# Curriculum for Grade 4

As students develop a more abstract understanding of numbers, we stretch their skills in both directions - with multi-digit whole numbers as well as decimals and fractions. Students learn traditional algorithms as well as other approaches that build math flexibility and fluency. In addition to performing operations with these numbers, students learn new ways to measure, convert units, round numbers, and compare numbers. A firm understanding of place value is the common thread running through all topics.

## MODULE 1. Place Value, Rounding, and Algorithms for Addition and Subtraction

### Topic A: Place Value of Multi-Digit Whole Numbers

Students work with whole numbers to 1,000,000 using number disks and the place value chart. They develop understanding of magnitudes of 10, as well as how multiplication and division relate to place value. Students also master the skill of recording large numbers, both in standard form with the appropriate commas and in expanded form.

#### Model multiplication by 10 using a disk model (Level 1)

#### Model multiplication by 10 using a disk model (Level 2)

#### Solve multiplication by 10 in unit form and number form

#### Solve multiplication by 10 in unit form and number form and model on a place value chart

#### Model division by 10 using a disk model (Level 1)

#### Model division by 10 using a disk model (Level 2)

#### Solve division by 10 in unit form and number form

#### Solve division by 10 in unit form and number form and model on a place value chart

### Topic B: Comparing Multi-Digit Whole Numbers

Students work with numbers in the thousands, ten thousands, and hundred thousands. Building upon previous knowledge, such as use of inequality symbols, they deepen their understanding of how to compare large numbers to several place values or numbers of different place value. As part of this understanding, they build their fluency in the base-10 system by finding 1,000, 10,000 and 100,000 more or less than a number.

#### Compare numbers in a place value chart (at their highest place value)

#### Compare numbers in a place value chart (at a place value other than their highest)

#### Compare numbers in a place value chart (at different place values)

#### Complete inequalities comparing multi-digit numbers

#### Order numbers in ascending and descending order using < and > (Part 1)

#### Order numbers in ascending and descending order using < and > (Part 2)

#### Order numbers in ascending and descending order using < and > (Part 3)

#### Determine 1,000 more or less than a number using a place value chart

#### Determine 10,000 more or less than a number using a place value chart

#### Determine 100,000 more or less than a number using a place value chart

#### Complete a statement comparing numbers with and without a place value chart (1,000 or 10,000 more or less)

#### Determine 1,000/10,000/100,000 more or less than a given number

#### Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 1)

#### Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 2)

### Topic C: Rounding Multi-Digit Whole Numbers

Using a number line to provide context, students first determine the midway point between two multi-digit numbers. They then progress to rounding using the number line and the midway point. Finally, students round 4-, 5-, and 6-digit numbers to any given place value without use of the number line.

#### Determine the midway point between two multi-digit numbers using a number line

#### Determine whether a number is greater or less than the midway point between two multi-digit numbers using a number line

#### Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 1)

#### Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 1)

#### Determine whether a multi-digit number rounds up or down to a given place value using a number line (Part 2)

#### Round a multi-digit number to the nearest thousand

#### Determine the round numbers nearest a given multi-digit number and whether that number rounds up or down using a number line (Part 2)

#### Determine whether a multi-digit number rounds up or down to a given place value (Part 1)

#### Determine whether a multi-digit number rounds up or down to a given place value (Part 2)

#### Round a multi-digit number to a given place value (Level 1)

#### Round a multi-digit number to a given place value (Level 2)

#### Round a multi-digit number to a given place value (Level 3)

#### Round a multi-digit number to various place values

### Topic D: Multi-Digit Whole Number Addition

Students use column addition to add multi-digit numbers. They begin with the support of a disk model to illustrate the underlying concepts. They learn to record addition problems as column addition, how to regroup and record this action, how to line up numbers of varying length, and how to regroup to a place value higher than the original numbers.

#### Add two 4-digit numbers with and without regrouping in one place using a disk model

#### Add two 4-digit numbers with and without regrouping in two places using column addition and a disk model

#### Add two 4-digit numbers with and without regrouping in one place using a disk model part II

#### Add multi-digit numbers with regrouping in multiple places using column addition

#### Add multi-digit numbers using the standard algorithm

### Topic E: Multi-Digit Whole Number Subtraction

Students use column subtraction to subtract multi-digit numbers. They begin with the support of a disk model to illustrate the underlying concepts. They learn to record subtraction problems as column subtraction, how to regroup and record this action, how to line up numbers of varying length, and how to regroup across zeros.

#### Subtract two 4-digit numbers with and without regrouping in two places using column subtraction and a disk model

#### Subtract multi-digit numbers with regrouping in multiple places using column subtraction

#### Subtract multi-digit numbers with regrouping across zeros using column subtraction

#### Subtract multi-digit numbers using the standard algorithm

## MODULE 2. Multi-Digit Multiplication and Division

### Topic A: Finding Area and Perimeter of a Rectangle

Students apply their understanding of measurement and area models to use the formulas for area and perimeter of a rectangle. They use the area model to find both the area and a missing side length. Students identify different ways of writing the same formula for both area and perimeter.

#### Determine the area of a rectangle by multiplying the lengths of its sides

#### Identify the formula for area of a rectangle and use it to solve a problem

#### Determine the area of a rectangle using the formula A = l x w

#### Determine the side length of a rectangle based on its area and width using the formula

#### Identify the formula for perimeter of a rectangle and use it to solve a problem

#### Identify the formula for perimeter of a rectangle

#### Determine the perimeter of a rectangle using the formula P = 2 x (l + w)

#### Determine the area and perimeter of the same rectangle

### Topic B: Multiplication by 10, 100, and 1,000

Students extend their understanding of multiplication to include powers of ten. They begin each exercise with the assistance of a place value chart, which illustrates the meaning behind the operation. Then, they build their fact fluency by solving equations mentally.

#### Multiply by 10 with and without a disk model

#### Multiply by 100 with and without a disk model

#### Multiply by 1,000 with and without a disk model

#### Divide by 10 with and without a disk model

#### Divide by 100 with and without a disk model

#### Divide by 1,000 with and without a disk model

#### Multiply a 1-, 2-, or 3-digit number by 10, 100, or 1,000

#### Multiply a 1-digit number by a round 2-digit number (Level 1)

#### Multiply a 1-digit number by a round 3-digit number (Level 1)

#### Multiply a 1-digit number by a round 2-digit number (Level 2)

#### Multiply a 1-digit number by a round 3-digit number (Level 2)

#### Multiply a 1-digit number by a round 2-digit number (Level 3)

#### Multiply a 1-digit number by a round 3-digit number (Level 3)

#### Solve multiplication equations with a 1-digit factor and a round 2- or 3-digit factor

#### Multiply a 2-digit round number by a 2-digit round number

### Topic C: Multiplication of up to Four Digits by Single-Digit Numbers

Students are gradually scaffolded through the steps of multiplying a multi-digit number by a single-digit number using the standard algorithm. They begin using a concrete disk model and a partial products method of recording. As they begin to work with the standard algorithm, they become more skilled and independent by regrouping, using zeros, using larger numbers, and receiving fewer prompts.

#### Solve a multiplication equation using partial products with and without and a disk model

#### Solve a multiplication equation with regrouping using partial products with and without and a disk model

#### Solve a multiplication equation including a zero using partial products with and without and a disk model

#### Solve a multiplication equation using the standard algorithm with and without and a disk model

#### Solve a multiplication equation with regrouping using the standard algorithm using a disk model

#### Solve a multiplication equation with regrouping using the standard algorithm (Level 1)

#### Solve a multiplication equation with regrouping using the standard algorithm (Level 2)

#### Solve a multiplication equation with regrouping using the standard algorithm (Level 3)

#### Solve a multiplication equation with regrouping using the standard algorithm (Level 4)

#### Solve a multiplication equation with regrouping while identifying steps of the standard algorithm

#### Solve a multiplication equation with regrouping using the standard algorithm (Level 5)

#### Solve a single multiplication equation using both partial products and the standard algorithm

#### Multiply to find the area of a rectangle

#### Multiply to find the area of a rectangle using partial products (Level 1)

#### Multiply to find the area of a rectangle using partial products (Level 2)

### Topic D: Division of Tens and Ones with Successive Remainders

Students divide 1- and 2-digit numbers to determine the number in each group or the number of groups. They use models to illustrate a word problem and equations to record their work. Students are introduced to the term "quotient" and a method for checking their answer. Students move from simple division to division with a remainder in this topic, and they learn to use long division notation.

#### Solve a division problem (number in each group) with a remainder based on a model

#### Solve a division problem (number of groups) with a remainder based on a model

#### Solve a division problem (number in each group) with a remainder using an array model

#### Solve a division problem (number of groups) with a remainder using an array model

#### Multiply to find multiples of a given number

#### List and identify multiples of a given number

#### Use multiples to find the quotient and remainder of a division problem

#### Model division (number in each group) with a remainder using a tape diagram

#### Model division (number of groups) with a remainder using a tape diagram

#### Solve a division problem with a remainder using the closest multiplication fact

#### Solve a division problem with a remainder

#### Solve a division word problem (number of groups) with a remainder using a tape diagram and an equation

#### Solve a division word problem (number in each group) with a remainder using a tape diagram and an equation

#### Model and solve a division problem, and identify the divisor

#### Model and solve a division problem using long division (single-digit quotient)

#### Solve a division problem (number in each group) with a remainder using a disk model

#### Model and solve a division problem using long division (two-digit quotient)

#### Model and solve a division problem that involves regrouping

#### Model and solve a division problem that involves regrouping using long division (two-digit quotient)

#### Model and solve a division problem that involves regrouping using long division (two-digit quotient) (Level 2)

#### Model and solve a division problem using long division by recording partial quotients

#### Use long division to solve problems with a 2-digit quotient

### Topic E: Reasoning with Divisibility

Students build a firm understanding of the concepts of factor, multiple, and divisible by, as well as the relationship among those concepts. They explore divisibility patterns/rules for 2, 3, 5, 6, 9, and 10. To build this understanding, students use manipulatives, arrays, long division, and the hundred chart.

#### Solve single-digit multiplication problems

#### Find factors of a given number by labeling arrays (Level 1)

#### Find factors of a given number by labeling arrays (Level 2)

#### Find factors of a given number by building and labeling arrays

#### List factor pairs for a given number and identify the number as prime or composite

#### Determine whether a given number is a factor of another given number

#### Use long division to determine whether a given number is a factor of another given number

#### Use long division to show that if a number is a factor of another number, its factors are also factors of that number

#### Use properties of multiplication to show that if a number is a factor of another number, its factors are also factors of that number

#### Determine multiples of a given factor

#### Identify the relationship between factors, multiples, and divisible by

#### Identify factors or multiples of a list of given numbers

#### Use long division to determine whether a given number is a multiple of another given number

#### Use long division to show that if a number is a multiple of another number, it is also a multiple of that number's factors

#### Use properties of multiplication to show that if a number is a multiple of another number, it is also a multiple of that number's factors

#### Identify multiples of 2, 5, and 10 on a hundred chart and identify patterns in the ones place of the multiples

#### Determine whether a given number is a multiple of 2, 5, or 10

#### Determine whether a given number is even or odd

#### Identify multiples of 3 and 9 on a hundred chart and identify patterns in the multiples

#### Determine whether a given number is a multiple of 3 or 9

#### Identify factors (2, 3, 5, 10) of a given multiple

#### Use a hundred chart to show that multiples of 2 and 3 are multiples of 6, and that multiples of 2 and 5 are multiples of 10

### Topic F: Division of Thousands, Hundreds, Tens, and Ones

Students divide numbers in the hundreds and thousands by single-digit numbers. They move from unit notation to standard notation to help facilitate mental math with large numbers. Understanding of the standard algorithm is supported by familiar models - a disk model and tape diagrams. Students are supported in dealing with various division challenges from regrouping to remainders to working with zero.

#### Multiply using unit notation and standard notation

#### Divide using a disk model

#### Divide using a disk model (with regrouping)

#### Divide using unit notation and standard notation (Level 1)

#### Divide using unit notation and standard notation (Level 2)

#### Divide using standard notation

#### Divide using a disk model (with regrouping) (Part 1)

#### Divide using long division and a disk model (with regrouping and a remainder) (Part 1)

#### Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

#### Divide using a disk model (with regrouping) (Part 3)

#### Divide using long division and a disk model (with regrouping and a remainder) (Part 2)

#### Divide using long division and a disk model (with regrouping and a remainder) (Part 3)

#### Divide using long division and a disk model (with regrouping and a remainder) (Part 4)

#### Divide using long division with partial quotients and a disk model

#### Divide using long division with partial quotients (Level 1)

#### Divide using long division with partial quotients (Level 2)

#### Divide across a zero using a disk model (with regrouping and a remainder)

#### Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 1)

#### Divide using a disk model with zero in the quotient (with regrouping)

#### Divide using long division and a disk model with zero in the quotient (with regrouping)

#### Divide across a zero using long division and a disk model (with regrouping and a remainder) (Part 2)

#### Solve division problems with a quotient of zero (with a remainder) (Level 1)

#### Solve division problems with a quotient of zero (with a remainder) (Level 2)

#### Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 1

#### Divide across a zero using long division with partial quotients and a disk model (with regrouping and a remainder) Part 2

#### Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 1

#### Divide across a zero using long division with partial quotients (with regrouping and a remainder) Part 2

#### Solve division word problems using long division and a tape diagram (with regrouping and a remainder)

#### Solve division word problems using long division and a tape diagram (with regrouping)

#### Divide using long division with partial quotients (Level 3)

#### Solve division word problems across zero using long division and a tape diagram (with regrouping)

#### Solve division word problems using long division and a tape diagram (with a remainder)

### Topic G: Multiplication of Two-Digit by Two-Digit Numbers

Students apply their prior knowledge of multiplication to multiply a 2-digit number by a 2-digit number. They use familiar tools and strategies, including a disk model, an area model, partial products, the distributive property, and the standard algorithm. To support their learning, students work extensively with multiples of 10.

#### Multiply a 2-digit number by 10

#### Identify a round number as a multiple of 10

#### Solve a word problem two different ways by regrouping factors

#### Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 last)

#### Multiply by splitting a round number into a multiple of 10 and regrouping factors based on a disk model (multiply by 10 first)

#### Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 1)

#### Multiply by splitting a round number into a multiple of 10 and regrouping factors (Level 2)

#### Rewrite an area model multiplication equation using the distributive property

#### Multiply to find the area of a rectangle using the distributive property

#### Multiply using partial products and the standard algorithm (one round number)

#### Multiply to find the area of a rectangle using the distributive property and the standard algorithm

#### Multiply using partial products and the standard algorithm

#### Multiply using the standard algorithm (one round number)

#### Multiply using the standard algorithm with regrouping (one round number)

#### Multiply using partial products and the standard algorithm with regrouping (Part 1)

#### Multiply using partial products and the standard algorithm with regrouping (Part 2)

#### Multiply using the standard algorithm (one round number)

## MODULE 3. Fraction Equivalence, Ordering, and Operations

### Topic A: Decomposition and Fraction Equivalence

Students learn everything about what a fraction is, how it is written, what it represents, and what its parts are called. They work with fractions both less than and greater than 1 as they model, record, and rename fractions. They explore fractions as part of a whole and also as points on a number line.

#### Label a shaded figure using fraction notation and shade a given fraction of a figure

#### Label a shaded figure using fraction notation and shade a given fraction of a figure (fractions greater than 1)

#### Label a missing fraction on a labeled number line

#### Place a fraction on a number line

#### Identify numerator and denominator in a fraction

#### Identify fractions with a given numerator or denominator

#### Model a fraction as the sum of its parts and record this as an equation

#### Model a fraction as the sum of its parts and record this as an equation (fractions greater than one)

#### Record a fraction as the sum of its parts

#### Record repeated addition of whole numbers as multiplication

#### Record repeated addition of fractions as multiplication

#### Record repeated addition of fractions as multiplication (fractions greater than 1)

#### Identify the multiplication expression that matches a given fraction

### Topic B: Fraction Equivalence Using Multiplication and Division

Students compose equivalent fractions based on a model. They then label the fractions and identify the factor or divisor that relates one to the other.

#### Identify, label, and compare equivalent fractions

#### Divide a model in two different ways to show and label equivalent fractions

#### Multiply to find equivalent fractions based on a model

#### Multiply to find equivalent fractions with and without a model

#### Complete the numerator or denominator in a larger equivalent fraction

#### Divide to find equivalent fractions based on a model

#### Divide to find equivalent fractions with and without a model

#### Complete the numerator or denominator in a smaller equivalent fraction

#### Solve problems related to equivalent fractions and multiplier

### Topic C: Fraction Comparison

Using familiar models and the number line, along with their ability to find equivalent fractions, students compare fractions. They explore strategies to find a common numerator or denominator, or to compare to a benchmark. Students work with fractions greater than and less than one.

#### Label and compare fractions with like denominators or like numerators based on a model

#### Place fractions with like denominators or like numerators on a number line and compare

#### Order four fractions with like denominators or like numerators based on a model

#### Compare fractions with like denominators or like numerators

#### Compare fractions to ½ with and without a number line

#### Solve word problems comparing a fraction to ½ using an equivalent fraction

#### Compare fractions by comparing each one to ½

#### Compare fractions by comparing each one to 1

#### Choose a strategy and use it to compare fractions

#### Compare fractions by comparing the remaining unit fraction using a number line and model

#### Compare fractions by finding a common numerator (when one numerator is a multiple of the other)

#### Compare fractions by finding a common denominator (when one denominator is a multiple of the other)

#### Compare fractions by finding a common denominator (when one denominator is not a multiple of the other)

#### Compare fractions by finding a common numerator or denominator (when one is a multiple of the other)

### Topic D: Fraction Addition and Subtraction

Students apply their understanding of fraction basics to add and subtract fractions. They work with familiar models and the number line to build understanding of the concepts behind the operations. In solving addition and subtraction problems, students convert among equivalent fractions, mixed numbers, and improper fractions.

#### Identify and add fractions with a common denominator based on a model

#### Add fractions with a common denominator with and without a number line

#### Add fractions with a common denominator

#### Add fractions with a common denominator and convert the sum to a mixed number (Level 1)

#### Subtract fractions with a common denominator with and without a number line

#### Subtract fractions with a common denominator with and without a number line

#### Subtract a fraction from 1

#### Rename a mixed number as a fraction to subtract a fraction

#### Subtract a fraction from a mixed number with and without renaming the mixed number as a fraction

#### Rename a fraction as an equivalent fraction

#### Add fractions with different denominators by finding a common denominator

#### Add fractions with different denominators and rename the sum as a mixed number

### Topic E: Extending Fraction Equivalence to Fractions Greater Than 1

To prepare for more complex work with addition and subtraction, students establish a firm understanding of mixed numbers and fractions greater than 1. They convert fractions to mixed numbers and vice versa. They find common denominators when one denominator is a factor of the other and when it is not.

#### Identify fractions as greater than, less than, or equal to 1

#### Label a model with a mixed number and identify its written form

#### Identify a mixed number on a number line

#### Label a model with a mixed number and a fraction greater than 1

#### Rename a mixed number as a fraction greater than 1 based on a model

#### Rename a mixed number as a fraction greater than 1

#### Rename a fraction greater than 1 as a mixed number based on a model

#### Rename a fraction greater than 1 as a mixed number

#### Match fraction addition to a mixed number and a fraction greater than 1

#### Identify a fraction greater than 1 and rename it as a mixed number

#### Label models with mixed numbers and compare using <, =, or >

#### Compare mixed numbers with different denominators (Part 1)

#### Compare fractions greater than 1 by renaming them as mixed numbers

#### Compare a fraction greater than 1 with a mixed number or a fraction greater than 1

#### Compare mixed numbers with different denominators (Part 2)

#### Compare mixed numbers with different denominators (Part 3)

#### Compare fractions greater than 1

### Topic F: Addition and Subtraction of Fractions by Decomposition

Students rely heavily on their understanding of fractions and mixed numbers to complete operations. To add and subtract, they break apart, regroup, and rename numbers. They gradually move from a step-by-step guided strategy to solving problems mentally.

#### Round a mixed number to the nearest whole with and without a number line

#### Estimate the sum or difference of two mixed numbers by rounding them to the nearest whole

#### Round an improper fraction to the nearest whole by converting it to a mixed number

#### Round mixed numbers and improper fractions to the nearest whole

#### Estimate the sum or difference of a mixed number and an improper fraction by converting the fraction to a mixed number

#### Add a whole number to a mixed number

#### Add a mixed number to a fraction with the same denominator

#### Add a mixed number to a fraction with the same denominator and write the sum without an improper fraction

#### Add a mixed number to a fraction with the same denominator by completing the whole (Level 1)

#### Add a mixed number to a fraction with the same denominator by completing the whole (Level 2)

#### Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 1)

#### Add two mixed numbers with the same denominator and write the sum without an improper fraction (Level 2)

#### Subtract a fraction from a mixed number with the same denominator (without converting to an improper fraction)

#### Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 1)

#### Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction (Level 2)

#### Subtract mixed numbers with the same denominator

#### Add and subtract mixed numbers with the same denominator

### Topic G: Repeated Addition of Fractions as Multiplication

Students translate their understanding of addition of fractions to multiplication. They transition from work with unit fractions to other fractions and mixed numbers. In solving equations and word problems, students rename solutions as mixed numbers without a fraction greater than 1.

#### Write a fraction as a sum of unit fractions

#### Identify multiplication of a unit fraction by a whole number that matches a given fraction

#### Multiply a whole number by a fraction by splitting it into a multiple of a unit fraction

#### Multiply a whole number by a fraction

#### Write repeated addition of fractions as a multiplication statement and rename the product as a mixed number

#### Multiply a whole number by a mixed number

#### Multiply a whole number by a mixed number and rename without a fraction greater than 1

#### Solve a word problem by multiplying a whole number by a mixed number

## MODULE 4. Decimal Fractions

### Topic A: Exploration of Tenths

Students develop their understanding of the decimal form of fractions in the tenths. The rely on familiar representations such as the number line, place value chart, and fraction models to support understanding. Students convert fractions less than and greater than one from fraction form to decimal form and word form.

#### Relate fractions in tenths to decimals with and without a number line

#### Rewrite a fraction in tenths as a decimal, and vice versa

#### Match fractions in tenths to their decimal form and word form

#### Determine how many more tenths to make a whole using a number line

#### Represent mixed numbers in decimal form using a number line

#### Rewrite a mixed number with tenths as a decimal, and vice versa

#### Convert between fraction form, decimal form, and word form with mixed numbers with tenths

#### Determine how many more tenths to make the next whole using a number line

#### Record a fraction model as a mixed number or a decimal with tenths

#### Relate tenths to one whole using a place value chart

#### Represent numbers greater than 10 tenths in decimal form

### Topic B: Tenths and Hundredths

Students hone their understanding of tenths, hundredths, and the relationship between the two. Beginning with fractional parts only, students convert between fraction, decimal, and unit form. After mastering this, they work with mixed numbers. Along the way, their understanding is supported by area models, disk models, and number lines.

#### Identify hundredths using fraction and decimal notation

#### Match hundredths decimals to unit form and rewrite a hundredths decimal in unit form

#### Label tenths and hundredths on an area model using fraction and decimal form

#### Compare equivalent tenths and hundredths in decimal form

#### Match equivalent tenths and hundredths in decimal and unit form

#### Show tenths and hundredths equivalencies using a disk model

#### Represent a hundredths number using a disk model

#### Identify points in the hundredths on a number line

#### Label a mixed number on an area model using fraction and decimal form

#### Match mixed numbers in fraction and decimal form, and rewrite a mixed number fraction in decimal form

#### Label a mixed number based on a disk model

### Topic C: Decimal Comparison

Students compare decimals in the hundredths using inequality signs and ordering. They rely on familiar representations of the area model, number line, and place value chart to build understanding. They also compare decimals to fractional numbers in unit form and fraction form.

#### Use <, =, and > to compare decimal measurements of length, mass, and volume

#### Use <, =, and > to compare decimal numbers based on an area model

#### Use <, =, and > to compare decimal numbers based on a number line

#### Use <, =, and > to compare decimal numbers based on a place value chart

#### Complete an inequality by choosing a mixed number, decimal, or decimal in unit form

#### Complete a double inequality statement based on measurements of length, mass, and volume

#### Order decimal numbers in a double inequality statement based on a number line

#### Order decimal numbers in a double inequality statement

#### Order four decimal numbers in ascending order

#### Order decimals, fractions, and decimal numbers in unit form in a double inequality statement based on a number line

#### Order decimals, mixed numbers, and decimal numbers in unit form in a double inequality statement

#### Order four decimals, mixed numbers, and decimal numbers in unit form in ascending order

### Topic D: Addition with Tenths and Hundredths

Students rely on their mastery of converting between decimals, fractions, and mixed numbers in order to add tenths and hundredths. They learn how to add different units (tenths to hundredths) in both fraction and decimal form. They also learn to record their sum without improper fractions.