by developing skip‐
counting rows as a strategy for multiplication. Arrays become a cornerstone of the module. Students use the language of multiplication as they understand what factors are and differentiate between the size of groups and the number of groups within a given context. In this module, the factors 2, 3, 4, 5, and 10 provide an entry point for moving into more difficult factors in later modules. The study of factors links Topics A and B; Topic B extends the study to division. Students understand division as an unknown factor problem and relate the meaning of unknown factors to either the number or the size of groups (3.OA.1.2, 3.OA.2.6). By the end of Topic B, students are aware of a fundamental connection between multiplication and division that lays the foundation for the rest of the module. The Distributive Property In Topic C, students use the array model and familiar skip‐counting strategies to solidify their understanding of 6 × 4 = _____ multiplication and practice related facts of 2 and 3. They become fluent enough with arithmetic patterns to “add” or “subtract” groups from known products to solve more complex multiplication problems (3.OA.1.1). They apply their skills to word problems using drawings and equations with a symbol to find the unknown factor (3.OA.1.3). This culminates in students using arrays to model the distributive property as they decompose units to multiply (3.OA.2.5).In (5 × 4) = 20 Topic D, students model, write, and solve partitive and measurement division problems with 2 and 3 (3.OA.1.2). Consistent skip‐counting strategies and the continued use of array models are pathways for students to naturally relate multiplication and division. Modeling advances as students use tape diagrams to represent multiplication and division. (1 × 4) = 4 A final lesson in this topic solidifies a growing understanding of the relationship between operations (3.OA.3.7). the routine for students who benefit from their friends’ support to identify patterns and try new strategies. (6 × 4) = (5 × 4) + (1 × 4) = 20 + 4 6 Originally introduced in Grade 2, Module 6 but treated as new vocabulary in this module. 7 Originally introduced in Grade 2, Module 6 but treated as new vocabulary in this module. 8
These are terms and symbols students have used or seen previously. Page 21 of 64 Students may takTopic E shifts students from simple understanding to analyzing the relationship between multiplication and division. Practice of both operations is combined—this time using units of 4—and a lesson is explicitly dedicated to modeling the connection between them (3.OA.3.7). Skip‐counting, the distributive property, arrays, number bonds, and tape diagrams are tools for both operations (3.OA.1.1, 3.OA.1.2). A final lesson invites students to explore their work with arrays and related facts through the lens of the commutative property as The Commutative Property
it relates to multiplication (3.OA.5). Topic F introduces the factors 5 and 10, familiar from skip‐counting in Grade 2. Students apply the multiplication and division strategies they have used to mixed practice with all of the factors included in Module 1 (3.OA.1.1, 3.OA.1.2, 3.OA.1.3). Students model relationships between factors, analyzing the arithmetic patterns that emerge to compose and decompose numbers, as they further explore the relationship between multiplication and division (3.OA.1.3, 3.OA.2.5, 3.OA.3.7). In the final lesson of the module, students apply the tools, representations, and concepts they have learned to problem solving with multi‐step word problems using all four operations (3.OA.1.3, 3.OA.4.8). They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types. The Mid‐Module Assessment follows 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 22 of 64 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 23 of 64 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 e 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. 

What do I see? Can I draw something? What conclusions can I make from my drawing? Page 24 of 64 Module Specific Notes: OA.1.3 and 1.4 start as Embedded standards in the first few topics, but then become focus standards in Topic F
Resources Math Studio Talk: Common Core Instruction for 3.OA Link: https://www.engageny.org/resource/math‐studio‐
talk‐common‐core‐instruction‐3oa Resource on how to use the Sprints to build fluency https://www.engageny.org/resource/nti‐
november‐2012‐rigor‐breakdown‐sprints‐fluency‐
in‐action Module Materials Personal white boards Class set dry erase markers, erasers Counters (18 per student) Linking cubes Chart paper Markers Paper strips Glue Additional Aligned Activities EnVisionMATH Center Activities: Topic 4‐ 4.1 * Toss and Talk Topic 4‐ 4.3 * Teamwork Topic 4‐ 4.5 ** Teamwork Topic 5‐ 5.7 ** Display the Digits Topic 6‐ 6.1 * Teamwork Topic 6‐ 6.6 * ** Clip and Cover Topic 6‐ 6.9 * ** Display the Digits Topic 7‐ 7.2 ** Toss and Talk Math Investigations Center Activities: Unit 5 Session 3.5‐ Making Multiplication Cards Unit 5 Session 4.4‐ Missing Factors Page 25 of 64 Standards 3.OA.1.1 3.OA.1.3 3.OA.1.2 3.OA.2.6 3.OA.1.3 3.OA.1.4 3.OA.1.1 3.OA.2.5 3.OA.1.3 3.OA.1.4 Topics and Objectives A B C Multiplication and the Meaning of the Factors Lesson 1: Understand equal groups of as multiplication. Lesson 2: Relate multiplication to the array model. Lesson 3: Interpret the meaning of factors—the size of the group or the number of groups. Division as an Unknown Factor Problem Lesson 4: Understand the meaning of the unknown as the size of the group in division. Lesson 5: Understand the meaning of the unknown as the number of groups in division. Lesson 6: Interpret the unknown in division using the array model. Multiplication Using Units of 2 and 3 Lessons 7–8: Demonstrate the commutativity of multiplication, and practice related facts by skip‐counting objects in array models. Lesson 9: Find related multiplication facts by adding and subtracting equal groups in array models. Lesson 10: 3.OA.1.2 3.OA.1.4 3.OA.2.6 3.OA.3.7 3.OA.1.3 3.OA.4.8 D Model the distributive property with arrays to decompose units as a strategy to multiply. Mid‐Module Assessment (Topics A‐C) Division Using Units of 2 and 3 Lesson 11: Model division as the unknown factor in multiplication using arrays and tape diagrams. Lesson 12: Interpret the quotient as the number of groups or the number of objects in each group using units of 2. Lesson 13: Interpret the quotient as the number of groups or the number of objects in each group using units of 3.  Lesson 12 and 13 have been combined. These lessons were similar content and similar objectives. The lessons will need to be honed to include problems containing units of 2 and 3. Page 26 of 64 3.OA.5 3.OA.7 3.OA.1 3.OA.2 3.OA.3 3.OA.4 3.OA.6 E Multiplication and Division Using Units of 4 Lesson 14: Skip‐count objects in models to build fluency with multiplication facts using units of 4. 3.OA.1.3 3.OA.2.5 3.OA.3.7 3.OA.4.8 3.OA.1.1 3.OA.1.2 3.OA.1.4 3.OA.2.6 F Lesson 15: Relate arrays to tape diagrams to model the commutative property of multiplication. Lesson 16: Use the distributive property as a strategy to find related multiplication facts. Lesson 17: Model the relationship between multiplication and division. Lesson 17 has been omitted. It is an extension of lesson 11 and can be used as an optional lesson. Distributive Property and Problem Solving Using Units of 2–5 and 10 Lessons 18: Apply the distributive property to decompose units. Lesson 19: Apply the distributive property to decompose units. Lesson 20: Solve two‐step word problems involving multiplication and division, and assess the reasonableness of answers. Lesson 21: Solve two‐step word problems involving all four operations, and assess the reasonableness of answers. End‐of‐Module Assessment: Topics A–F Page 27 of 64 Topic A: Multiplication and the Meaning of Factors
Lesson 1 introduces students to multiplication, starting with the concept of repeated addition, which is familiar from Grade 2. Students use repeated addition to find totals; for example, they use counters to make 6 equal groups of 2. They learn to recognize equal groups of counters as units and count units using the language of groups and unit form: “6 equal groups of 2 counters make 12 counters,” or “6 twos make 12.” By the end of Lesson 1, students use the multiplication symbol to represent these descriptions as more efficient multiplication equations. In Lesson 2, students relate the equal groups of objects in scattered configurations from Lesson 1 to the array model, exploring the correspondence between 1 equal group and 1 row. They begin to distinguish between the number of groups and the size of groups as they count rows and how many in 1 row to write multiplication facts. Students recognize the efficiency of arrays as they skip‐count to find totals. In Lesson 2, students use the following vocabulary: row, array, number of groups, and size of groups. Lesson 3 solidifies students’ ability to differentiate the meaning of factors. Students model dividing a whole into equal groups as well as analyze equal groups in scattered configurations and arrays to determine whether factors represent the number of groups or the size of groups. They create pictures, number bonds, and multiplication equations to model their understanding. In this topic, students use a variety of factors since these lessons emphasize understanding the concept of multiplying rather than finding totals. Later topics limit facts to those involving one or two specific factors, allowing students to build fluency with simpler facts before moving on to more difficult ones. Math Florida Date/ Objective/ Standards/ Assessment / Performance Day of the Academic Language Lesson Essential Question Mathematical Tasks school year Practice Approx. Date: journals OBJ: Target
Rituals and Routines
During your 30 minute 08/15/2015 centers Students will become centers block, use this time  Interactive Journals manipulatives familiar with math Embedded to deliver the Ritual and  Centers Routine lessons using the 8 Day: 1 core instruction rituals and routines.  Introduce Sprints Mathematical Practices. GRRM Fluency  Accountable Talk They are designed to be *common board EQ:  Manipulatives short 30 minute activities configuration How can I become Mathematical that introduce students to Expectations familiar with math Practices During Centers Block: Rituals and Routines Lesson the Standards for Home learning rituals and routines? Mathematical Practices CHAMPs and effective modeling of transitions strategies. Notes:
Approx. Date: 08/16/2015 Day: 2 OBJ: Students will understand equal groups of as multiplication. Target
3.OA.1.1 Embedded 3.OA.1.3 Fluency 3.OA.1.1 equal groups
multiplication multiply skip‐count efficient multiplication sentence Module 1
Topic A Lesson 1: Understand equal groups of as multiplication. Materials Need For Lesson: Personal white boards Counters (12 per student) 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 Page 28 of 64 Approx. Date: 8/17/15 Day: 3 EQ: How do I understand equal groups of as multiplication? Mathematical Practices MP3 OBJ: Students will relate multiplication to the array model. EQ: How do I relate multiplication to the array model? Target
3.OA.1.1 Embedded 3.OA.1.3 Fluency 3.OA.1.1 Mathematical Practices Mathematical Practices and effective modeling of strategies. Notes:
May need to introduce/review tape diagrams and number bonds for the application problem. skip‐counting
group‐counting repeated addition row column array number of groups size of groups multiplication sentence Module 1
Topic A Lesson 2: Relate multiplication to the array model. Materials Need For Lesson: Personal white boards 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: 8/18/15 Day: 4 OBJ: Student will complete Baseline assessment Flex Day: Baseline Assessment. This day is added as a Baseline Assessment
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. Curriculum Associates recommends for 3rd grade students to complete this in separate1‐ 2, 40 minute sessions, not a consecutive 80 minutes. Notes:
Approx. Date: 8/19/16 Day: 5 OBJ: Student will complete Baseline assessment Flex Day: Baseline Assessment. This day is added as a Baseline Assessment
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. Curriculum Associates recommends for 3rd grade students to complete this in separate1‐ 2, 40 minute sessions, not a consecutive 80 minutes. Notes: Page 29 of 64 Approx. Date: 8/22/15 Day: 6 8/23/16 Day: 7 OBJ: Students will interpret the meaning of factors. EQ: How do I interpret the meaning of factors? OBJ: Students will complete I‐Ready Diagnostic. Target
3.OA.1.1 Embedded 3.OA.1.3 Fluency 3.OA.1.1 Mathematical Practices Notes:
factors
divide skip‐counting group‐counting repeated addition row column array multiplication sentence Module 1
Topic A Lesson 3: Interpret the meaning of factors—the size of the group or the number of groups. Materials Need For Lesson: Personal white boards Counters 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. 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. Curriculum Associates recommends for 3rd grade students to complete this in separate1‐ 2, 40 minute sessions, not a consecutive 80 minutes. I‐Ready Diagnostic
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. Curriculum Associates recommends for 3rd grade students to complete this in separate1‐ 2, 40 minute sessions, not a consecutive 80 minutes. I‐Ready Diagnostic
Notes:
8/24/16 Day: 8 OBJ: Students will complete I‐Ready Diagnostic. Notes:
Page 30 of 64 Topic B:Division as an Unknown Factor Problem
The study of factors links Topics A and B. Topic B extends the study to division. Students continue to use a variety of factors in this topic as the emphasis in these lessons rests on conceptually understanding division and learning to interpret problems by writing division equations. Students understand division as an unknown factor problem, and in Lessons 4 and 5, they relate the meaning of the unknown in division to the size of groups and the number of groups, respectively. They work through word problems that help give meaning through context and then analyze more abstract drawings. In Lesson 6, students explore division in the context of the array model, interpreting arrays by writing division equations. Through the array, students relate the unknown factor in multiplication to the quotient in division. They use arrays to write multiplication equations and find unknown factors, then write division equations where the quotient represents the same as the unknown factor. By the end of this topic, students use the vocabulary terms quotient and unknown factor, and discussion moves toward solidifying understanding of the relationship between multiplication and division Date/ Day of the school year Objective/ Essential Question Approx. Date: 8/25/16 Day: 9 OBJ: Students will understand the meaning of the unknown as the size of the group in division. EQ: How do I understand the meaning of the unknown as the size of groups in division? Approx. Date: 8/26/16 Day: 10 OBJ: Students will understand the meaning of the unknown as the number of groups in division. EQ: How do I understand the meaning of the unknown as the Math Florida Standards/ Mathematical Practice Target
3.OA.1.2 3.OA.2.6 Embedded 3.OA.1.3 3.OA.1.4 Fluency 3.OA.1.1 Mathematical Practices MP.2 Notes:
Target
3.OA.1.2 3.OA.2.6 Embedded 3.OA.1.3 3.OA.1.4 Fluency 3.OA.1.1 3.OA.1.2 Academic Language Lesson Assessment / Performance Tasks Unknown
Division Factor Size of group Fair share Divided by Number of groups Module 1
Topic B Lesson 4: Understand the meaning of the unknown as the size of the group in division. Materials Needed For Lesson: Personal white boards Counters 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. Divided by
Equal groups Division sentence Unknown Division Factor Size of group Fair share Number of groups Module 1
Topic B Lesson 5: Understand the meaning of the unknown as the number of groups in division. Materials Needed For Lesson: Personal white boards 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 31 of 64 number of groups in division? Approx. Date: 8/29/16 Day: 11 OBJ: Students will interpret the unknown in division using the array model. EQ: How do I interpret the unknown in division using the array model. Mathematical Practices MP.3 Notes:
Target
3.OA.1.2 3.OA.2.6 Embedded 3.OA.1.3 3.OA.1.4 Fluency 3.OA.1.1 3.OA.1.2. Mathematical Practices Notes:
Division sentence
Quotient Unknown factors Module 1
Topic C Lesson 6: Interpret the unknown in division using the array model. Materials Needed For Lesson: Personal white boards 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 32 of 64 Topic C: Multiplication Using Units of 2 and 3 In Topic C, students begin building fluency with facts of 2 and 3 using the array model and familiar skip counting strategies. Lessons 7 and 8 introduce the new complexity of manipulating arrays to study the commutative property. Students learn to distinguish rows from columns as they rotate arrays 90 degrees, noticing that the meaning of the factors changes depending on the orientation of the array. Students write two different multiplication sentences to interpret the same array. These lessons emphasize the equivalence of facts by demonstrating, for example, that 2 groups of 8 and 8 groups of 2 have the same product. Students observe the pattern and begin to recognize commutativity as a strategy for solving twice as many facts. Lessons 9 and 10 introduce the distributive property as a strategy for multiplication. In Lesson 9, students use arrays to decompose unknown facts as the sum or difference of two known facts. For example, they analyze an array to see that 7 × 3 can be decomposed as 2 rows of 3 + 5 rows of 3. In Lesson 10, students learn to write the decomposition as (5 × 3) + (2 × 3) = 21. They explain each step of the solving process in anticipation of the work they are expected to complete independently on the Mid‐Module Assessment. Date/ Day of the school year Approx. Date: 8/30/15 Day: 12 Objective/ Essential Question OBJ: Students will demonstrate the commutativity of multiplication, and practice related facts by skip‐counting objects in array models. EQ: How do I demonstrate the commutativity of multiplication and by skip‐count objects in array models? Math Florida Standards/ Assessment / Performance Academic Language Lesson Mathematical Tasks Practice During your 30 minute Target
Commutative
Module 1
3.OA.1.1 Commutative Topic B centers block, use this time 3.OA.2.5 property Lesson 7: Demonstrate the commutativity of to deliver the Ritual and Commutativity multiplication, and practice related facts by skip‐
Routine lessons using the 8 Embedded Rotate counting objects in array models. Mathematical Practices. 3.OA.1.3 Column They are designed to be 3.OA.1.4 Multiplication Materials Need For Lesson: short 30 minute activities times Personal white boards that introduce students to Fluency the Standards for 3.OA.1.1 Mathematical Practices 3.OA.1.2 and effective modeling of 3.OA.3.7 strategies. Mathematical Practices MP.7 Notes:
Students don’t need to master the academic language (commutative, commutativity, commutative property) they just need to be familiar with it to move forward in this module. Page 33 of 64 Approx. Date: 8/31/16 Day: 13 Approx. Date: 9/1/16 Day: 14 distribute
distributive property decompose OBJ: Students will find related multiplication facts by adding and subtracting equal groups in array models. EQ: How do I find related multiplication facts by adding and subtracting equal groups in array models? Target
3.OA.1.1 3.OA.2.5 Embedded 3.OA.1.3 3.OA.1.4 Fluency 3.OA.3.7 3.OA.1.1 Mathematical Practices OBJ: Students will model the distributive property with arrays as a strategy to multiply. EQ: How do I use the distributive property as a strategy to multiply? Module 1
Target
parenthesis
Topic C 3.OA.1.1 distribute Lesson 10: Model the distributive property with arrays 3.OA.2.5 equation to decompose units as a strategy to multiply. decompose Embedded distributive property 3.OA.1.3 Materials Needed For Lesson: 3.OA.1.4 Personal white boards Linking Cubes Fluency 3.OA.3.7 3.OA.1.1 Mathematical Practices MP.4 Notes: Students are not required to master the academic language “distributive property” they need to be familiar with it to move forward in this module. The word distribute should be introduced into their everyday classroom language; such as, “Please distribute these papers to the class.” Module 1
Topic C Lesson 9: Find related multiplication facts by adding and subtracting equal groups in array models. Materials Needed For Lesson: Personal white boards Notes:
Students are not required to master the academic language “distributive property” they need to be familiar with it to move forward in this module. The word distribute should be introduced into their everyday classroom language; such as, “Please distribute these papers to the class.” Page 34 of 64 Approx. Date: 9/2/16 Day: 15 OBJ: Students will show mastery of standards introduced in Module 1 Topics A‐C. EQ: How can I use strategies I’ve learned to help me as a mathematician? Target
3.OA.1.1 3.OA.1.2 3.OA.2.5 3.OA.2.6 Notes:
Module 1
Mid‐Module Assessment Topics A‐C Mid‐Module Assessment Topics A‐C Topic D: Division Using Units of 2 and 3
In Topic D, students solve two types of division situations—partitive (group size unknown) and measurement (number of groups unknown)—using factors of 2 and 3. Students build on their background knowledge of tape diagrams and apply it to represent division. In Lesson 11, the tape diagram is used as a tool to help students recognize and distinguish between types of division. By the end of Lessons 11 and 12, students independently draw and label tape diagrams that help them to compare and analyze problems that may use the same division sentence but have quotients representing different things. Lesson 13 solidifies growing understanding that the unknown can also be found from the related multiplication sentence. Students initially work through word problems using arrays and tape diagrams to practice solving the two types of division and then transition to problem solving using abstract division and multiplication equations. Date/ Day of the school year Approx. Date: 9/6/16 Day: 16 Objective/ Essential Question OBJ: Students will model division as the unknown factor in multiplication using arrays and tape diagram. Math Florida Standards/ Mathematical Practice Target
3.OA.1.2 3.OA.1.4 3.OA.2.6 Embedded 3.OA.3.7 3.OA.1.3 Academic Language quotient
dividend divisor unit tape diagram Lesson Module 1
Topic D Lesson 11: Model division as the unknown factor in multiplication using arrays and tape diagrams. Materials Needed For Lesson: Personal white boards Assessment / Performance Tasks Page 35 of 64 EQ: How do I model division as the unknown factor in multiplication? Approx. Date: 9/7/16 Day: 17 OBJ: Students will interpret the quotient as the number of groups or the number of objects in each using units of two and three. EQ: How do I interpret the quotient? 3.OA.4.8
Fluency 3.OA.1.1 3.OA.3.7 Mathematical Practices MP.4 Notes: Guide students to make connections to help them remember the name tape diagram. bracket
Module 1
Target
Topic D 3.OA.1.2 Lesson 12 and 13: Interpret the quotient as the number 3.OA.1.4 of groups or the number of objects in each group using 3.OA.2.6 units of 2 and 3. Embedded Materials Needed For Lesson: 3.OA.3.7 Personal white boards 3.OA.1.3 3.OA.4.8 Fluency OA.1.1 OA. 3.7 Mathematical Practices MP.5 Notes: Lesson 12 and 13 have been combined. These lessons were similar content and similar objectives. The lessons will need to be honed to include problems containing units of 2 and 3. Page 36 of 64 Topic E: Multiplication and Division Using Units of 4 Topic E begins by introducing students to multiplication by 4 through skip‐counting objects in array models in Lesson 14. Students revisit the commutative property in Lesson 15, this time modeling commutativity using both arrays and tape diagrams. For example, students might initially draw a 2 × 4 array and a 4 × 2 array. Then, they see 2 bars of equal length, one with 4 equal parts and the other with 2 equal parts. Now, they have arrays that show (2 × 4) = (4 × 2), as well as tape diagrams that reflect the equality. In Lesson 16, students examine the distributive property in greater depth. This lesson introduces the 5 + n pattern as a strategy for finding unknown facts involving 4. For example, students know that 4 × 5 is 20, so 4 × 6 is the same as 20 + 4 more, which totals 24. By Lesson 17, practice of multiplication and division facts is dedicated to modeling the relationship between operations using facts of 4. Math Florida Date/ Objective/ Standards/ Assessment / Performance Day of the Academic Language Lesson Essential Question Mathematical Tasks school year Practice Target
Approx. Date: OBJ: Module 1
3.OA.2.5 9/8/16 Students will skip‐
Topic E count object in 3.OA.3.7 Lesson 14: Skip‐count objects in models to build fluency Day: 18 models to build with multiplication facts using units of 4. fluency with Embedded multiplication facts 3.OA.1.1 using units of four. 3.OA.1.2 Materials Needed For Lesson: 3.OA.1.3 Personal white boards EQ: 3.OA.1.4 How do I build 3.OA.2.6 fluency with multiplication facts? Fluency 3.OA.3.7 Mathematical Practices MP.4 Notes:
Approx. Date: OBJ: Target
commutative Module 1
9/9/16 Students will relate 3.OA.2.5 property Topic E arrays to tape Lesson 15: Relate arrays to tape diagrams to model the Day: 19 diagrams to model Embedded commutative property of multiplication. the commutative 3.OA.1.3 Materials Needed For Lesson: property of Personal white boards multiplication. Fluency 3.OA.1.1 3.OA.3.7 Page 37 of 64 Approx. Date: 9/12/16 Day: 20 EQ: How do I model the commutative property of multiplication, by relating arrays to tape diagram? OBJ: Students will use the distributive property as a strategy to find related multiplication facts. EQ: How do I find related multiplication facts? Mathematical Practices MP.7 Notes:
Target
3.OA.2.5 Embedded 3.OA.1.3 Fluency 3.OA.1.1 3.OA.1.3 3.OA.3.7 Mathematical Practices MP.7 Notes: distributive property distribute decompose commutative property Module 1
Topic E Lesson 16: Use the distributive property as a strategy to find related multiplication facts. Materials Needed For Lesson: Personal white boards Page 38 of 64 Topic F: Distributive Property and Problem‐Solving using Units of 2‐5 and 10
Topic F introduces the factors 5 and 10, familiar from skip‐counting in Grade 2. Students apply the multiplication and division strategies they have learned to mixed practice with all of the factors included in Module 1. Students model relationships between factors and decompose numbers as they further explore the relationship between multiplication and division. This culminates in Lessons 18 and 19 as students decompose the dividend in a division sentence to practice the distributive property with division. For example, students decompose 28 ÷ 4 as (20 ÷ 4) + (8 ÷ 4) = 5 + 2 = 7. In the final lessons of the module, students apply the tools, representations, and concepts they have learned to solve multi‐step word problems. They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types. Lesson 20 focuses on word problems involving multiplication and division, while Lesson 21 increases the complexity of problem solving by including word problems involving all four operations. Date/ Day of the school year Approx. Date: 9/13/16 Day: 21 Approx. Date: 9/14/16 Day: 22 Objective/ Essential Question OBJ: Students will apply the distributive property to decompose units when multiplying. EQ: How do I apply the distributive property to decompose units while multiplying? OBJ: Students will apply the distributive property to decompose units when dividing. EQ: How do I apply the distributive property to decompose units while dividing? Math Florida Standards/ Academic Language Lesson Mathematical Practice Target
distributive Module 1
3.OA.2.5 property Topic F decompose Lesson 18: Apply the distributive property to decompose units. Embedded 3.OA.1.4 Materials Needed For Lesson: Fluency Personal white boards 2.NBT.2.5 Mathematical Practices Notes:
Lesson 17 has been omitted. It is an extension of lesson 11 and can be used as an optional lesson. Target
distributive Module 1
3.OA.2.5 property Topic F decompose Lesson 19: Apply the distributive property to decompose units. Embedded 3.OA.1.4 Materials Needed For Lesson: Fluency Personal white boards 3.OA.1.1 3.OA.2.5 3.OA.3.7 Mathematical Practices Notes: Assessment / Performance Tasks Page 39 of 64 Approx. Date: 9/15/16 Day: 23 Approx. Date: 9/16/16 Day: 24 OBJ: Students will solve two‐step word problems involving multiplication and division and assess the reasonableness of answers. EQ: How do I solve two‐
step word problems involving multiplication and division and check for reasonableness? OBJ: Students will solve two‐step word problems with all four operations and assess the reasonableness of their answers. EQ: How do I solve two‐
step word problems with all four operations and check for reasonableness? two‐step
Module 1
Target
reasonableness Topic F 3.OA.2.5 Lesson 20: Solve two‐step word problems involving multiplication and division, and assess the Embedded reasonableness of answers. 3.OA.1.3 Fluency Materials Needed For Lesson: 3.OA.1.1 Personal white boards 3.OA.3.7 Mathematical Practices MP.7 Notes: Students are not required to master the academic language “commutative property” they need to be familiar with it to move forward in this module. two‐step
Module 1
Target
reasonableness Topic F 3.OA.4.8 operations Lesson 21: Solve two‐step word problems involving all four operations, and assess the reasonableness of Embedded answers. 3.OA.1.1 3.OA.1.2 3.OA.1.3 Materials Needed For Lesson: 3.OA.1.4 3.OA.2.5 Chart paper 3.OA.2.6 Markers 3.OA.3.7 Paper strips 3.NBT.1.2 Glue Fluency 3.OA.1.1 3.OA.3.7 Mathematical Practices MP.1 Notes: Page 40 of 64 Approx. Date: 9/19/16 Day: 25 Approx. Date: 9/20/16 Day: 26 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? 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
3.OA.1.1 3.OA.1.2 3.OA.1.3 3.OA.1.1 3.OA.2.5 3.OA.2.6 3.OA.3.7 3.OA.4.8 Notes:
End‐of‐Module Assessment: Topics A‐F
End‐of‐Module Assessment: Topics A‐F Target
3.OA.1.1 3.OA.1.2 3.OA.1.3 3.OA.1.1 3.OA.2.5 3.OA.2.6 3.OA.3.7 3.OA.4.8 FLEX DAY
Use this time to review and remediate previously taught standards based on data. The recommendation is to use direct supported materials. Review and Remediate previously taught standards Notes:
Page 41 of 64 Quarter 1 Module 2 DUVAL COUNTY PUBLIC SCHOOLS
Math Curriculum Lesson Guide
Course: Unit # Dates/Pacing: Grade 3 Math Place Value and Problem Solving with Units of Measure 9/21/16‐ 10/14/16, 18 Days Use place value understanding and properties of operations to perform multi‐digit arithmetic.9 3.NBT.1.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Cognitive Complexity: Level: 1 Recall 3.NBT.1.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. MAFS 3.MD.1.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts 3.MD.1.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one‐step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Cognitive Complexity: Level: 2 Basic Application of Skills & Concepts 9
3.NBT.3 is taught in Module 3. Page 42 of 64 Test Items Specifications Content Standard 3.NBT.1.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Items may contain whole numbers up to 1,000. Assessment Limits Context Equation Editor GRID Matching Item Multiple Choice Multiselect Table Item No context Complexity Level Level: 1 Recall Item Types Achievement Levels Level 2 Level 3 uses place value understanding to round a three‐digit number to the nearest 10 uses place value understanding to round whole numbers (up to 1,000) to the nearest 10 or 100 Level 4 uses place value understanding to round whole numbers to both the nearest 10 and 100 where the digit to the left is also affected (e.g., round 199 to the nearest ten) Level 5
determines missing original number when given a number that has been rounded Page 43 of 64 Content Standard MAFS.3.NBT.1.2 Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addends and sums are less than or equal to 1,000. Assessment Limits Minuends, subtrahends, and differences are less than or equal to 1,000. Items may not require students to name specific properties. Equation Editor Item Types GRID Multiple Choice Multiselect Table Item No context Context Level: 2 Basic Application of Skills & Concepts Complexity Level Achievement Levels Level 2 Level 3 adds and subtracts within 1,000 when regrouping is not required Level 4 fluently adds and subtracts within fluently adds and subtracts within 1,000 using strategies and algorithms 1,000; explains the method used in finding a sum or difference based on place value, properties of operations, and/or the relationship between addition and subtraction Level 5
determines an error and shows the correct answer Page 44 of 64 Content Standard MAFS.3.MD.1.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.. Clocks may be analog or digital. Assessment Limits Digital clocks may not be used for items that require telling or writing time in isolation Equation Editor Item Types GRID Multiple Choice Multiselect Table Item No context Context Level: 2 Basic Application of Skills & Concepts Complexity Level Achievement Levels Level 2 Level 3 tells and writes time to the nearest minute solves one‐step word problems involving addition or subtraction of time intervals in minutes, including the use of a number line Level 4 solves one‐step word problems involving addition or subtraction of time intervals in minutes Level 5
solves two‐step real‐world problems involving addition and subtraction of time intervals in minutes Page 45 of 64 Content Standard MAFS.3.MD.1.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one‐step word problems involving masses or volumes that are given in the same units.. Items may not contain compound units such as cubic centimeters (cm3) or finding the geometric volume of a Assessment Limits container. Items may not require multiplicative comparison (e.g., “times as much/many”). Unit conversions are not allowed. Equation Editor Item Types GRID Multiple Choice Multiselect Allowable Context Complexity Level Level: 2 Basic Application of Skills & Concepts Achievement Levels Level 2 Level 3 measures liquid volumes and masses estimates liquid volume and mass of of objects using models and standard objects using standard units; solves units one‐step word problems involving any of the four operations Level 4 [intentionally left blank] Level 5
[intentionally left blank] Page 46 of 64 Teacher Academic Language 
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About (with reference to rounding and estimation, an answer that is not precise) Addend (the numbers that are added together in an addition equation, e.g., in 4 + 5, the numbers 4 and 5 are the addends) Capacity (the amount of liquid that a particular container can hold) Continuous (with reference to time as a continuous measurement) Endpoint10 (used with rounding on the number line; the numbers that mark the beginning and end of a given interval) Gram (g, unit of measure for weight) Interval (time passed or a segment on the number line) Halfway (with reference to a number line, the midpoint between two numbers, e.g., 5 is halfway between 0 and 10) Kilogram (kg, unit of measure for mass) Liquid volume (the space a liquid takes up) Liter (L, unit of measure for liquid volume) Milliliter (mL, unit of measure for liquid volume) Plot (locate and label a point on a number line) Point (a specific location on the number line) Reasonable (with reference to how plausible an answer is, e.g., “Is your answer reasonable?”) Round11 (estimate a number to the nearest 10 or 100 using place value) Second (a unit of time) Standard algorithm (for addition and subtraction) ≈ (symbol used to show that an answer is approximate) Familiar Terms and Symbols12 
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Analog clock (a clock that is not digital) Centimeter (cm, unit of measurement) Compose (change 10 smaller units for 1 of the next larger unit on the place value chart) Divide (e.g., 4 ÷ 2 = 2) Estimate (approximation of the value of a quantity or number) 10
Originally introduced in Grade 2, but treated as new vocabulary in this module. 11 Originally introduced in Grade 2, but treated as new vocabulary in this module. 12
These are terms and symbols students have used or seen previously. Page 47 of 64 Place Value and Problem Solving with Units of Measure OVERVIEW In this 25‐day module, students explore measurement using kilograms, grams, liters, milliliters, and intervals of time in minutes. Students begin by learning to tell and write time to the nearest minute using analog and digital clocks in Topic A (3.MD.1.1). They understand time as a continuous measurement through exploration with stopwatches, and use the number line, a continuous measurement model, as a tool for counting intervals of minutes within 1 hour (3.MD.1.1). Students see that an analog clock is a portion of the number line shaped into a circle. They use both the number line and clock to represent addition and subtraction problems involving intervals of minutes within 1 hour (3.MD.1.1). Introduced in Topic B, kilograms and grams are measured using digital and spring scales. Students use manipulatives to build a kilogram and then decompose it to explore the relationship between the size and weight of kilograms and grams (3.MD.1.2). An exploratory lesson relates metric weight and liquid volume measured in liters and milliliters, highlighting the coherence of metric measurement. Students practice measuring liquid volume using the vertical number line and a graduated beaker (3.MD.1.2). Building on the estimation skills with metric length gained in Grade 2, students in Grade 3 use kilograms, grams, liters, and milliliters to estimate the weights and liquid volumes of familiar objects. Finally, they use their estimates to reason about solutions to one‐step addition, subtraction, multiplication, and division word problems involving metric weight and liquid volume given in the same units (3.MD.1.2). Now more experienced with measurement and estimation using different units and tools, students further develop their skills by learning to round in Topic C (3.NBT.1.1). They measure and then use place value understandings and the number line as tools to round two‐, three‐, and four‐digit measurements to the nearest ten or hundred (3.NBT.1.1, 3.MD.1.1, 3.MD.1.2). Students measure and round to solve problems in Topics D and E (3.NBT.1.1, 3.MD.1.1, 3.MD.1.2). In these topics, they use estimations to test the reasonableness of sums and differences precisely calculated using standard algorithms. From their work with metric measurement, students have a deeper understanding of the composition and decomposition of units. They demonstrate this understanding in every step of the addition and subtraction algorithms with two‐ and three‐digit numbers, as 10 units are changed for 1 larger unit or 1 larger unit is changed for 10 smaller units (3.NBT.1.2). Both topics end in problem solving involving metric units or intervals of time. Students round to estimate, and then calculate precisely using the standard algorithm to add or subtract two‐ and three‐digit measurements given in the same units (3.NBT.1.1, 3.NBT.1.2, 3.MD.1.1, 3.MD.1.2). Page 48 of 64 Module Specific Notes: Resources Resource on how to use the Sprints to build fluency https://www.engageny.org/resource/nti‐
november‐2012‐rigor‐breakdown‐sprints‐fluency‐
in‐action Grade 3 Math: Subtraction with renaming 3.NBT.2 https://www.engageny.org/resource/nti‐
november‐2012‐session‐1‐a‐story‐of‐units‐
subtraction‐with‐renaming Math Studio Talk: Common Core Instruction for 3.NBT and 3.NF https://www.engageny.org/resource/math‐studio‐
talk‐common‐core‐instruction‐3nbt‐and‐3nf Module Materials Personal white boards Class set dry erase markers, erasers Counters (18 per student) Classroom clock (accurate and in working condition) Class set analog clocks Class set of centimeter rulers 1 kg weight 1 kg benchmark bag of beans Digital metric scales (one per group) Pan balance Rice (at least 1kg) Pinto Beans Popcorn kern Quart‐size sealable bags Gallon‐size sealable bags Metric spring scales (one per group) Set of weights in one gram, ten gram, and hundred gram Beakers (liter and milliliter) Empty 2‐liter bottles 12 clear plastic cups Dropper Measuring containers (cup, pint, quart, gallon) One pitcher per group 1 permanent marker Digit cards (for place value) Bathroom scale Milliliter beakers Meter stick Blank paper New pencil Water Place value blocks Additional Aligned Activities EnVisionMATH Center Activities: Topic 12‐ 12.1 * ** Clip and Cover Topic 12‐ 12.4 * ** Clip and Cover Topic 12‐ 12.5 * ** Toss and Talk Topic 15‐ 15‐3 * ** Teamwork Math Investigations Center Activities: Page 49 of 64 Standards Topics and Objectives 3.NBT.2 3.MD.1 A Time Measurement and Problem Solving Lesson 1: Explore time as a continuous measurement using a stopwatch. Lesson 1 was omitted because it is not included in the Test Item Specifications. Lesson 2: Relate skip‐counting by fives on the clock and telling time to a continuous measurement model, the number line. Lesson 3: Count by fives and ones on the number line as a strategy to tell time to the nearest minute on the clock. Lesson 4: Solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock. enVision 12‐5: Solve problems involving elapsed time beyond 1 hour. (This lesson has been added for experience with elapsed time beyond one hour.) Lesson 5: 3.NBT.2 3.MD.2 Solve word problems involving time intervals within 1 hour by adding and subtracting on the number line. B Measuring Weight and Liquid Volume in Metric Units Lesson 6: Build and decompose a kilogram to reason about the size and weight of 1 kilogram, 100 grams, 10 grams, and 1 gram. Lesson 7: Develop estimation strategies by reasoning about the weight in kilograms of a series of familiar objects to establish mental benchmark measures. Lesson 8: Solve one‐step word problems involving metric weights within 100 and estimate to reason about solutions. Lesson 9: Decompose a liter to reason about the size of 1 liter, 100 milliliters, 10 milliliters, and 1 milliliter. Lesson 10: Estimate and measure liquid volume in liters and milliliters using the vertical number line. Lesson 11: Solve mixed word problems involving all four operations with grams, kilograms, liters, and milliliters given in the same units. Mid‐Module Assessment: Topics A–B 3.NBT.1 3.MD.1 3.MD.2 C Rounding to the Nearest Ten and Hundred Lesson 12: Round two‐digit measurements to the nearest ten on the vertical number line. Lesson 13: Lesson 14: 3.NBT.2 3.NBT.1 Round two‐ and three‐digit numbers to the nearest ten on the vertical number line. Round to the nearest hundred on the vertical number line. D Two‐ and Three‐Digit Measurement Addition Using the Standard Algorithm Lesson 15‐16 Add measurements using the standard algorithm to compose larger units once and twice. (Lessons 15 and 16 have been Page 50 of 64 combined. They have the same objective composing larger numbers once and twice)
3.MD.1 3.MD.2 Lesson 17: Estimate sums by rounding and apply to solve measurement word problems. Lesson 17 has been omitted in an effort to introduce all concepts prior to FSA. Consider teaching this lesson on a flex day). 3.NBT.2 3.NBT.1 3.MD.1 3.MD.2 E Two‐ and Three‐Digit Measurement Subtraction Using the Standard Algorithm Lesson 18: Decompose once to subtract measurements including three‐digit minuends with zeros in the tens or ones place. Lesson 19: Decompose twice to subtract measurements including three‐digit minuends with zeros in the tens and ones places. End‐of‐Module Assessment: Topics A–E Page 51 of 64 Topic A: Time Measurement and Problem Solving
Lesson 1 is an exploration in which students use stopwatches to measure time as a physical quantity. They might, for example, time how long it takes to write the fact 7 × 8 = 56 forty times or measure how long it takes to write numbers from 0 to 100. Students time their own segments as they run a relay, exploring the continuity of time by contextualizing their small segment within the number of minutes it takes the whole team to run. Lesson 2 builds students’ understanding of time as a continuous unit of measurement. This lesson draws upon the Grade 2 skill of telling time to the nearest 5 minutes (2.MD.3.7) and the multiplication learned in Module 1 as students relate skip‐counting by fives and telling time to the number line. They learn to draw the model, labeling hours as endpoints and multiples of 5 (shown below). Through this work, students recognize the analog clock as a portion of the number line shaped into a circle and, from this point on, use the number line as a tool for modeling and solving problems. Lesson 3 increases students’ level of precision as they read and write time to the nearest minute. Students draw number line models that represent the minutes between multiples of 5 (number line model shown below). They quickly learn to apply the strategy of counting by fives and some ones to read time to the nearest minute on the clock. In preparation for Lessons 4 and 5, students add minutes by counting on the number line and clock. For example, they might use the count by fives and some ones strategy to locate 17 minutes and then keep counting to find 4 minutes more. In Lesson 4, students begin measuring time intervals in minutes within 1 hour to solve word problems. They reinforce their understanding of time as a continuous unit of measurement by counting forward and backward using the number line and the clock. They might solve, for example, a problem such as, “Beth leaves her house at 8:05 a.m. and arrives at school at 8:27 a.m. How many minutes does Beth spend traveling to school?” Lesson 5 carries problem solving with time a step further. Students measure minute intervals and then add and subtract the intervals to solve problems. Students might solve problems such as, “I practiced the piano for 25 minutes and the clarinet for 30 minutes. How long did I spend practicing my instruments?” Calculations with time in this lesson—and throughout Grade 3—never cross over an hour or involve students converting between hours and minutes. Page 52 of 64 Date/ Day of the school year Approx. Date: 9/21/16 Day: 27 Approx. Date: 9/22/16 Day: 28 Objective/ Essential Question OBJ: Students will relate skip‐counting by fives on the clock and telling time to a continuous measurement model—the number line. EQ: How do I relate skip‐
counting by fives on the clock and telling time to the number line? OBJ: Students will count by fives and one on the number line as a strategy to tell time to nearest minute on the clock. EQ: What strategies can I use to tell time to the nearest minute on the clock? Math Florida Standards/ Mathematical Practice Target 3.MD.1.1 3.NBT.1.2 Embedded 3.OA.1.1 Fluency 3.OA.1 2.MD.7 3.MD.1 Academic Language analog
interval continuous Lesson Module 2
Topic A Lesson 2: Relate skip‐counting by fives on the clock and telling time to a continuous measurement model, the number line. Materials Needed For Lesson: Classroom clock in working order Personal white boards Class set of centimeter rulers Analog clock Assessment / Performance Tasks Mathematical Practices MP.4 Notes: Lesson 1 was omitted because it is not included in the Test Item Specifications. Reference lesson 1 concept development to activate background knowledge about length of 1 minute and explore time as a continuous measurement. analog
Module 2
Target interval Topic A 3.MD.1.1 Lesson 3: Count by fives and ones on the number line as 3.NBT.1.2 a strategy to tell time to the nearest minute on the clock. Embedded 3.OA.1.1 Materials Needed For Lesson: Fluency Personal white boards Analog clock 2.MD.7 Class set of centimeter rulers 3.MD.1 3.MD.1 3.OA.1 Mathematical Practices MP.6 Notes: Page 53 of 64 Approx. Date: 9/23/16 Day: 29 Approx. Date: 9/26/16 Day: 30 OBJ: Students will solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock. EQ: How do I solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock? OBJ: Students will solve problems involving elapsed time. EQ: How do I solve problems involving elapsed time? Target 3.MD.1.1 3.NBT.1.2 Embedded Fluency 3.OA.1 3.MD.1 3.MD.1 Module 2
Topic A Lesson 4: Solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock. Materials Needed For Lesson: Demonstration analog clock Personal white board Number line template Clock (Lesson 3 Template) Mathematical Practices MP.6 Notes: Target 3.MD.1.1 3.NBT.1.2 Embedded 3.OA.1.1 Fluency Mathematical Practices MP.4 interval
enVision
Topic 12 Lesson 12‐5 I Do: The Pose the Problem portion on TE Topic 12 pg. 312B Guided Practice: Number 17 on TE Topic 12 pg. 313 They Do: Numbers 5, 6, 16, 21 Exit Ticket: Quick Check Review for Topic 12, Lesson 4 Materials Needed For Lesson: Personal white boards Class set of analog clocks Notes: This lesson has been added for experience with elapsed time beyond one hour. Approx. Date: 9/27/16 Day: 31 OBJ: Students will solve word problems involving time intervals within beyond an hour by adding and Target 3.MD.1.1 3.NBT.1.2 Embedded 3.OA.1.1 Fluency Module 2
Topic A Lesson 5: Solve word problems involving time intervals within 1 hour by adding and subtracting on the number line. Materials Needed For Lesson: Personal white boards Do You Have a Minute? Performance task is located under attachments on link above. Page 54 of 64 subtracting on the number line. EQ: How do I solve word problems involving intervals of time? 3.OA.1 3.MD.1 3.MD.1 Class set of analog clocks. Mathematical Practices Notes: Although the lesson was drafted to stay within the hour, adjust Lesson 5 to include elapsed time problems beyond 60 minutes. Page 55 of 64 Topic B: Measuring Weight and Liquid Volume in Metric Units
Lessons 6 and 7 introduce students to metric weight measured in kilograms and grams. Students learn to use digital scales as they explore these weights. They begin by holding a kilogram weight to get a sense of its weight. Then, groups of students work with scales to add rice to clear plastic zippered bags until the bags reach a weight of 1 kilogram. Once the bags reach that weight, students decompose a kilogram using ten‐frames. They understand the quantity within 1 square of the ten‐frame as an estimation of 100 grams. Upon that square they overlay another ten‐frame, zooming in to estimate 10 grams. Overlaying once more leads to 1 gram. Students relate the decomposition of a kilogram to place value and the base ten system. Throughout this two‐day exploration, students reason about the size and weight of kilograms and grams in relation to one another without moving into the abstract world of conversion. They perceive the relationship between kilograms and grams as analogous to 1 meter decomposed into 100 centimeters. They build on Grade 2 estimation skills with centimeters and meters (2.MD.1.3) using metric weight. Students use scales to measure a variety of objects and learn to estimate new weights using knowledge of previously measured items. Their work with estimation in Topic B lays a foundation for rounding to estimate in the second half of the module. In Lesson 8, students use scales to measure the weight of objects precisely, and then use those measurements to solve one‐step word problems with like units. Word problems require students to add, subtract, multiply, and divide. Students apply estimation skills from Lesson 7 to reason about their solutions. Notice that these lessons refer to metric weight rather than mass. This choice was made based on the K–5 Geometric Measurement progressions document that accompanies the CCSSM, which suggests that elementary school students may treat mass units as weight units.13 Technically these are not equivalent, but the units can be used side by side as long as the object being measured stays on earth.14 If students have already been introduced to the distinction between weight and mass, it may be appropriate to use the word mass rather than weight. In Lessons 9 and 10, students measure liquid volume in liters using beakers and the vertical number line. This experience lends itself to previewing the concept and language of rounding: Students might estimate, for example, a given quantity as halfway between 1 and 2 or nearer to 2. Students use small containers to decompose 1 liter and reason about its size. This lays a conceptual foundation for Grade 4 work with milliliters and the multiplicative relationship of metric measurement units (4.MD.1.1). In these lessons, students solve one‐step word problems with like units using all four operations. Topic B culminates in solving one‐step word problems with like units. Lesson 11 presents students with mixed practice, requiring students to add, subtract, multiply, and divide to find solutions to problems involving grams, kilograms, liters, and milliliters.
Math Florida Date/ Objective/ Standards/ Assessment / Performance Day of the Academic Language Lesson Essential Question Mathematical Tasks school year Practice Approx. OBJ: Target kilogram
Module 2
Date: Students will build and 3.MD.1.2 gram Topic B 9/28/16 decompose a kilogram metric Lesson 6: Build and decompose a kilogram to reason to reason about the Embedded units about the size and weight of 1 kilogram, 100 grams, 10 grams, and 1 gram. Day: 32 size in comparison to 3.NBT.1.2 other metric units. Fluency Materials Needed For Lesson: 3.MD.1 Personal white boards 1 kg weight 13Page 2 of the K–5, Geometric Measurement progression document reads, “The Standards do not differentiate between weight and mass.” 14
Page 2 of the K–5, Geometric Measurement progression document reads, “…mass is the amount of matter in an object. Weight is the force exerted on the body by gravity. On the earth’s surface, the distinction is not important (on the moon, an object would have the same mass, would weight [sic] less due to the lower gravity).” To keep focused, these lessons purposefully do not introduce the distinction between weight and mass because it is not needed at this level. Page 56 of 64 EQ: Mathematical How do I reason about Practices the size of a kilogram? MP.6 Approx. Date: 9/29/16 Day: 33 Approx. Date: 9/30/16 Day: 34 OBJ: Students will develop estimation strategies by reasoning about the weight in kilograms of familiar objects to establish benchmark measures. EQ: What strategies could I use to estimate the weight of an object? OBJ: Students will solve one‐step word problems involving metric weights within 100. Students will estimate to reason about solutions. EQ: How do I solve one‐
step word problems involving metric weights within 100? What strategies do I use to reason about solutions? (Answer: estimation) 1 kg benchmark bag of beans
Digital metric scale Pan balance Rice Gallon‐size sealable bags Notes: Target 3.MD.1.2 Embedded 3.OA.1.1 Fluency 3.OA.1 3.MD.2 3.MD.2 Mathematical Practices MP.4 Notes: Module 2
Topic B Lesson 7: Develop estimation strategies by reasoning about the weight in kilograms of a series of familiar objects to establish mental benchmark measures. Materials Needed For Lesson: Personal white boards Digital metric scale (in grams) Metric spring scale Set of weights in one gram, ten gram, and hundred gram kilogram
gram benchmark estimation metric units reason Module 2
Topic B Lesson 8: Solve one‐step word problems involving metric weights within 100 and estimate to reason about solutions. Materials Needed For Lesson: Personal white boards Digital metric scale (in grams) Metric spring scale 1 kg bag of rice Baggie of 80 pinto beans per pair of students Baggie of 30 popcorn kernels per pair of students Mathematical Practices Notes: Target 3.MD.1.2 Embedded 3.OA.1.1 3.OA.1.3 3.OA.4.8 Fluency 3.MD.2 3.MD.2 3.OA.1 kilogram
gram benchmark estimation metric units Page 57 of 64 Approx. Date: 10/3/16 Day: 35 Approx. Date: 10/4/16 Day: 36 Approx. Date: 10/5/16 Day: 37 OBJ: Students will decompose a liter to reason about the size of one liter, 100 milliliters, ten milliliters, and one milliliter. EQ: How do I reason about the size of liters and milliliters? Target 3.MD.1.2 Embedded Fluency 3.MD.2 Mathematical Practices Notes: OBJ: Target Students will estimate 3.MD.1.2 and measure liquid volume in liters and Embedded milliliters using the 3.OA.1.1 vertical number line. Fluency EQ: 3.MD.2 How do I estimate and 3.MD.2 measure liquid 3.OA.1 volume? Mathematical Practices MP.6 Notes: OBJ: Target Students will solve 3. MD.1.2 mixed word problems involving all four Embedded operations with 3.NBT.1.1 grams, kilograms, 3.NBT.1.3 liters, and milliliters. 3.OA.1.3 3.OA.4.8 EQ: How do I solve mixed Fluency word problems 3.NBT.3 capacity
liter liquid volume milliliter Module 2
Topic B Lesson 9: Decompose a liter to reason about the size of 1 liter, 100 milliliters, 10 milliliters, and 1 milliliter. Materials Needed For Lesson: Personal white boards Beaker Empty 2‐liter bottle 12 clear plastic cups Dropper Measuring containers (cup, pint, quart, gallon) capacity
liter liquid volume milliliter Module 2
Topic B Lesson 10: Estimate and measure liquid volume in liters and milliliters using the vertical number line. Materials Needed For Lesson: Personal white boards I liter beaker One pitcher per group One empty 2‐liter bottle per group 1 clear plastic cup per group 1 permanent marker capacity
liter liquid volume milliliter Module 2
Topic B Lesson 11: Solve mixed word problems involving all four operations with grams, kilograms, liters, and milliliters given in the same units. Materials Needed For Lesson: Personal white boards Digit cards (for place value) Bathroom scale Page 58 of 64 involving all four operations with grams, kilograms, liters, and milliliters? Approx. Date: 10/6/16 Day: 38 3.NBT.1 3.MD.1 Mathematical Practices MP.7 Notes: OBJ: Target Students will 3.MD.1.1 complete Mid‐Module 3.MD.1.2 Assessment for Module 2. Embedded 3.NBT1.1 EQ: 3.NBT.1.2 How do I solve mixed word problems Fluency involving all four operations with Mathematical grams, kilograms, Practices liters, and milliliters? Notes: Spring scales (one per group)
Digital scales (one per group) Milliliter beakers Module 2 Mid‐Module Assessment
Module 2 Mid‐Module Assessment Page 59 of 64 Topic C: Rounding to the Nearest Ten and Hundred
Topic C builds on students’ Grade 2 work with comparing numbers according to the value of digits in the hundreds, tens, and ones places (2.NBT.1.4). Lesson 12 formally introduces rounding two‐digit numbers to the nearest ten. Rounding to the leftmost unit usually presents the least challenging type of estimate for students, and so here the sequence begins. Students measure two‐digit intervals of minutes and metric measurements, and then use place value understanding to round. They understand that when moving to the right across the places in a number, the digits represent smaller units. Intervals of minutes and metric measurements provide natural contexts for estimation. The number line, presented vertically, provides a new perspective on a familiar tool. Students continue to use the vertical number line in Lessons 13 and 14. Their confidence with this tool by the end of Topic C lays the foundation for further work in Grades 4 and 5 (4.NBT.1.3, 5.NBT.1.4). In Lesson 13, the inclusion of rounding three‐digit numbers to the nearest ten adds new complexity to the previous day’s learning. Lesson 14 concludes the module as students round three‐ and four‐digit numbers to the nearest hundred. Date/ Day of the school year Approx. Date: 10/7/16 Day: 39 Math Florida Standards/ Mathematical Practice OBJ: Target Students will round 3.NBT.1.1 two‐digit measurements to the Embedded nearest ten on the 3.MD.1.2 vertical number line. Fluency EQ: 3.MD.1.1 How do I round two‐
3.NBT.1.3 digit measurements to 3.NBT.1.1 the nearest ten? Mathematical Practices MP.6 Objective/ Essential Question Academic Language round
vertical half‐way tick marks end points ones tens about number line Lesson Module 2
Topic C Lesson 12: Round two‐digit measurements to the nearest ten on the vertical number line. Materials Needed For Lesson: Personal white boards 100 milliliter beaker Water 4 bags of rice (premeasured at 4 different weights within 100 ml) 4 containers of water (pre‐measured with 4 different volumes within 100 ml) Ruler Meter stick Blank paper New pencil Digital scale Gram weights Demonstration clock Classroom wall clock Assessment / Performance Tasks Notes: Prior to teaching this lesson, please read the notes concerning the Notes on Materials embedded in the lesson. Page 60 of 64 Approx. Date: 10/10/16 Day: 40 Approx. Date: 10/11/16 Day: 41 about Module 2
Target vertical Topic C 3.NBT.1.1 number line Lesson 13: Round two‐ and three‐digit numbers to the round nearest ten on the vertical number line. Embedded tens 3.MD.1.1 ones 3.MD.1.2 tick marks Materials Needed For Lesson: half‐way Personal white boards Fluency end points Digit cards (for place value) 3.NBT.1.1 approximate 3.NBT.1.3 3.OA.1.1 Mathematical Practices MP.6 Notes: Prior to teaching the lesson, please read notes on symbols embedded in the lesson. OBJ: Module 2
Target hundreds
Students will round to 3.NBT.1.1 Topic C tick marks the nearest hundred Lesson 14: Round to the nearest hundred on the estimate on the vertical Embedded vertical number line vertical number line. half‐way number line. 3.MD.1.2 round nearest Materials Needed For Lesson: EQ: Fluency end points Personal white boards How do I use the 3.NBT.1.1 Unlabeled place value chart template vertical number line to 3.NBT.1.3 Digit cards (for place value) round to the nearest Place value blocks hundred? Mathematical Practices MP.6 OBJ: Students will round two and three‐digit numbers to the nearest ten on the vertical number line. EQ: How do I round two‐
digit and three‐digit numbers to the nearest ten? Notes: Page 61 of 64 Topic D: Two‐and Three‐Digit Measurement Addition Using the Standard Algorithm
In Topic D, students revisit the standard algorithm for addition, which was first introduced in Grade 2 (2.NBT.2.7). In this topic, they add two‐ and three‐digit metric measurements and intervals of minutes within 1 hour. Lesson 15 guides students to apply the place value concepts they practiced with rounding to model composing larger units once on the place value chart. They use the words bundle and rename as they add like base ten units, working across the numbers unit by unit (ones with ones, tens with tens, hundreds with hundreds). As the lesson progresses, students transition away from modeling on the place value chart and move toward using the standard algorithm. Lesson 16 adds complexity to the previous day’s learning by presenting problems that require students to compose larger units twice. Again, students begin by modeling on the place value chart, this time renaming both the ones and tens places. Lesson 17 culminates the topic with applying addition involving renaming to solving measurement word problems. Students draw tape diagrams to model problems. They round to estimate the sums of measurements and then solve problems using the standard algorithm. By comparing their estimates with precise calculations, students assess the reasonableness of their solutions. Date/ Day of the school year Approx. Date: 10/12/16 Day: 42 Math Florida Standards/ Assessment / Performance Academic Language Lesson Mathematical Tasks Practice OBJ: Module 2
Target horizontal
Students will add Topic D 3.NBT.1.2 vertical measurements using Lesson 15: Add measurements using the standard rename (regroup) tens the standard algorithm to compose larger units once. Embedded ones algorithm to compose 3.NBT.1.1 standard algorithm larger units through 3.MD.1.2 place value the tens and hundreds Materials Needed For Lesson: place. Personal white boards Fluency 2 beakers 3.MD.1.2 EQ: Water 3.NBT.1.1 How do I will add Unlabeled place value chart template (Lesson 14) measurements using Place value blocks Mathematical the standard Practices algorithm? MP.7 Notes: Lesson 15 and 16 were combined due to same objective. Lesson 15 requires renaming/regrouping ONCE, but lesson 16 requires renaming/regrouping TWICE. Include problems from Lesson 16 problem set that require students to rename/regroup twice. Objective/ Essential Question Page 62 of 64 Topic E: Two‐ and Three‐Digit Measurement Subtraction Using the Standard Algorithm Students work with the standard algorithm for subtraction in Topic E. As in Topic D, they use two‐ and three‐digit metric measurements and intervals of minutes within 1 hour to subtract. The sequence of complexity that builds from Lessons 18–20 mirrors the progression used for teaching addition. In Lesson 18, students begin by decomposing once to subtract, modeling their work on the place value chart. They use three‐digit minuends that may contain zeros in the tens or ones place. Students move away from the magnifying glass method used in Grade 2 (see Grade 2, Module 4) but continue to prepare numbers for subtraction by decomposing all necessary digits before performing the operation. By the end of the lesson, they are less reliant on the model of the place value chart and practice using the algorithm with greater confidence. Lesson 19 adds the complexity of decomposing twice to subtract. Minuends may include numbers that contain zeros in the tens and ones places. Lesson 20 consolidates the learning from the two prior lessons by engaging students in problem solving with measurements using the subtraction algorithm. As in Lesson 17, students draw to model problems, round to estimate differences, and use the algorithm to subtract precisely. They compare estimates with solutions and assess the reasonableness of their answers. Lesson 21 synthesizes the skills learned in the second half of the module. Students round to estimate the sums and differences of measurements in word problem contexts. They draw to model problems and apply the algorithms to solve each case introduced in Topics D and E precisely. As in previous lessons, students use their estimates to reason about their solutions. Page 63 of 64 Date/ Day of the school year Objective/ Essential Question Approx. Date: 10/13/16 Day: 43 OBJ: Students will decompose to subtract three‐digit measurements with a zero in the tens OR ones place. EQ: How do I decompose to subtract three‐digit measurements with a zero in the tens OR ones place? Approx. Date: 10/14/16 Day: 44 OBJ: Students will decompose to subtract three‐digit measurements with a zero in the tens AND ones place. EQ: How do I decompose to subtract three‐digit measurements with a zero in the tens AND ones place? Math Florida Standards/ Assessment / Performance Academic Language Lesson Mathematical Tasks Practice vertical
Target Module 2
place value 3.NBT.1.2 Topic E ones Lesson 18: Decompose once to subtract measurements tens Embedded including three‐digit minuends with zeros in the tens or hundreds 3.NBT.1.1 ones place. bundle 3.MD.1.1 unbundle (regroup) 3.MD.1.2 three‐digit Materials Needed For Lesson: minuends Fluency Personal white boards 3.OA.1.1 Unlabeled place value chart template (Lesson 14) 3.NBT.1.2 Mathematical Practices MP.2 Notes: Lesson 17 was omitted in an effort to introduce all concepts prior to FSA. Consider using this lesson on a flex day. decompose
Module 2
Target standard algorithm Topic E 3.NBT.1.2 expression Lesson 19: Decompose twice to subtract measurements unbundle (regroup) including three‐digit minuends with zeros in the tens Embedded and ones places. 3.NBT.1.1 3.MD.1.2 Materials Needed For Lesson: Fluency Personal white boards 3.NBT.1.1 3.NBT.1.2 3.MD.1.1 Mathematical Practices Notes: Read notes on multiple means of representation embedded in this lesson. Page 64 of 64