4TH GRADE NUMBER

OPERATIONS AND ALGEBRAIC THINKING 

Use the four operations with whole numbers to solve problems

Numbers of the Week Use as morning work or homework.

4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Sample Activity:
Multiplication as Comparison Problems

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
Sample Activity:
Word Problems: Multiplicative Comparison

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Sample Activities:
Word Problems: Interpreting Remainders
Math Literature Link: A Remainder of One
Math Literature Link: Bean Thirteen
Math Literature Link: The Great Divide
Math Literature Link: Snowflake Bentley
Math Literature Link: 365 Penguins
Also included in 4th Grade Math Centers:
Word Problems: Multi-Step 
Remainder Riddle

Gain familiarity with factors and multiples

4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Sample Activities:
Exploring Multiples
Prime or Composite?
Also included in 4th Grade Math Centers:
Prime Numbers Investigation
Finding all Factors of a Number
Climb the Factor Ladder
How Many Factors?
Factor Riddles

Generate and analyze patterns

4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Sample Activity:
Square Numbers
Patterns in Squares
Also included in 4th Grade Math Centers:
Square Number Skyscraper
Patterns in Rectangles
Triangular Numbers
Patterns in Products
Numeric Patterns

NUMBER AND OPERATIONS IN BASE TEN 

Generalize place value understanding for multi-digit whole numbers

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700÷70=10 by applying concepts of place value and division.
Sample Activity:
Comparing Digits
Also included in 4th Grade Math Centers:
True or False? - Place Value Sort
True or False? - Rename It!

4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Sample Activities:
Place Value Triangle
Numeral, Word and Expanded Form
Also included in 4th Grade Math Centers:
What Number am I?
Place Value Puzzle
Compare

4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.
Sample Activities:
What's the Nearest Hundred? (4-digit)
Roll and Round: Nearest Hundred (4-digit)
Also included in 4th Grade Math Centers:
Roll and Round: Nearest Thousand (5-digit)
Roll and Round: Nearest Ten (3-digit)
What's the Nearest Ten? (3-digit)
What's the Nearest Ten? (4-digit)
What's the Nearest Thousand? 
What's the Nearest Ten Thousand?

Use place value understanding and properties of operations to perform multi-digit arithmetic

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Sample Activities:
Make the Largest Sum
Also included in 4th Grade Math Centers:
Addition and Subtraction Board
Make the Smallest Sum
Write and Solve (v. 1-2)

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
Sample Activities:
Use Partial Products to Multiply (v. 1-3)
Multiplication Strategy: Doubling and Halving
Double and Halve (v. 1)
Make the Largest Product (3 x 1-digit)
Multiplication Race (1 x 3-digit)
Also included in 4th Grade Math Centers:
Model Multiplication with Base Ten Blocks
Make the Largest Product (4 x 1-digit)
Make the Largest Product (2 x 2-digit)
Make the Smallest Product (3 x 1-digit)
Make the Smallest Product (4 x 1-digit)
Make the Smallest Product (2 x 2-digit)
Use an Area Model to Multiply (v. 1-3)
Estimate Products by Rounding
Multiply by 10s, 100s and 1000s
Write and Solve: Multiplication
Multiplication Race (2 x 2-digit)
Double and Halve (v. 2)
Decompose a Factor

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
Sample Activities:
Division Strategy: Partial Quotients (v. 1)
Division Strategy: Partition the Dividend (v. 1)
Estimate the Quotient (v. 1)
Also included in 4th Grade Math Centers:
Division Strategy: Partial Quotients (v. 2) 
Who Has the Largest Quotient? (v. 1)
Who Has the Largest Quotient? (v. 2)
Estimate the Quotient (v. 2)
Write It, Solve It, Check It! (v. 1)
Write It, Solve It, Check It! (v. 2)
Remainders 

NUMBER AND OPERATIONS: FRACTIONS

Extend understanding of fraction equivalence and ordering

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (nxa)/(nxb) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Sample Activity:
Build a Fraction Wall
Equivalent Fractions: Dominoes
Also included in 4th Grade Math Centers:
Equivalent Fractions on a Multiplication Grid
Equivalent Fractions: Set Model
Equivalent Fraction Roll
Is it Equivalent?

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with comparisons with symbols >, =, or <. and justify the conclusions, e.g., by using a visual fraction model.
Sample Activities:
Birthday Fractions 
Who Ate More?
Also included in 4th Grade Math Centers:
Comparing Fractions to a Benchmark 
Snack Time                      

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

4.NF.B.3 Understand a fraction a/b with a>1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Sample Activities:
Adding Like Fractions
Subtracting Like Fractions
Math Literature Link: Picture Pie (v. 2)
Also included in 4th Grade Math Centers:
Fraction Addition with Pattern Blocks
Sense or Nonsense Problems
Peter's Chocolate Bar 

b. Decompose a fraction into a sum of fraction with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8
Sample Activities:
Decompose a Fraction
Pizza Share 

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 
Sample Activities:
Add and Compare: Mixed Numbers
Also Included in 4th Grade Math Centers:
Word Problems: Adding and Subtracting Mixed Numbers 
Renaming Fractions Greater Than One
Subtract and Compare: Mixed Numbers

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Sample Activities:
Subtract and Compare
Included in 4th Grade Math Centers:
Word Problems: Adding and Subtracting Fractions
Write and Solve: Fractions
Add and Compare

4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number:
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product of 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).
Sample Activity:
Triangle Fractions
Also Included in 4th Grade Math Centers:
Multiply a Unit Fraction by a Whole Number
Quadrilateral Fractions

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) =(nxa)/b).
Sample Activity:
Multiply a Fraction by a Whole Number

c. Solve word problems involving multiplication of a fraction by a whole number, e.g. by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Sample Activity:
Math Literature Link: Full House
Also Included in 4th Grade Math Centers:
Word Problems:  Multiply a Fraction by a Whole Number 
Word Problems: Multiply a Mixed Number by a Whole Number 

Understand decimal notation for fractions, and compare decimal fractions

4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Sample Activity:
Sums of One
Also included in 4th Grade Math Centers:
Add Fractions with Denominators 10 & 100

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Sample Activity:
Fractions and Decimals

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Sample Activity:
Comparing Decimals
Also Included in 4th Grade Math Centers:
Decimal Sort