4 Nbt 5 Homework Helper

Number & Operations in Base Ten – 4th Grade

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

CCSS.Math.Content.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.

Teacher Notes
The teacher needs to understand how place value helps students find the product in multi-digit multiplication problem.  It is important to use multi-digit multiplication problems to reenforce place value. Example: “Four tens times three tens is twelve tens.  Regroup and put one in the hundreds and two in the tens.”
Students who develop flexibility in breaking numbers apart have a better understanding of the importance of place value and the distributive property in multi-digit multiplication.

Student Knowledge Goals

I know various strategies for multiplication (e.g., partial products, arrays, etc.).
I know that multiplication is the same as repeated addition.
I know visual models can be used to show multiplication.

I understand the properties of multiplication.
I can interpret and use visual models for multiplication.

I can explain the strategy I used to solve a multiplication problem.

I can show my thinking by creating rectangular arrays.
I can show my thinking by creating area models.
I can write an equation to a model of a multiplication problem.

Vocabulary
area model
Commutative Property of Multiplication
Distributive Property of Multiplication over Addition
equal groups
equation
factor
Identity Property of Multiplication
partial product
place value
product
rectangular array
strategy

Lessons
Engage NY Module 3 B-4 – Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically.
Engage NY Module 3 B-5 – Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns.
Engage NY Module 3 B-6 – Multiply two-digit multiples of 10 by two-digit multiples of 10 with the area model.
Engage NY Module 3 C-7– Multiplication of up to Four Digits by Single-Digit:  Use place value disks to represent two-digit by one-digit multiplication.
Engage NY Module 3 C-8 – Extend the use of place value disks to represent three- and four-digit by one-digit multiplication.
Engage NY Module 3 C-9 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.
Engage NY Module 3 C-10 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.
Engage NY Module 3 C-11 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.

Student Video Lessons
Learn Zillion – Multiply Multi-Digit Whole Numbers
Learn Zillion – Solve multiplication problems
Study Jams – Distributive Property
Virtual Nerd – Multiplication

Online Problems, Games, and Assessments
Khan Academy – Questions and Video Lessons
Multiply 1-digit numbers by 2-digit numbers
Multiply 1-digit numbers by 3-digit or 4-digit numbers
Multiplication patterns over increasing place values
Properties of multiplication
Distributive property: find the missing factor
Multiply using the distributive property
Multiply a 2-digit number by a 2-digit number: complete the missing steps
Multiply a 2-digit number by a 2-digit number
Multiply numbers ending in zeroes

Printables
Multiplication – Single & Multi-Digit
4.NBT.B.5 – 60 pages of PDF worksheets

 

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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

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 Read Aloud Task Card:
A Remainder of One
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:
Finding all Factors of a Number
Factor Riddles

Prime Numbers Investigation
Game: Climb the Factor Ladder
Game: How Many Factors?

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
Also included in 4th Grade Math Centers:
Triangular Numbers
Number Patterns
Patterns in Products
Patterns in Squares
Patterns in Rectangles

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?
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)
Game: Roll and Round: Nearest Hundred (4-digit)
Also included in 4th Grade Math Centers:
What's the Nearest Ten? (3-digit)
What's the Nearest Ten? (4-digit)
What's the Nearest Thousand? 
Roll and Round:
Nearest Ten (3-digit)

Nearest Thousand (5-digit)

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:
Make the Smallest Sum
Write and Solve
Addition and Subtraction Board

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
Use an Area Model to Multiply (v. 1-3)

Estimate Products by Rounding
Multiply by 10s, 100s and 1000s
Decompose a Factor

Multiplication Race (2 x 2-digit)
Double and Halve (v. 2)
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)
Write and Solve: Multiplication

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)
Write It, Solve It, Check It! (v. 1)
Write It, Solve It, Check It! (v. 2)
Remainders Game






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