4th Grade Mathematics Curriculum
Course Description:
The 4th Grade Mathematics course
Course Essential Questions:
TBD
4th Grade State Assessment Information:
Approximate Percentage of Questions Assessing Each Strand
Strand:
Percent:
Time allotted:
Number Sense and Operations:
45%
(11 weeks)
Algebra:
14%
(2 weeks)
Geometry:
12%
(1 week)
Measurement:
17%
(4 weeks)
Probability and Statistics:
12%
(3 weeks)
Units:
(Unit 2, 3, 4, 5, 6,)
(Unit 2, 3, 5, 6)
(Unit 7)
(Unit 8)
(Unit 1)
Additional Information:
4th Grade Mathematical Language – to be included
Post-March 3rd Grade Performance Indicators
The 3rd Grade state performance indicators below are denoted by the state as post-test.
Therefore, students will be responsible for this knowledge of the 4th Grade assessment.
Attention should be given to them during the normal course of instruction or during review.
3.N.14 Explore equivalent fractions (1/2, 1/3, 1/4).
3.N.15 Compare and order unit fractions (1/2, 1/3, 1/4) and find their approximate locations on a
number line
3.N.19 Develop fluency with single-digit multiplication facts Assess Post- March for above 5 x
10. In context
3.N.20 Use a variety of strategies to solve multiplication problems with factors up to 12 x 12
3.N.22 Demonstrate fluency and apply single-digit division facts Assess Post- March for above
50 divided by 10 and grade 3 for below 50 divided by 10. In context
3.N.23 Use tables, patterns, halving, and manipulatives to provide meaning for division
3.N.25 Estimate numbers up to 500 Post-March for numbers past 200
3.N.26 Recognize real world situations in which an estimate (rounding) is more appropriate
3.A.1 Use the symbols <, >, = (with and without the use of a number line) to compare whole
numbers and unit fractions (1/2,1/3,1/4,1/5,1/6, and 1/10) Post-March for fractions
3.G.2 Identify congruent and similar figures
3.S.1 Formulate questions about themselves and their surroundings
3.S.2 Collect data using observation and surveys, and record appropriately
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4th Grade Local Math Standards
Numbering Key: Local.Grade level.Mathematics strand*.standard #
e.g. L.4.N.5 (L = local; 4 = 4th Grade; N = Number Sense and Operations; 5 = 5th standard)
Number and Operations
L.4.N.1
Representation
and Notation
L.4.N.2
L.4.N.3
Place Value
Number Order
L.4.N.4
Addition and
Subtraction
L.4.N.5
Estimation
L.4.N.6
Number
Theory
L.4.N.7
Properties and
Laws
L.4.N.8
Computation
and Facts
L.4.N.9
Multiplication
and Division
L.4.N.10
Fractions
L.4.N.11
Decimals
Algebra
L.4.A.1
L.4.A.2
Geometry
L.4.G.1
Read and write whole numbers 0 to 10,000; read and write fractions (see
L.4.N.10); read and write decimals to hundredths place (see L.4.N.11); convert
between fractions and decimals (to hundredths).
Understand numbers including place value from hundredths to ten-thousands.
Compare and order whole numbers to 10,000; compare and order unit fractions or
proper fractions with common denominators (halves thru sixths and tenths);
compare and order decimals to hundredths; use the symbols <, >, =, and ≠.
Add and subtract 5-digit whole numbers and understand that addition and
subtraction are inverse operations; add and subtract fractions (see L.4.N.10) and
decimals (see L.4.N.11)
Develop estimation strategies and skills (including rounding to nearest 10, 100, or
1,000); estimate answers before solving problems and compare estimate with
outcome to determine the reasonableness of results.
Count by 1000's; identify when multiplication results in even versus odd numbers
Recognize patterns for products and quotients including fact families; use and
explain the associative property of multiplication (e.g. (2 * 3) * 4 = 2 * (3 * 4))
Master multiplication and division facts with products and dividends up to 144;
develop fluency multiplying and dividing by multiples of 10 and 100 up to 1,000
(e.g. 20 * 300).
Multiply two-digit by one- and two-digit numbers; divide two-digit by one-digit
numbers (with and without remainders); recognize multiplication and division as
inverse operations and as repeated addition or subtraction, respectively.
Develop understanding of fractions (including as division of whole numbers);
recognize and find equivalent fractions (halves thru sixths, and tenths); compare
and order (see L.4.N.3) fractions; add and subtract proper fractions with common
denominators.
Develop understanding of decimals (to hundredths place) as part of a whole; read,
write, and order (see L.4.N.3) decimals to hundredths (connect to money
application); add and subtract decimals to hundredths place.
Recognize, describe, extend, and create numeric and geometric patterns; analyze a
Patterns and
Representations numeric input and output pattern or function and state the rule (e.g. each number is
Solving
Equations and
Inequalities
Shapes and
Figures
L.4.G.4
Points, Lines,
and Angles
L.4.G.5
Perimeter,
Area, and
Volume
multiplied by 3)
Express relationships as open sentences; find a value or values that make an open
sentence true including sentences containing the symbols < or >.
Identify and name polygons (triangle, quadrilateral, pentagon, hexagon, octagon)
connecting names to number of sides; define and identify parts of threedimensional shapes (vertices, faces, edges).
Draw and identify points, line segments and rays; draw and identify intersecting,
perpendicular, and parallel lines; draw angles and classify as acute, right, obtuse,
or straight.
Find the perimeter of polygons given the lengths of its sides; find the area of a
rectangle by counting squares
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Measurement
L.4.M.1
Time
L.4.M.2
Length
L.4.M.3
L.4.M.4
Money
Mass
L.4.M.5
Volume
Statistics and Probability
L.4.S.1
Collect and
L.4.S.2
Display Data
Analyze Data
Problem Solving
L.4.PS.1
Organization
L.4.PS.2
Strategies
L.4.PS.3
Reflection
Reasoning and Proof
L.4.RP.1
Communication
L.4.CM.1
Connections
L.4.CN.1
Representations
L.4.Rep.1
Calculate elapsed time in hours and half hours (not crossing A.M. or P.M) and in
days and weeks (using a calendar)
Estimate, measure (using appropriate tools and units (i.e. 1/4 inches and whole
centimeters and meters)), compare, and order the lengths (heights) of objects;
know and understand equivalent standard units: 12 inches = 1 foot, 3 feet = 1
yard).
Determine an amount of change in dollars and cents.
Estimate, measure (grams and kilograms), and compare the mass of objects using
appropriate tools.
Estimate, measure (milliliters and liters), and compare the volume (capacity) of
objects using appropriate tools.
Collect (using observations, surveys, and experiments), record, and display realworld data with tables and graphs (e.g. pictographs, bar graphs).
Read and interpret data from displays (e.g. line graphs); draw conclusions and
make predictions from data or graphs.
Analyze situations (identify the problem, identify needed information, find
relationships, observe patterns, and generate possible strategies) and organize work
to solve problems (e.g. use Auburn Problem Solving Process).
Solve problems using a variety of strategies and representations (e.g. modeling
with manipulatives, drawing pictures or diagrams, making a list or chart, and
process of elimination).
Estimate possible solutions; examine solution to ensure it is reasonable in context
of problem; compare solution to original estimate; verify results.
Make conjectures; support (or refute) a mathematical statement or conjecture as
true or false including the use of (counter)examples and explain reasoning; support
mathematical ideas verbally, numerically, algebraically, pictorally, and in writing.
Decode and comprehend mathematics expressed verbally and in writing; clearly
and coherently communicate mathematical thinking verbally, pictorally,
numerically and in writing using appropriate mathematical vocabulary and
symbols; organize and accurately label work.
Recognize and use connections among branches of mathematics and real life (e.g.
estimate and represent the number of apples in a tree, determine the number of
buses required for a field trip, use a multiplication grid to solve odd and even
number problems)
Represent mathematical ideas in a variety of ways (verbally, in writing, pictorally,
numerically, algebraically, or with physical objects); switch among different
representations; investigate similarities and differences between representations.
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Math 4 Unit Sequence and Timeline:
Unit 1
Length:
Timeframe:
Graphing and Facts Review (D.1, D.2)
~ 3 weeks
Start of September to late September
Unit 2
Length:
Timeframe:
Place Value (N.1, N.2, N.3, N.5, N.6)
~ 3 weeks
Late September to Mid-October
Unit 3
Length:
Timeframe:
Adding and Subtracting Whole Numbers (N.4, A.1,A.2)
~ 3 weeks
Late October to Mid-November
Unit 4
Length:
Timeframe:
Time and Money (M.1, M.3)
~ 3 weeks
Mid-November to Mid-December
Unit 5
Length:
Timeframe:
Multiplication (N.5, N.6, N.7, N.8, N.9, A.1, A.2)
~ 3 weeks
Mid-December to Early January
Unit 6
Length:
Timeframe:
Division (N.7, N.8, N.9)
~ 3 weeks
Early January to Late January
Unit 7
Length:
Timeframe:
Geometry (G.1, G.4, G.5)
~ 2 weeks
Late January to Mid-February
Unit 8
Length:
Timeframe:
Measurement (M.2, M.4, M.5)
~ 2 weeks
February
State Assessment Review and Administration
Length:
~ 2 weeks
Timeframe: February 27 to March 10 (State Assessment: 3/8, 3/9, and 3/10)
Unit 9
Length:
Timeframe:
Fractions (N.1, N.3, N.10)
~ 3 weeks
Mid-March to Late March
Unit 10
Length:
Time frame:
Decimals (N.1, N.3, N.11)
~ 3 weeks
Early April to Late April
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Unit 11
Length:
Timeframe:
Geometry (G.4)
~ 2 weeks
Early May to Mid-May
Unit 12
Length:
Timeframe:
Multiplication of 2 Digit Factors (N.5, N.7, N.8, N.9)
~ 3 weeks
Mid-May to Early June
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Unit 1
Graphing and Facts Review (D.1, D.2)
Length:
~ 3 weeks
Timeframe: Start of September to late September
State Standards (Shaded statements are identified as Post-March Indicators):
4.S.2
Collect data using observations, surveys, and experiments and record appropriately
4.S.3
Represent data using tables, bar graphs, and pictographs
4.S.4
Read and interpret line graphs
4.S.5
Develop and make predictions that are based on data
4.S.6
Formulate conclusions and make predictions from graphs
Local Standards (Stricken text is covered in a different unit):
L.4.S.1
Collect (using observations, surveys, and experiments), record, and display real-world
data with tables and graphs (e.g. pictographs, bar graphs).
L.4.S.2
Read and interpret data from displays (e.g. line graphs); draw conclusions and make
predictions from data or graphs.
Big Ideas:
Graphs and tables can be used to represent data.
Essential Questions:
What is the difference between a bar graph and pictograph?
When given a table of data, why do we graph it?
What are the benefits of knowing your basic facts?
Prior Knowledge:
To identify and read pictographs and bar graphs
To display data on a table
Knowledge of the terms key and scale
Knowledge of problem solving steps
Unit Objectives:
To represent data on a table
To represent data on a bar graph, using an appropriate scale and labels
To represent data on a pictograph, using an appropriate key and symbols
To formulate conclusions and make predictions from graphs (i.e. pictographs, bar and
line graphs)
To review addition and subtraction, through computation problems and problem solving.
Resources:
SFAW Math, pages 2, 3, 10-13, 20-27, 34, 35
Review Template:
Addition with regrouping
Solve: 14 + 88
AECSD 4th Grade Mathematics.doc
Solve: 462 + 79
Solve: 188 + 966
7
Subtraction with regrouping
Solve: 52 − 19
Solve: 281 − 34
Place Value up to Thousands
Write in standard form:
AECSD 4th Grade Mathematics.doc
Solve: 860 − 325
four hundred sixteen
seven hundren one
three thousand, eight hundred fifty
8
Unit 2
Place Value (N.1, N.2, N.3, N.5, N.6)
Length:
~ 3 weeks
Timeframe: Late September to Mid-October
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.1
Skip count by 1,000’s
4.N.2
Read and write whole numbers to 10,000
4.N.3
Compare and order numbers to 10,000
4.N.4
Understand the place value structure of the base ten number system: 10 ones = 1 ten,
10 tens = 1 hundred, 10 hundreds = 1 thousand, 10 thousands = 1 ten thousand
4.N.5
Recognize equivalent representations for numbers up to four digits and generate them
by decomposing and composing numbers
4.N.26 Round numbers less than 1,000 to the nearest tens and hundreds
4.N.27 Check reasonableness of an answer by using estimation
4.A.2
Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare
whole numbers and unit fractions and decimals (up to hundredths)
Local Standards (Stricken text is covered in a different unit):
L.4.N.1
Read and write whole numbers 0 to 10,000; read and write fractions (see
L.4.N.10); read and write decimals to hundredths place (see L.4.N.11); convert
between fractions and decimals (to hundredths).
L.4.N.2
Understand numbers including place value from hundredths to ten-thousands.
L.4.N.3
Compare and order whole numbers to 10,000; compare and order unit fractions or
proper fractions with common denominators (halves thru sixths and tenths);
compare and order decimals to hundredths; use the symbols <, >, =, and ≠.
L.4.N.5
Develop estimation strategies and skills (including rounding to nearest 10, 100, or
1,000); estimate answers before solving problems and compare estimate with
outcome to determine the reasonableness of results.
L.4.N.6
Count by 1000's; identify when multiplication results in even versus odd numbers
Big Ideas:
Place value allows us to represent larger and larger numbers while only using 10 digits.
Essential Questions:
What if there was no place value?
What is the difference between a digit and a number?
When and why would you round a number?
When do you use the different forms of numbers?
Prior Knowledge:
To know place value up to thousands
To compare and order whole numbers up to 1,000
To round whole numbers up to hundreds
To read and write numbers up to 1,000
Unit Objectives:
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To know place value up to ten thousands
To read and write whole numbers up to 10,000
To compare and order whole numbers up to ten thousands using the symbols <, >, =, & ≠
To estimate (round) whole numbers up to 10, 000
Resources:
SFAW Math, pages 52-55, 62, 63, 65-72
Review Template:
Ordering Whole Numbers
Order from least to greatest:
Rounding Whole Numbers
Round to the nearest ten:
Round to the nearest hundred:
156, 152, 165, 180
1010, 999, 1001, 1000
5,687; 5,876; 6,578; 5,867
85
96
19
125
34
678
Comparing Whole Numbers (using the symbols <, >, or =)
167 O 162
688 O 145
8,909 O
8,990
Problem Solving:
The digit in my ones place is twice the digit in my hundreds place. The digit in my thousands
place is 5. The sum of my digits is 14. What number am I?
Extension: What are all of the possible numbers that I could be?
The greatest recorded depth of the Antarctic ice sheet was recorded at 15,400 feet. A mile is
5,280 feet. About how many miles thick is the ice? Explain your answer.
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Unit 3
Adding and Subtracting Whole Numbers (N.4, A.1,A.2)
Length:
~ 3 weeks
Timeframe: Late October to Mid-November
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.14 Use a variety of strategies to add and subtract numbers up to 10,000
4.A.1
Evaluate and express relationships using open sentences with one operation
4.A.3
Find the value or values that will make an open sentence true, if it contains < or >
4.A.4
Describe, extend, and make generalizations about numeric (+, -, *, /) and geometric
patterns
4.A.5
Analyze a pattern or a whole-number function and state the rule, given a table or an
input/output box
Local Standards (Stricken text is covered in a different unit):
L.4.N.4
Add and subtract 5-digit whole numbers and understand that addition and
subtraction are inverse operations; add and subtract fractions (see L.4.N.10) and
decimals (see L.4.N.11)
L.4.A.1
Recognize, describe, extend, and create numeric and geometric patterns; analyze a
numeric input and output pattern or function and state the rule (e.g. each number
is multiplied by 3)
L.4.A.2
Express relationships as open sentences; find a value or values that make an open
sentence true including sentences containing the symbols < or >.
Big Ideas:
Adding and subtracting are life skills.
The values on both sides of the equals sign must be the same.
Essential Questions:
How do you use inverse operations to check problems?
When do you need to regroup?
What is a variable in a number sentence?
Prior Knowledge:
To add and subtract three-digit whole numbers with and without regrouping
To describe, extend and create numeric patterns
Unit Objectives:
To add and subtract 5-digit whole numbers with and without regrouping
To recognize and use addition and subtraction as inverse operations
To find the value or values that make an open sentence true, using the symbols < or > and
the variable n
To analyze a numeric input and output pattern
To determine the next output value in a numeric input and output pattern
To state a rule for a numeric input and output pattern
To identify key words when solving addition and subtraction word problems
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Resources:
SFAW Math, pages 32, 33, 134, 135 (Algebra reference), 93-117
Review Template:
Money
Write the least amount of dollars or coins needed to make each amount:
$0.55
$0.96
$7.05
Patterns
Complete the next three numbers in the pattern:
3, 6, 9, 12, __, __, __
10, __, 20, __, 30, 35, __
150, 200, 250, 300, ___, ___, ___
Property of Addition
Solve: (3 + 8) + 5 = 3 + (8 + ?)
Solve: (2 + 6) + 9 = 2 + (? + 9)
Solve: 4 + (0 + 6)= ? + (0 + 6)
Problem Solving:
Gail and Toby ran for student council president. A total of 405 student voted. Gail got 247
votes. How many students voted for Toby? Who won the election?
Ken wants to buy a larger tank so he can have more fish. The pet store owner said that 2 fish can
live in 1 gallon of water, 5 fish in 2 gallons, 8 fish in 3 gallons, or 11 fish in 4
gallons.
Complete the chart to show how many fish can live in larger fish tanks.
Number of Gallons
of Water
1
2
3
4
5
6
7
Number of
__ Fish __
2
5
8
11
Explain the rule you used to complete the pattern.
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Unit 4
Time and Money (M.1, M.3)
Length:
~ 3 weeks
Timeframe: Mid-November to Mid-December
State Standards (Shaded statements are identified as Post-March Indicators):
4.M.8
Make change, using combined coins and dollar amounts
4.M.9
Calculate elapsed time in hours and half hours, not crossing A.M./P.M.
4.M.10 Calculate elapsed time in days and weeks, using a calendar
Local Standards (Stricken text is covered in a different unit):
L.4.M.1
Calculate elapsed time in hours and half hours (not crossing A.M. or P.M) and in
days and weeks (using a calendar)
L.4.M.3
Determine an amount of change in dollars and cents.
Big Ideas:
Elapsed time is applicable to students’ lives (ex. going to the movies).
An understanding of money is essential in every day living.
Essential Questions:
How do you find elapsed time for a certain activity?
Why is it important to know how to find change?
What are the symbols used in writing money amounts?
Why are they (the symbols) important to record?
Prior Knowledge:
To tell time to the nearest minute
To know the value of each coin
To count and represent money amounts (using $0.00)
Unit Objectives:
To add and subtract money amounts, using $0.00
To determine the amount of change in dollars and cents
To calculate elapsed time in hours and half hours withou crossing A.M. or P.M.
To calculate elapsed time in days in weeks, using a calendar
Lessons Outline:
Lesson 1 Review Counting Money
To know the value of each coin
To count and represent money amounts (using $0.00)
Textbook: Pages 126-127
Practice Workbook 3-12 p. 45
Lesson 2 Adding and Subtracting Money
To add and subtract money amounts, using $0.00
Textbook: Pages 128-129
Practice Workbook p. 46
Lesson 3 Exploring Making Change
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To determine the amount of change in dollars and cents
Textbook: Pages 130-131
Practice Workbook p. 47
*This lesson will most likely take a few days. See Resources ... for more
lessons and practice.
Lesson 4 Review Telling Time
To tell time to the nearest minute
Textbook: Pages 74-75
Resouces available
Practice Workbook p. 25
Lesson 5 Review Telling Time
To tell time to the nearest minute
Textbook: Pages 76-77
Practice Workbook p. 26
See resource: Matching game on cardstock
Lesson 6 Elapsed Time
To calculate elapsed time in hours and half hours
Do not use lesson from SFAW.
Use lesson from resources – Lesson 6 Elapsed Time
*This lesson will need 2-3 days to master
Lesson 7 Exploring the Calendar
To calculate elapsed time in days in weeks, using a calendar
Textbook: Pages 80-81
Practice Workbook 28
Additional Resources:
Vocabulary:
Decimal point
Analog clock
Digital clock
A.M.
P.M.
Elapsed time
Ordinal number
Leap year
Century
Decade
Lessons relating to time and money that should not be done:
3-15 Exploring Algebra
3-16
Review Template:
Commutative Property of Multiplication
Solve: 6 × 7 = 7 × ?
4×3=?×4
AECSD 4th Grade Mathematics.doc
?×8=8×7
14
Fact Families
Complete or create a fact family:
4, 7, 3
3 + 4= 7
7 – 4= 3
7 – __ = 4
15, 7, 8
6, 2, 12
__ + __ = __
__ × __ = __
__ + __ = __
__ + __ = __
__ × __ = __
__ − __ = __
__ ÷ __ = __
__ − __ = __
__ ÷ __ = __
Subtraction Across Zeroes
Solve: 40 − 24
Solve: 305 − 117
Solve: 900 − 425
Problem Solving:
1. Amy bought a glue stick for $0.56 and 2 pencils for $0.12 each. How much change should
she get back from $5?
2. Students want to buy playground equipment. They can buy a complete basketball set for
$300 or they can buy the items separately.
Complete Basketbal Set
Basketball Equipment
Set Includes
Pole $125
Pole, Backstop, Net and 4 Balls!
Backstop $45
Only $300
Net $15
Basketballs $30 each
Which is the better deal? Explain why.
3. A group of 5 friends put their money together, hoping that they could all go to the movies.
This is how much they gave: $7.25, $5.50, $8.10, $3.25, and $6.90. If a movie
ticket costs $6.00, will they have enough money? Explain your answer.
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Unit 5
Multiplication (N.5, N.6, N.7, N.8, N.9, A.1, A.2)
Length:
~ 3 weeks
Timeframe: Mid-December to Early January
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.6
Understand, use, and explain the associative property of multiplication
4.N.13 Develop an understanding of the properties of odd/even numbers as a result of
multiplication
4.N.16 Understand various meanings of multiplication and division
4.N.17 Use multiplication and division as inverse operations to solve problems
4.N.18 Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with
and without regrouping)
4.N.20 Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000
4.N.26 Round numbers less than 1,000 to the nearest tens and hundreds
4.N.27 Check reasonableness of an answer by using estimation
4.A.1
Evaluate and express relationships using open sentences with one operation
4.A.3
Find the value or values that will make an open sentence true, if it contains < or >
4.A.4
Describe, extend, and make generalizations about numeric (+, -, *, /) and geometric
patterns
4.A.5
Analyze a pattern or a whole-number function and state the rule, given a table or an
input/output box
Local Standards (Stricken text is covered in a different unit):
L.4.N.5
Develop estimation strategies and skills (including rounding to nearest 10, 100, or
1,000); estimate answers before solving problems and compare estimate with
outcome to determine the reasonableness of results.
L.4.N.6
Count by 1000's; identify when multiplication results in even versus odd numbers
L.4.N.7
Recognize patterns for products and quotients including fact families; use and
explain the associative property of multiplication (e.g. (2 * 3) * 4 = 2 * (3 * 4))
L.4.N.8
Master multiplication and division facts with products and dividends up to 144;
develop fluency multiplying and dividing by multiples of 10 and 100 up to 1,000
(e.g. 20 * 300).
L.4.N.9
Multiply two-digit by one- and two-digit numbers; divide two-digit by one-digit
numbers (with and without remainders); recognize multiplication and division as
inverse operations and as repeated addition or subtraction, respectively.
L.4.A.1
Recognize, describe, extend, and create numeric and geometric patterns; analyze a
numeric input and output pattern or function and state the rule (e.g. each number
is multiplied by 3)
L.4.A.2
Express relationships as open sentences; find a value or values that make an open
sentence true including sentences containing the symbols < or >.
Big Ideas:
Basic facts, estimation, and place value are used to understand multiplication.
Multiplication is a shortcut for repeated multiplication of the same amount.
Numbers can be grouped in different ways without affecting the product of the numbers.
AECSD 4th Grade Mathematics.doc
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Essential Questions:
What is multiplication?
Does the product change when you change the grouping of multiplication?
Prior Knowledge:
To multiply numbers with products up to 144
Mastery of multiplication facts with single-digit factors
To identify and apply the multiplication properties of 0 and 1 (identity property)
To understand fact families
Unit Objectives:
To master multiplication facts with products up to 144
To recognize patterns for products
To recognize and create multiplication fact families
To use and explain the associative property
To multiply two-digit numbers by one-digit numbers
To recognize when the product of two numbers will be odd or even
To find the value or values of an open multiplication sentence that will make the sentence
true, using < or >
To analyze a numeric input and output pattern and state the rule
To determine the next output value in a numeric input and output pattern
To state a rule for a numeric input and output pattern
To identify key words when solving multiplication word problems
Resources:
SFAW Math, 147-160 (Review of Facts), 199-205, 209-215, 224-227, 230-233
Review Template:
Comparing Unit Fractions: Compare the following fractions using <, >, or =
1/2 O 1/3
1/6 O 1/4
1/5 O 1/10
Division Facts
Solve: 56 ÷ 8 = ___ Solve: 28 ÷ 4 = ___ Solve: 49 ÷ 7 = ___
Algebraic Equations
Solve: n + 8 = 11
Solve: 16 + n = 25
Solve: 25 + 50 = n
Problem Solving:
1. Dan wants to have 2 pencils for every week of school. If there are 36 weeks of school, how
many pencils will he need?
2.
(3 × 7) × 14 = 3 × (7 × 14)
Is the number sentence true? Explain how you know whether or not the number sentence is true?
3. Linda and Casey started with 48 boxes of Girl Scout cookies. They went out together to sell
cookies for four days. Each day, they sold 6 boxes. How many cookies did they have left on the
fourth day? How many days will it take them to sell all of the cookies?
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Unit 6
Division (N.7, N.8, N.9)
Length:
~ 3 weeks
Timeframe: Early January to Late January
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.16 Understand various meanings of multiplication and division
4.N.17 Use multiplication and division as inverse operations to solve problems
4.N.20 Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000
4.N.21 Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and
without remainders)
4.N.22 Interpret the meaning of remainders
Local Standards (Stricken text is covered in a different unit):
L.4.N.7
Recognize patterns for products and quotients including fact families; use and
explain the associative property of multiplication (e.g. (2 * 3) * 4 = 2 * (3 * 4))
L.4.N.8
Master multiplication and division facts with products and dividends up to 144;
develop fluency multiplying and dividing by multiples of 10 and 100 up to 1,000
(e.g. 20 * 300).
L.4.N.9
Multiply two-digit by one- and two-digit numbers; divide two-digit by one-digit
numbers (with and without remainders); recognize multiplication and division as
inverse operations and as repeated addition or subtraction, respectively.
Big Ideas:
Division is sharing equally and repeated subtraction.
Essential Questions:
What is division?
What are the steps in solving a division problem? Why?
What is a remainder and why do we have them?
How do you use inverse operations to check problems?
Prior Knowledge:
Mastery of division facts with single-digit quotients
To know how to divide with dividends up to 144
To know the 0 and 1 property of division
To understand fact families
Unit Objectives:
To master division facts with quotients up to 144
To recognize patterns for quotients
To recognize and create division fact families
To divide two-digit dividends by single-digit numbers with and without remainders
To divide three-digit dividends (not required) by single-digit numbers with and without
remainders
To find the value or values of an open division sentence that will make the sentence true,
using < or >
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To analyze a numeric input and output pattern and state the rule
To identify key words when solving division word problems
To recognize multiplication and division as inverse operations
Resources:
SFAW Math, pages 165-183 (Division Facts and Word Problems), 291-305, 316, 317, 320, 321
Review Template:
Open Sentences
Complete the sentence to make it true:
10 + > 12
5+8< 6+
Open Sentences
Complete the sentence to make it true:
6 × < 18
24 > 8 ×
+7< 8
7×6
7×7
Place Value
Write the number for the word form:
Sixteen thousand, five hundred sixty-two
Twenty-nine thousand, seventy-eight
Three hundred thousand, two
Problem Solving
One night Ali was paid $12.00 for baby-sitting from 5:00 p.m. to 8:00 p.m. How much was she
paid for each hour?
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Unit 7
Geometry (G.1, G.4, G.5)
Length:
~ 2 weeks
Timeframe: Late January to Mid-February
State Standards (Shaded statements are identified as Post-March Indicators):
4.G.1
Identify and name polygons, recognizing that their names are related to the number of
sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)
4.G.2
Identify points and line segments when drawing a plane figure
4.G.3
Find perimeter of polygons by adding sides
4.G.4
Find the area of a rectangle by counting the number of squares needed to cover the
rectangle
4.G.5
Define and identify vertices, faces, and edges of three-dimensional shapes
Local Standards (Stricken text is covered in a different unit):
L.4.G.1
Identify and name polygons (triangle, quadrilateral, pentagon, hexagon, octagon)
connecting names to number of sides; define and identify parts of threedimensional shapes (vertices, faces, edges).
L.4.G.4
Draw and identify points, line segments and rays; draw and identify intersecting,
perpendicular, and parallel lines; draw angles and classify as acute, right, obtuse,
or straight.
L.4.G.5
Find the perimeter of polygons given the lengths of its sides; find the area of a
rectangle by counting squares
Big Ideas:
Polygons and three-dimensional shapes can be found all around us.
A difference exists between perimeter and area.
Essential Questions:
What is the difference between a polygon and a three-dimensional shape?
When do you need to find the perimeter?
When do you need to find the area?
What polygons or three-dimensional figures are found in your house?
How do the number of vertices, faces, and edges change when you look at a polygon and
a three-dimensional figure?
Prior Knowledge:
To identify similar and congruent figures
To identify and perform transformations (slide, flip, or turn)
To identify and draw lines of symmetry
To define two-dimensional shapes
To name, describe, and compare three-dimensional shapes
Unit Objectives:
To review similar and congruent figures, transformations, and symmetry (see prior
knowledge)
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To identify and name polygons, recognizing that their names are related to the number of
sides and angles
To define and identify parts of three-dimensional shapes (vertices, faces, edges)
To identify points and line segments when drawing a plane figure
To find perimeter by adding sides
To find the area of a rectangle by counting the number of squares needed to cover the
rectangle
Resources:
SFAW Math, pages 343-347, 352-356 (Review of similar/congruent), 360-361, 362 and 363
(Review of symmetry), 367-371
Review Template:
Adding and Subtracting Money
Solve: $0.55 + $3.99
Solve: $5.00 − $2.76
Solve: $31.09 + $8.77
Elapsed Time
Determine the amount of time that has elapsed.
6:30 am – 10:00 am
12:45 pm – 3:45 pm
8:00 pm – 11:30 pm
Multiplication
Write a multiplication fact for the following addition sentences.
3 + 3 + 3 + 3 = __________
7 + 7 + 7 + 7 + 7 + 7 = __________
4 + 4 = ___________
Multiplication
Write the multiplication fact that will help solve the division problem.
81 ÷ 9 = ___________
36 ÷ 3 = ___________
77 ÷ 7 = ___________
Problem Solving:
1. Michael, Colin, Nick and Steve are standing in line.
*Michael and Nick are next to each other.
*Colin is last in line.
*Steve is not next to either Colin or Nick.
Write the order in which the boys are standing.
2. Brian’s dog had 8 puppies.
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Each puppy was either all black, all tan, or all white.
There were 2 black puppies.
There were twice as many white puppies as tan puppies.
How many white puppies did Brian’s dog have? Explain how you found your answer.
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Unit 8
Measurement (M.2, M.4, M.5)
Length:
~ 2 weeks
Timeframe: February
State Standards (Shaded statements are identified as Post-March Indicators):
4.M.1
Select tools and units (customary and metric) appropriate for the length being
measured
4.M.2
Use a ruler to measure to the nearest standard unit (whole, 1/2 and 1/4 inches, whole
feet, whole yards, whole centimeters, and whole meters)
4.M.3
Know and understand equivalent standard units of length: 12 inches = 1 foot, 3 feet =
1 yard
4.M.4
Select tools and units appropriate to the mass of the object being measured (grams and
kilograms)
4.M.5
Measure mass, using grams
4.M.6
Select tools and units appropriate to the capacity being measured (milliliters and liters)
4.M.7
Measure capacity, using milliliters and liters
Local Standards (Stricken text is covered in a different unit):
L.4.M.2
Estimate, measure (using appropriate tools and units (i.e. 1/4 inches and whole
centimeters and meters)), compare, and order the lengths (heights) of objects;
know and understand equivalent standard units: 12 inches = 1 foot, 3 feet = 1
yard).
L.4.M.4
Estimate, measure (grams and kilograms), and compare the mass of objects using
appropriate tools.
L.4.M.5
Estimate, measure (milliliters and liters), and compare the volume (capacity) of
objects using appropriate tools.
Big Ideas
All over the world, different tools and units are used to measure length, mass, and
volume.
Essential Questions:
How does estimation save you time and effort?
When would you need exact measurements?
Prior Knowledge:
Estimating, measuring, and comparing volumes
Estimating, measuring, and comparing masses
Estimating and measuring lengths (1/2 inches and yards)
Knowledge of the appropriate tools to measure length, (customary), mass, and volume
Unit Objectives:
To select tools and units for measuring length (customary and metric)
To use a ruler to measure length to the nearest standard unit (whole, 1/2, and 1/4 inches,
whole feet, whole yards, whole centimeters, whole meters)
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To know and understand equivalent standard units of length (12 inches = 1 foot, 3 feet =
1 yard)
To estimate, measure, and compare mass, using grams and kilograms
To estimate, measure, and compare volume, using milliliters and liters
Resources:
SFAW Math, pages 413-419, 503-507, 510-513
Review Template:
Multiplication Patterns
Solve: 3 × 6 = ___
3 × 60 = ___
3 × 600 = ___
4 × 8 = ___
4 × 80 = ___
4 × 800 = ___
6 × 7 = ___
6 × 70 = ___
6 × 700 = ___
Multiplication
Solve: 50 × 8 = ___
44 × 3 = ___
852 × 5 = ___
Division with Remainders
Solve: 65 ÷ 8 = ___
38 ÷ 6 = ___
59 ÷ 9 = ___
Problem Solving:
In the space below, draw a rectangle that is 8 centimeters long and 5 centimeters wide. What is
the perimeter of the rectangle?
Each child in Miss Benton’s class is making a 1-yard long paper chain. So far, Tina has made 20
inches of her chain. How many more inches does she still have to make?
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State Assessment Review and Administration
Length:
~ 2 weeks
Timeframe: February 27 to March 10 (State Assessment: 3/8, 3/9, and 3/10)
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Unit 9
Fractions (N.1, N.3, N.10)
Length:
~ 3 weeks
Timeframe: Mid-March to Late March
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.7
Develop an understanding of fractions as locations on number lines and as divisions of
whole numbers
4.N.8
Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and
tenths) using manipulatives, visual models, and illustrations
4.N.9
Use concrete materials and visual models to compare and order unit fractions or
fractions with the same denominator (with and without the use of a number line)
4.N.23 Add and subtract proper fractions with common denominators
4.A.2
Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare
whole numbers and unit fractions and decimals (up to hundredths)
Local Standards (Stricken text is covered in a different unit):
L.4.N.1
Read and write whole numbers 0 to 10,000; read and write fractions (see
L.4.N.10); read and write decimals to hundredths place (see L.4.N.11); convert
between fractions and decimals (to hundredths).
L.4.N.3
Compare and order whole numbers to 10,000; compare and order unit fractions or
proper fractions with common denominators (halves thru sixths and tenths);
compare and order decimals to hundredths; use the symbols <, >, =, and .
L.4.N.10
Develop understanding of fractions (including as division of whole numbers);
recognize and find equivalent fractions (halves thru sixths, and tenths); compare
and order (see L.4.N.3) fractions; add and subtract proper fractions with common
denominators.
Big Ideas:
Fractions are a representation of parts to a whole.
In unit fractions, the larger the denominator, the smaller amount.
Essential Questions:
What patterns do you notice among numerators and denominators of equivalent
fractions?
How does finding equivalent fractions help you compare fractions?
Why doesn’t the denominator change when you add or subtract fractions with common
denominators?
Prior Knowledge:
To name fractions
To understand and represent unit fractions
To know the meaning of numerator and denominator
Unit Objectives:
To recognize and write equivalent fractions (halves, thirds, fourths, fifths, sixths, and
tenths)
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To compare and order unit fractions or fractions with the same denominator (with and
without a number line), using concrete materials and visual models
To add and subtract proper fractions with common denominators
Resources:
SFAW Math, pages 385-391 (Review of Fractions), 398-403, 406-407, 431-433, 443-445
Review Template:
Multiplying Money
Solve: $1.36 × 5 = _____
$4.08 × 3 = _____
$7.82 × 7 = _____
Subtracting Money
Solve: $2.00 − $0.46 = _____
$5.00 − $2.33 = _____
$8.75 − $7.88 = _____
Finding Change
Solve: Amount Paid: $5
Price: $3.75
Change: ______
Amount Paid: $10
Price: $5.99
Change: ______
Amount Paid: 1 five-dollar bill, 3 one-dollar bills
Price: $4.35
Change: ______
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Unit 10
Decimals (N.1, N.3, N.11)
Length:
~ 3 weeks
Time frame: Early April to Late April
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.10 Develop an understanding of decimals as part of a whole
4.N.11 Read and write decimals to hundredths, using money as a context
4.N.12 Use concrete materials and visual models to compare and order decimals (less than 1)
to the hundredths place in the context of money
4.N.24 Express decimals as an equivalent form of fractions to tenths and hundredths
4.N.25 Add and subtract decimals to tenths and hundredths using a hundreds chart
4.A.2
Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare
whole numbers and unit fractions and decimals (up to hundredths)
Local Standards (Stricken text is covered in a different unit):
L.4.N.1
Read and write whole numbers 0 to 10,000; read and write fractions (see
L.4.N.10); read and write decimals to hundredths place (see L.4.N.11); convert
between fractions and decimals (to hundredths).
L.4.N.3
Compare and order whole numbers to 10,000; compare and order unit fractions or
proper fractions with common denominators (halves thru sixths and tenths);
compare and order decimals to hundredths; use the symbols <, >, =, and ≠
L.4.N.11
Develop understanding of decimals (to hundredths place) as part of a whole; read,
write, and order (see L.4.N.3) decimals to hundredths (connect to money
application); add and subtract decimals to hundredths place.
Big Ideas:
Decimals are fractional parts of a whole number.
Every (non-repeating) decimal can be expressed as a fraction whose denominator is a
multiple of ten.
When comparing decimals, compare each place in order until one is larger than the other.
Essential Questions:
How is a whole number different than a decimal?
What does a decimal look like using words?
What does a decimal look like using digits?
When you have two decimals, how do you know which is larger?
Prior Knowledge:
To identify that decimal points are used in money
Unit Objectives:
To read and write decimals up to the hundredths
To order decimals up to the hundredths
To compare decimals up to hundredths, using <, >, =, and ≠.
To add and subtract decimals
To express decimals as an equivalent form of fractions to tenths and hundredths
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Resources:
SFAW Math, pages 475-479, 482-487, 492-499
Review Template:
Equivalent Fractions
Write an equivalent fraction.
Rounding
Round to the nearest hundred.
1/2 = __
2/3 = __
4/10 = __
567 rounds to ____
349 rounds to ____
999 rounds to ____
Estimating the sum
Estimate the sum to the nearest hundred.
AECSD 4th Grade Mathematics.doc
234 + 275 = ____
505 + 333 = ____
881 + 192 = ____
29
Unit 11
Geometry (G.4)
Length:
~ 2 weeks
Timeframe: Early May to Mid-May
State Standards (Shaded statements are identified as Post-March Indicators):
4.G.2
Identify points and line segments when drawing a plane figure
4.G.6
Draw and identify intersecting, perpendicular, and parallel lines
4.G.7
Identify points and rays when drawing angles
4.G.8
Classify angles as acute, obtuse, right, and straight
Local Standards (Stricken text is covered in a different unit):
L.4.G.4
Draw and identify points, line segments and rays; draw and identify intersecting,
perpendicular, and parallel lines; draw angles and classify as acute, right, obtuse,
or straight.
Big Ideas:
Cities are designed with intersecting, perpendicular, and parallel lines.
Most buildings are constructed with right angles.
Points and line segments are the building blocks of geometric shapes.
Essential Questions:
What is the difference between intersecting, perpendicular, and parallel lines?
How are angles classified?
Prior Knowledge:
None identified.
Unit Objectives:
To identify and draw a point, a line segment, and a line.
To identify and draw intersecting, perpendicular, and parallel lines
To identify points and rays when drawing angles
To classify angles as acute, obtuse, right, and straight
Resources:
SFAW Math, pages 350-351, 358-359
Review Template:
Adding Fractions
Solve: 1/4 + 2/4 = __
Subtracting Fractions
Solve: 9/10 − 3/10 = ___
2/6 + 2/6 = __
1/10 + 6/10 = __
4/8 − 1/8 = ___
5/5 − 4/5 = ___
Decimals
Write the decimal:
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30
four tenths
______
seven hundredths
______
nine and sixty two hundredths ______
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Unit 12
Multiplication of 2 Digit Factors (N.5, N.7, N.8, N.9)
Length:
~ 3 weeks
Timeframe: Mid-May to Early June
State Standards (Shaded statements are identified as Post-March Indicators):
4.N.26 Round numbers less than 1,000 to the nearest tens and hundreds
4.N.27 Check reasonableness of an answer by using estimation
4.N.20 Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000
4.N.16 Understand various meanings of multiplication and division
4.N.18 Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with
and without regrouping)
4.N.19 Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with
and without regrouping)
Local Standards (Stricken text is covered in a different unit):
L.4.N.5
Develop estimation strategies and skills (including rounding to nearest 10, 100, or
1,000); estimate answers before solving problems and compare estimate with
outcome to determine the reasonableness of results.
L.4.N.7
Recognize patterns for products and quotients including fact families; use and
explain the associative property of multiplication (e.g. (2 * 3) * 4 = 2 * (3 * 4))
L.4.N.8
Master multiplication and division facts with products and dividends up to 144;
develop fluency multiplying and dividing by multiples of 10 and 100 up to 1,000
(e.g. 20 * 300).
L.4.N.9
Multiply two-digit by one- and two-digit numbers; divide two-digit by one-digit
numbers (with and without remainders); recognize multiplication and division as
inverse operations and as repeated addition or subtraction, respectively.
Big Ideas:
Basic facts, estimation, and place value are used to understand multiplication.
Essential Questions:
How is mental math helpful when estimating products?
Prior Knowledge:
Mastery of basic facts up to products of 144
Knowledge of multiplying two-digit by one-digit numbers
Unit Objectives:
To estimate products of two-digit factors
To explore multiplication patterns
To multiply two-digit by two-digit numbers
Resources:
SFAW Math, pages 249-255, 260-263
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Review Template:
Comparing Decimals
Write the decimals in order from greatest to least.
.3, .8, .1, .6
.72, .7, .25, .3
.9, 1.5, 1.48, .92
Converting Fractions to Decimals
Change each fraction to a decimal:
1/10 = ___
Place Value
Give the value of each underlined digit.
14, 350
56,921
AECSD 4th Grade Mathematics.doc
4/10 = ___
35/100 = ___
85,730
33