# Curriculum for Grade 4

## Driven by Pedagogy, Supported by Technology (and not vice versa),

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

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.

A. Relate tens to hundreds to thousands by magnitudes of 10 (Part 1)B. Relate tens to hundreds to thousands by magnitudes of 10 (Part 2)C. Exchange disks into the millions using a place value chartD. Multiply to show powers of 10 on a place value chartE. Complete multiplication expressions based on powers of 10F. Arrange place value labels in orderG. Divide to show powers of 10 on a place value chartH. Complete division expressions based on powers of 10I. Represent values of disks as numbers in standard form with commasJ. Identify comma placement in numbers to one millionK. Convert numbers from standard form to expanded formL. Identify the value of a digit in a given number

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.

A. Compare numbers in a place value chart (at their highest place value)B. Compare numbers in a place value chart (at a place value other than their highest)C. Compare numbers in a place value chart (at different place values)D. Complete inequalities comparing multi-digit numbersE. Order numbers in ascending and descending order using < and > (Part 1)F. Order numbers in ascending and descending order using < and > (Part 2)G. Order numbers in ascending and descending order using < and > (Part 3)H. Determine 1,000 more or less than a number using a place value chartI. Determine 10,000 more or less than a number using a place value chartJ. Determine 100,000 more or less than a number using a place value chartK. Complete a statement comparing numbers with and without a place value chart (1,000 or 10,000 more or less)L. Determine 1,000/10,000/100,000 more or less than a given numberM. Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 1)N. Order numbers in a pattern increasing or decreasing by 1,000 or 10,000 (Level 2)

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.

A. Determine the number that is halfway between two 4-digit numbers using a number lineB. Round a 4-, 5-, or 6-digit number to its highest place value using a number lineC. Round a 5- or 6-digit number to the thousands or ten thousands place using a number lineD. Round a multi-digit number to a given place valueE. Round a 6-digit number to various place values

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.

A. Add two 4-digit numbers with and without regrouping in one place using a disk modelB. Add two 4-digit numbers with and without regrouping in two places using column addition and a disk modelC. Add multi-digit numbers with regrouping in multiple places using column additionD. Add multi-digit numbers using the standard algorithm

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.

A. Subtract two 4-digit numbers with and without regrouping in one place using column subtraction and a disk modelB. Subtract two 4-digit numbers with and without regrouping in two places using column subtraction and a disk modelC. Subtract multi-digit numbers with regrouping in multiple places using column subtractionD. Subtract multi-digit numbers with regrouping across zeros using column subtractionE. Subtract multi-digit numbers using the standard algorithm

### MODULE 3. Multi-Digit Multiplication and Division

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.

A. Determine the area of a rectangle by multiplying the lengths of its sidesB. Identify the formula for area of a rectangle and use it to solve a problemC. Determine the area of a rectangle using the formula A = l x wD. Determine the side length of a rectangle based on its area and width using the formulaE. Identify the formula for perimeter of a rectangle and use it to solve a problemF. Identify the formula for perimeter of a rectangleG. Determine the perimeter of a rectangle using the formula P = 2 x (l + w)H. Determine the area and perimeter of the same rectangle

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.

A. Multiply a single-digit number by 10B. Multiply a single-digit number by 100C. Multiply a single-digit number by 1,000D. Multiply a 2-digit number by 10E. Multiply a 2-digit number by 100F. Multiply a 3-digit number by 10G. Multiply a 1-, 2-, or 3-digit number by 10, 100, or 1,000H. Multiply a 1-digit number by a round 2-digit number (Level 1)I. Multiply a 1-digit number by a round 3-digit number (Level 1)J. Multiply a 1-digit number by a round 2-digit number (Level 2)K. Multiply a 1-digit number by a round 3-digit number (Level 2)L. Multiply a 1-digit number by a round 2-digit number (Level 3)M. Multiply a 1-digit number by a round 3-digit number (Level 3)N. Solve multiplication equations with a 1-digit factor and a round 2- or 3-digit factorO. Multiply a 2-digit round number by a 2-digit round number (Level 1)P. Multiply a 2-digit round number by a 2-digit round number (Level 2)Q. Solve multiplication equations with round 2-digit factors

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.

A. Solve a multiplication equation using partial products with and without and a disk modelB. Solve a multiplication equation with regrouping using partial products with and without and a disk modelC. Solve a multiplication equation including a zero using partial products with and without and a disk modelD. Solve a multiplication equation using the standard algorithm with and without and a disk modelE. Solve a multiplication equation with regrouping using the standard algorithm using a disk modelF. Solve a multiplication equation with regrouping using the standard algorithm (Level 1)G. Solve a multiplication equation with regrouping using the standard algorithm (Level 2)H. Solve a multiplication equation with regrouping using the standard algorithm (Level 3)I. Solve a multiplication equation with regrouping using the standard algorithm (Level 4)J. Solve a multiplication equation with regrouping while identifying steps of the standard algorithmK. Solve a multiplication equation with regrouping using the standard algorithm (Level 5)L. Solve a single multiplication equation using both partial products and the standard algorithmM. Multiply to find the area of a rectangleN. Multiply to find the area of a rectangle using partial products (Level 1)O. Multiply to find the area of a rectangle using partial products (Level 2)

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.

A. Record a division problem and quotient (number in each group) based on a modelB. Record a division problem and quotient (number of groups) based on a modelC. Solve a division problem (number in each group) with a remainder based on a modelD. Solve a division problem (number of groups) with a remainder based on a modelE. Solve a division problem (number in each group) with a remainder using an array modelF. Solve a division problem (number of groups) with a remainder using an array modelG. Multiply to find multiples of a given numberH. List and identify multiples of a given numberI. Use multiples to find the quotient and remainder of a division problemJ. Model division (number in each group) with a remainder using a tape diagramK. Model division (number of groups) with a remainder using a tape diagramL. Solve a division problem with a remainder using the closest multiplication factM. Solve a division problem with a remainderN. Solve a division word problem (number of groups) with a remainder using a tape diagram and an equationO. Solve a division word problem (number in each group) with a remainder using a tape diagram and an equationP. Subtract using column subtractionQ. Model and solve a division problem, and identify the divisorR. Model and solve a division problem using long division (single-digit quotient)S. Solve a division problem (number in each group) with a remainder using a disk modelT. Model and solve a division problem using long division (two-digit quotient)U. Model and solve a division problem that involves regroupingV. Model and solve a division problem that involves regrouping using long division (two-digit quotient)W. Model and solve a division problem that involves regrouping using long division (two-digit quotient) (Level 2)X. Model and solve a division problem using long division by recording partial quotientsY. Use long division to solve problems with a 2-digit quotient

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.

A. Solve single-digit multiplication problemsB. Find factors of a given number by labeling arrays (Level 1)C. Find factors of a given number by labeling arrays (Level 2)D. Find factors of a given number by building and labeling arraysE. List factor pairs for a given number and identify the number as prime or compositeF. Determine whether a given number is a factor of another given numberG. Use long division to determine whether a given number is a factor of another given numberH. Use long division to show that if a number is a factor of another number, its factors are also factors of that numberI. Use properties of multiplication to show that if a number is a factor of another number, its factors are also factors of that numberJ. Determine multiples of a given factorK. Identify the relationship between factors, multiples, and divisible byL. Identify factors or multiples of a list of given numbersM. Use long division to determine whether a given number is a multiple of another given numberN. Use long division to show that if a number is a multiple of another number, it is also a multiple of that number's factorsO. 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 factorsP. Identify multiples of 2, 5, and 10 on a hundred chart and identify patterns in the ones place of the multiplesQ. Determine whether a given number is a multiple of 2, 5, or 10R. Determine whether a given number is even or oddS. Identify multiples of 3 and 9 on a hundred chart and identify patterns in the multiplesT. Determine whether a given number is a multiple of 3 or 9U. Identify factors (2, 3, 5, 10) of a given multipleV. 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