Curriculum for Grade 5
Grade Description: Students dig more deeply into place value patterns and operations. Their understanding grows to include decimals in the hundredths and thousandths, operations with fractions and decimals, multi-digit multiplication and division with remainders, area models, properties of multiplication and division, estimation, and measuring volume. We introduce the coordinate plane (quadrant I), which students use to solve problems.
MODULE 1. Place Value and Decimal Fractions
Topic A: Multiplicative Patterns on the Place Value Chart
Relying on solid understanding of the place value chart and powers of ten, students multiply and divide to solve problems with a decimal number as a factor or quotient.
Multiply by 10 with and without a place value chart
Multiply by 100 with and without a place value chart
Multiply by 1,000 with and without a place value chart
Multiply by 10, 100, and 1,000
Complete a pattern of multiplication by 10 or 100
Divide by 10 with and without a place value chart
Divide by 100 with and without a place value chart
Divide by 1,000 with and without a place value chart
Divide by 10, 100, and 1,000
Identify and complete a pattern of division by 10 or 100
Factor out powers of 10 to multiply numbers with a single non-zero digit
Multiply numbers with a single non-zero digit
Record the relationship between hundredths and thousandths using a place value chart
Multiply a decimal number by 10 with and without a place value chart
Multiply a decimal number by 100 with and without a place value chart
Multiply a decimal number by 1,000 with and without a place value chart
Multiply a decimal number by 10, 100, and 1,000
Complete a pattern of multiplication by 10, 100, and 1,000
Divide a decimal number by 10 with and without a place value chart
Divide a decimal number by 100 with and without a place value chart
Divide a decimal number by 1,000 with and without a place value chart
Divide a number by 10, 100, and 1,000
Complete a pattern of division by 10, 100, and 1,000
Represent repeated multiplication of 10 as 10 with an exponent
Represent 10 with an exponent as repeated multiplication
Multiply a decimal number by 10 with an exponent
Divide a number by 10 with an exponent
Topic B: Decimal Fractions and Place Value Patterns
Students use familiar symbols (<, =, >) to compare numbers to the thousandths place. They identify, compose, and arrange numbers of equal and unequal length.
Record a decimal number in expanded notation
Compare numbers to the hundredths place with and without a place value chart
Complete inequalities that compare numbers to the hundredths place
Arrange decimal numbers in order from smallest to greatest (Level 1)
Arrange decimal numbers in order from smallest to greatest (Level 2)
Arrange decimal numbers in order from smallest to greatest (Level 3)
Topic C: Place Value and Rounding Decimal Fractions
Using a number line to provide context, students first determine the midway point between two decimal numbers. They then progress to rounding using the number line and the midway point. Finally, students round decimal numbers to any given place value without use of the number line.
Determine the midway point between two decimal numbers on a number line
Determine whether a decimal number is greater or less than halfway between two points on a number line
Compose and apply a rule for rounding numbers
Determine whether a decimal number rounds up or down
Round a given number by first determining its nearest tenths
Round a given number to the hundredths, tenths, and ones place
Round a decimal number to a given place value (Level 1)
Round a decimal number to a given place value (Level 2)
Round a decimal number to a given place value (Level 3)
Round a decimal number to a given place value (Level 4)
Topic D: Adding and Subtracting Decimals
Based on the familiar disk model, students add and subtract numbers to the thousands place. They add and subtract in equations that require regrouping and learn to use the standard algorithm (column addition and column subtraction).
Add numbers to the hundredths place with regrouping using a disk model
Add numbers to the thousandths place with regrouping using a disk model
Add numbers to the thousandths place with regrouping using column addition and a disk model
Add numbers to the thousandths place with regrouping using column addition
Subtract numbers to the hundredths place with regrouping using a disk model
Subtract numbers to the thousandths place with regrouping using a disk model
Subtract numbers to the thousandths place with regrouping using column subtraction and a disk model
Subtract numbers of different lengths to the thousandths place with regrouping using column subtraction and a disk model
Subtract numbers to the thousandths place with regrouping using column subtraction
Topic E: Multiplying Decimals
Students take the first steps in understanding multiplication of a decimal number. Working with a single-digit whole number and a decimal number, students work step-by-step through the process using the familiar disk model. They trade disks to model regrouping and explore the importance of decimal point placement.
Multiply a decimal number with regrouping using a disk model
Multiply a decimal number with regrouping using a disk model and the standard algorithm
Compare multiplying a whole number with multiplying a decimal number with the same digits
Multiply a decimal number by converting it to a whole number and converting the product back to a decimal
Topic F: Dividing Decimals
Students rely on familiar models and procedures to apply their division knowledge to decimals. Step-by-step, they learn to correctly work through regrouping, using a new place value, using zeros, and placing a decimal in their quotient.
Divide a decimal number by a single-digit number based on a model
Divide a decimal number by a single-digit number with and without regrouping based on a model
Divide a decimal number by a single-digit number with and without regrouping based on a model
Divide a decimal number by a single-digit number with regrouping to a new place value based on a model
Divide a decimal number by a single-digit number with and without regrouping using long division and a model
Use long division to divide a decimal number by a single-digit number with and without regrouping
Use long division to divide a decimal number by a single-digit number with quotients that include 0
Use long division to divide a decimal number by a single-digit number with regrouping to a new place value
MODULE 2. Multi-Digit Whole Number and Decimal Fraction Operations
Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication
Students work with round numbers in the tens, hundreds, and thousands to see how factoring out can make mental multiplication easier. In doing so, they apply properties of multiplication.
Factor out 10, 100, or 1,000 from a given number
Solve multiplication problems using the associative and commutative properties
Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 1)
Solve a multi-digit multiplication problem mentally
Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 2)
Round multi-digit numbers to estimate the area of a rectangle
Round multi-digit numbers to estimate the product
Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication
Students hone their use of the standard algorithm for multiplication, working with multi-digit numbers. They master the use of regrouping and working across zeros. To further their conceptual understanding, the standard algorithm is presented alongside other strategies, such as the area model and factoring out powers of 10.
Solve multiplication problems using the standard algorithm (Level 1)
Solve multiplication problems using the standard algorithm (Level 2)
Multiply multi-digit numbers by factoring out powers of 10 and using the associative property
Develop and test an algorithm for multiplying by a factor with a single non-zero digit
Use the strategy of factoring out powers of 10 to solve multi-digit multiplication problems
Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 1)
Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 2)
Multiply two 2-digit numbers using the standard algorithm and the strategy of factoring out powers of ten (Level 3)
Use the area model to multiply two 2-digit numbers
Multiply two 2-digit numbers using the concept of partial products
Multiply multi-digit numbers using the concept of partial products (Level 1)
Multiply multi-digit numbers using the concept of partial products (Level 2)
Multiply multi-digit numbers using the concept of partial products (Level 3)
Multiply two 3-digit numbers using the concept of partial products (Level 1)
Multiply two 3-digit numbers using the concept of partial products (Level 2)
Multiply 3- and 4-digit numbers using the concept of partial products
Multiply up to 5-digit numbers using the concept of partial products
Topic C: Decimal Multi-Digit Multiplication
Students further their understanding multiplication of a decimal number by increasing the number of digits in factors. Working with a 2- or 3-digit whole number and a decimal number in the tenths or hundredths, students work step-by-step through the process using the standard algorithm. They learn how to place a decimal in their answer and how to estimate to check the reasonableness of their answer.
Multiply a 2-digit decimal number by a 2-digit whole number using partial products with an area model
Multiply a 2-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)
Multiply a 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)
Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 2)
Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 3)
Multiply a decimal number by a round number by factoring out powers of 10
Multiply a decimal number by a round number
Round a multi-digit number to a given place (Level 2)
Round a multi-digit number to a given place (Level 1)
Estimate the product of a decimal number and a 3-digit whole number (Part 1)
Estimate the product of a decimal number and a 3-digit whole number (Part 2)
Estimate the product of a decimal number and a 3-digit whole number then solve using the standard algorithm
Topic D: Mental Strategies for Multi-Digit Whole Number Division
Students rely on their understanding of powers of 10, division, place value, and rounding to divide multi-digit whole numbers mentally.
Divide round numbers by powers of 10
Divide by factoring out powers of 10 from the divisor
Divide multi-digit round numbers mentally
List the multiples of a given 2-digit round number
Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 1)
Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 2)
Estimate a quotient by finding the nearest multiple
Estimate a quotient of a multi-digit division equation (Level 1)
Estimate a quotient of a multi-digit division equation (Level 2)
Topic E: Partial Quotients and Multi-Digit Whole Number Division
Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.
Divide a group of objects into groups of given size with a remainder
Find the quotient and remainder by using multiples of the divisor
Find the quotient and remainder by subtracting the divisor from the dividend (Part 1)
Find the quotient and remainder by subtracting the divisor from the dividend (Part 2)
Estimate the quotient, then solve using long division with a 1-digit quotient (Part 1)
Estimate the quotient, then solve using long division with a 1-digit quotient (Part 2)
Solve using long division with a 1-digit quotient
Solve using long division with a 1-digit quotient (overestimate)
Solve using long division with a 1-digit quotient (underestimate)
Solve using long division with a 1-digit quotient
Solve using long division with a 2-digit quotient (Part 1)
Solve using long division with a 2-digit quotient (over and underestimate)
Solve using long division with a 2-digit quotient (Part 2)
Solve using long division with a 3-digit quotient
Solve using long division with a 3-digit quotient (over and underestimate) (Part 1)
Solve using long division with a 3-digit quotient (over and underestimate) (Part 2)
Topic F: Partial Quotients and Multi-Digit Decimal Division
Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.
Rename decimal numbers in unit form
Rename a number in unit form as a decimal number
Rename a whole number in unit form and decimal form
Divide a decimal by a whole number (with and without using unit form)
Divide a decimal number by 10 or 100
Divide a decimal number by a multiple of 10 or 100
Estimate the quotient of a decimal number divided by a 2-digit number (Level 1)
Estimate the quotient of a decimal number divided by a 2-digit number (Level 2)
Solve long division to the tenths place
Solve long division to the hundredths place
Solve long division of a decimal number (Level 1)
Solve long division of a decimal number (Level 2)
Solve long division of a decimal number (Level 3)
Use long division to solve a word problem with a decimal quotient
Use long division to solve area problems with a decimal quotient
MODULE 3. Addition and Subtraction of Fractions
Topic A: Equivalent Fractions
Students are introduced to the basics of fraction equivalency. They learn to multiply to find an equivalent fraction and to divide to reduce a fraction. The concepts of common factors and greatest common factor are also introduced and applied.
Label the numerator and denominator in a fraction
Write an equivalent fraction (larger) based on a given multiple or denominator
Write an equivalent fraction (smaller) based on a given divisor, numerator, or denominator
Complete equivalent fractions
Identify common factors of two given numbers
Identify a common factor of two given numbers and divide both by the common factor
Reduce a fraction to its simplest form by dividing by the greatest common factor
Topic B: Making Like Units Pictorially
Students rely on their knowledge of fraction equivalence to work through all aspects of adding and subtracting with fractions and mixed numbers. With plenty of visual support and step-by-step prompting, they work with like and unlike denominators. Students learn to convert between mixed numbers and fractions to solve problems, write their answer in simplest form, and solve word problems.
Add fractions with like denominators
Rewrite an improper fraction as a mixed number
Add fractions with like denominators and rewrite the sum as a mixed number
Divide shapes into an equal number of parts (precursor to finding common denominators)
Add fractions with unlike denominators (multiply denominators to find a common denominator)
Rename fractions with unlike denominators (Level 1)
Rename fractions with unlike denominators (Level 2)
Add fractions with unlike denominators and rewrite the sum as a mixed number
Add fractions with unlike denominators and rewrite the sum in simplest form (Part 1)
Add fractions with unlike denominators and rewrite the sum in simplest form (Part 2)
Subtract fractions with like denominators
Subtract fractions with unlike denominators (multiply denominators to find a common denominator)
Subtract fractions with unlike denominators
Rewrite a mixed number as an improper fraction
Subtract a fraction from a mixed number with like denominators (rename the mixed number as a fraction)
Subtract a fraction from a mixed number with unlike denominators (rename the mixed number as a fraction)
Subtract a fraction from a mixed number with unlike denominators and rewrite the difference in simplest form
Subtract a fraction from a mixed number with unlike denominators to solve a word problem
Subtract a fraction from 1 whole to solve a word problem
Subtract two fractions from 1 whole to solve a word problem
Add fractions to solve a word problem
Topic C: Making Like Units Numerically
Students increase the complexity of the addition and subtraction operations they can solve by using mixed numbers. They reinforce and apply their understanding of number equivalence as they rename numbers to solve problems.
Add a mixed number and a whole number with like denominators
Subtract a fraction or a mixed number from a whole number with like denominators with and without a number line
Add a mixed number and a fraction with like denominators
Add mixed numbers with like denominators
Add mixed numbers with unlike denominators (Level 1)
Add mixed numbers with unlike denominators (Level 2)
Subtract mixed numbers with like denominators
Subtract mixed numbers with unlike denominators (Level 1)
Subtract a fraction from a mixed number with like denominators (rename the mixed number)
Subtract mixed numbers with unlike denominators (Level 2)
Subtract mixed numbers with unlike denominators (Level 3)
Topic D: Further Applications
To support more complex understanding of operations with fractions, students are supported by visual models, the number line, and diagrams. They apply their knowledge of fractions to estimate sums and differences and solve multi-step word problems with mixed numbers.
Compare fractions with unlike denominators to 1/2 to estimate the sum
Compare fractions with unlike denominators to a missing unit to estimate the sum
Compare fractions with unlike denominators to estimate the difference of a mixed number minus a fraction
Add multiple mixed numbers and fractions
Solve a multi-step word problem with mixed numbers with unlike denominators (Part 1)
Solve a multi-step word problem with mixed numbers with unlike denominators (Part 2)
MODULE 4. Multiplication and Division of Fractions and Decimal Fractions
Topic A: Line Plots of Fraction Measurements
Students combine their knowledge of measurement, rounding, and mixed numbers to create line plots. They then analyze the data, requiring them to perform operations with mixed numbers.
Round to the nearest half inch on a ruler
Round to the nearest half inch on a ruler to create a line plot and analyze the data
Round to the nearest quarter inch on a ruler
Round to the nearest quarter inch on a ruler to create a line plot and analyze the data
Round to the nearest eighth of a foot on a ruler
Round to the nearest eighth of an inch on a ruler to create a line plot and analyze the data
Topic B: Fractions as Division
To solidify their understanding of fractions as division, students work to convert between the two, using fractions greater than and less than one. They then work step by step to make sense of the remainder of a division problem as a fraction. Equipped with this understanding, students solve increasingly complex division word problems.
Rewrite division of whole numbers as a fraction based on a model
Rewrite division of whole numbers as a fraction and match a fraction to its related division equation
Relate division to fractions
Relate division to fractions greater than one
Divide and report the remainder as a fraction based on a model
Rename a fraction greater than one as a mixed number (Level 1)
Rename a fraction greater than one as a mixed number (Level 2)
Solve fraction word problems based on a model (Level 1)
Solve fraction word problems based on a model (Level 2)
Solve fraction word problems based on a model (Level 3)
Solve fraction word problems based on a model (Level 4)
Solve fraction word problems based on a model (Level 5)
Topic C: Multiplication of a Whole Number by a Fraction
Students begin by finding a unit fraction of a whole number and other fractions of a whole number using familiar models. They then relate that process to multiplication. To multiply a whole number by a fraction, students learn to find common factors and reduce either before or after multiplying.
Determine fractions of a whole number based on a model (Level 1)
Determine fractions of a whole number based on a model to solve a word problem
Determine fractions of a whole number based on a model (Level 2)
Determine fractions of a whole number based on a model (Level 3)
Determine a whole number given a fraction of that number based on a model
Multiply a whole number by a fraction
Relate a fraction of a whole number to multiplication and solve
Determine a fraction of a measurement by converting units and multiplying
Determine common factors of two whole numbers
Divide whole numbers by a common factor
Reduce a fraction by dividing by a common factor
Reduce factors before multiplying a whole number by a fraction (Level 1)
Reduce factors before multiplying a whole number by a fraction (Level 2)
Multiply a whole number by a fraction by reducing before or after multiplying
Topic D: Fraction Expressions and Word Problems
Students synthesize their understanding of fractions and operations to build and solve expressions. Familiar models support their learning, and word problems put the skills in context.
Match operations to the terms sum, difference, product, and quotient
Compose an expression based on text
Compose a compound expression based on text (Part 1)
Compose a compound expression based on text (Part 2)
Compose a compound expression based on text (Part 3)
Compose a compound equation based on a model and solve (Part 1)
Compose a compound equation based on a model and solve (Part 2)
Solve compound equations with parentheses and fractions
Solve a word problem by multiplying a whole number by a fraction (Level 1)
Solve a word problem by multiplying a whole number by a fraction (Level 2)
Topic E: Multiplication of a Fraction by a Fraction
Students learn to multiply fractions by starting with unit fractions and the support of an area model. They then progress to multiplication that involves mixed numbers, reducing, and units of measure.
Multiply unit fractions using an area model
Multiply fractions using an area model
Multiply fractions (reduce before multiplying)
Multiply fractions (reduce before or after multiplying)
Solve word problems by multiplying fractions using an area model
Rename a mixed number as a fraction to multiply by a fraction
Convert measurements by multiplying a whole number by a fraction
Convert measurements by multiplying fractions
Convert multiplication by a decimal to multiplication by a fraction and solve
Multiply by 0.1 using a place value chart
Multiply by 0.01 using a place value chart
Multiply by 0.1 or 0.01
Decompose a decimal number to multiply
Determine the placement of the decimal point in the product of two decimal numbers
Multiply two decimal numbers using column multiplication (Part 1)
Multiply two decimal numbers using column multiplication (Part 2)
Multiply two decimal numbers using column multiplication (Part 3)
Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems
Students explore the effects of multiplying by less than, equal to, and greater than 1. They solve multiplication problems, provide missing factors, and complete inequalities to solidify their understanding.
Multiply a fraction by a fraction equal to 1
Identify a missing factor as a fraction equal to 1
Identify patterns in multiplying by fractions less than, equal to, and greater than 1
Use <, =, and > to compare the result of multiplying by fractions less than, equal to, and greater than 1
Identify a fraction that will complete a multiplication inequality
Convert a fraction less than one to decimal form (Level 1)
Convert a fraction greater than one to decimal form
Convert a fraction less than one to decimal form (Level 2)
Convert a fraction less than one to decimal form using division
Convert a fraction greater than one to decimal form using division
Determine the outcome of multiplication using <, =, or > (Part 1)
Complete inequalities involving multiplication by a decimal number
Determine the outcome of multiplication using <, =, or > (Part 2)
Determine the outcome of multiplication using <, =, or > (Part 3)
Topic G: Division of Fractions and Decimal Fractions
Students rely upon their understanding of multiplying fractions to learn how to divide fractions. With the assistance of familiar models such as tape diagrams and area models, they learn different ways to approach dividing with fractions. At this stage, they use unit fractions with whole numbers and unit fractions with unit fractions.
Rewrite an equation with multiplication by a fraction as a division equation based on a model
Compose a division equation with a fraction based on a model
Divide a whole number by a unit fraction based on a tape diagram
Relate division by a unit fraction to multiplication by the denominator
Divide a whole number by a unit fraction by multiplying by the denominator
Divide a whole number by a unit fraction
Divide a unit fraction by a whole number based on a tape diagram (Part 1)
Divide a unit fraction by a whole number based on a tape diagram (Part 2)
Divide a unit fraction by a whole number
Multiply a unit fraction by a unit fraction with and without an area model (Part 1)
Multiply a unit fraction by a unit fraction with and without an area model (Part 2)
Relate division by a whole number to multiplication by a unit fraction
Solve division equations with unit fractions and whole numbers
Multiply a decimal number by a power of ten
Simplify a fraction using the basic property of fractions
Convert a fraction to a given denominator using the basic property of fractions
Convert between division expressions and fractions
Complete fraction expressions using the basic property of fractions
Convert fractions with decimal denominators to fractions with whole number denominators (Level 1)
Convert fractions with decimal denominators to fractions with whole number denominators (Level 2)
Convert fractions with decimal denominators to fractions with whole number denominators (Level 3)
Convert fractions with decimal denominators to fractions with whole number denominators (Level 4)
Convert division expressions with decimal divisors to expressions with whole number divisors (Level 1)
Convert division expressions with decimal divisors to expressions with whole number divisors (Level 2)
MODULE 5: Algebraic Expressions
Topic A: Solving Complex Missing Addend Equations
Students solve increasingly complex missing addend equations. In these pre-algebra equations, the challenge is not in the number values but in the logic of how numbers and equations can be combined to solve for numbers represented by symbols.