March 1

Module 4

In module 4, students rename fractions greater than 1 as mixed numbers, generate equivalent fractions, compare fractions with unlike units, and add and subtract fractions and mixed numbers with like units. Students also multiply fractions and mixed numbers by whole numbers.

TOPIC C Compare Fractions (5 LESSONS)

Students use various methods to compare fractions less than 1, fractions greater than 1, and mixed numbers. They consider the relationship between the numbers and use what they know about unit fractions to compare fractions to benchmark numbers such as 0, 1/2 , and 1. When the fractions have related numerators or denominators, students use what they know about generating equivalent fractions to rename one fraction to create a common numerator or common denominator. They rename both fractions as equivalent fractions to compare any two fractions. They use similar methods to compare fractions greater than 1 and mixed numbers.

TOPIC B Equivalent Fractions (6 lessons)

Students generate equivalent fractions and equivalent mixed numbers. They decompose fractional units to find an equivalent fraction with smaller units and record their work with multiplication. They compose fractional units to find an equivalent fraction with larger units and record their work with division. Students use area models, as well as tape diagrams and number lines, to represent fractions and compose or decompose fractional units to generate equivalent fractions.

TOPIC A Fraction Decomposition and Equivalence (6 lessons)

Students decompose fractions into a sum of unit fractions and into a sum of non-unit fractions. They use familiar models such as number bonds, tape diagrams, and number lines to represent fractions. They recognize that the area model may be a useful model to represent fractions. Students decompose fractions greater than 1 into a sum of a whole number and a fraction less than 1. This decomposition helps students rename fractions greater than 1 as equivalent mixed numbers. Students express mixed numbers as a sum of a whole number and a fraction less than 1. Then they rename the whole number as an equivalent fraction that they then add to the fraction. This helps students rename mixed numbers as equivalent fractions greater than 1.

Module 3

Multiplication and Division of Multi-Digit Numbers

In module 3, students multiply numbers of up to four digits by one-digit numbers and two-digit numbers by two-digit numbers. Students also divide numbers of up to four digits by one-digit numbers, resulting in whole-number quotients and remainders.

TOPIC B Division of Thousands, Hundreds, Tens, and Ones

Module 2

In module 2, students multiply two-digit numbers by one-digit numbers by using the distributive property. They divide two- and three-digit numbers by one-digit numbers by using the break apart and distribute strategy. Students apply their multiplication skills to convert customary units of length. They also identify factors and multiples of numbers within 100.

Topic A

Students begin multi-digit multiplication and division by multiplying and dividing multiples of 10 by one-digit numbers. They develop conceptual understanding by representing the multiplication and division with place value disks or on a place value chart and by naming multiples of 10 in unit form. Students multiply and divide by using equations. They apply the associative property of multiplication which allows them to make use of familiar facts to multiply (e.g., 5×60=5×6×10=(5×6)×10). To divide, students rename two-digit and three-digit multiples of 10 as tens to make use of familiar division facts, and they relate division to an unknown factor problem. Students multiply and divide to find the area or unknown side length of a rectangle with the newly formalized area formula: A = l x w.

Topic B

Students multiply two-digit numbers by one-digit numbers by using the distributive property. They decompose the two-digit numbers into tens and ones and then multiply each part by the one-digit number. Students use a place value chart, an area model, and equations to represent the multiplication. Equations are written in both unit form and standard form to record the multiplication represented in the models. When multiplying by using equations, they write or think about numbers in unit form and recognize that, although the units change, the multiplication facts are familiar. Students apply their learning to solve one-step word problems. An optional lesson at the end of the topic provides an opportunity for students to use simplifying strategies, such as compensation and decomposition, to multiply.

Module 1

TOPIC C Rounding Multi-Digit Whole Numbers 6 LESSONS: 10-15

Students name multi-digit numbers in unit form in different ways by using smaller units (e.g., 245,000 as 24 ten thousands 5 thousands or 245 thousands), and they find 1 more or 1 less of a given unit in preparation for rounding on a vertical number line. Students round four-digit, five-digit, and six-digit numbers to the nearest thousand, ten thousand, and hundred thousand. They determine an appropriate rounding strategy to make useful estimates for a given context.

TOPIC B Place Value and Comparison within 1,000,000 5 Lessons: 5-9

Students name the place value units of ten thousand, hundred thousand, and million. They recognize the multiplicative relationship between place value units—the value of a digit in one place is ten times as much as the value of the same digit in the place to its right. Students write and compare numbers with up to 6 digits in standard, expanded, word, and unit forms.

Students identify, represent, and interpret multiplicative comparisons in patterns, tape diagrams, multiplication equations, measurements, and units of money. They describe the relationship between quantities as times as much as or use other language as applicable to a given context (e.g., times as many as, times as long as, times as heavy as). Students use multiplication or division to find an unknown quantity in a comparison.
• How can you describe a multiplication relationship between numbers?
• How can multiplication equations and tape diagrams represent times as many situations?

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