Download Mathematics Pacing Resource Document

Mathematics Pacing Resource Document
4.C.7
Standard: 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication
(associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the
distributive property.
Teacher Background Information:
This standard references properties (rules about how numbers work) of multiplication. This extends past previous expectations, in which students
were asked to identify properties. While students DO NOT need to not use the formal terms of these properties, student must understand that
properties are rules about how numbers work, and they need to be flexibly and fluently applying each of them in various situations. Students represent
expressions using various objects, pictures, words and symbols in order to develop their understanding of properties. They multiply by 1 and 0 and
divide by 1. They change the order of numbers to determine that the order of numbers does not make a difference in multiplication (but does make a
difference in division). Given three factors, they investigate changing the order of how they multiply the numbers to determine that changing the order
does not change the product. They also decompose numbers to build fluency with multiplication.
The associative property states that the sum or product stays the same when the grouping of addends or factors is changed. For example, when a
student multiplies 7 x 5 x 2, a student could rearrange the numbers to first multiply 5 x 2 = 10 and then multiply 10 x 7 = 70.
Example:
The commutative property (order property) states that the order of numbers does not matter when you are adding or multiplying numbers. For
example, if a student knows that 6 x 3 = 18, then they also know that 3 x 6 = 18. The array below could be described as a 6 x 3 array for 6 columns and
3 rows, or a 3 x 6 array for 3 rows and 6 columns. There is no “fixed” way to write the dimensions of an array as rows x columns or columns x rows.
Students should have flexibility in being able to describe both dimensions of an array.
It is not intuitively obvious to children that 3 x 8 is the same as 8 x 3 or that, in general, the order of the numbers makes no difference.
Example:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.7
Standard: 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication
(associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the
distributive property.
Teacher Background Information:
It may not be essential for students to know the distributive property in the form of a x (b + c) = (a x b) + (a x c).
But the concept involved is very useful in relating one basic fact to another, and it is also involved in the development of two-digit computation.
The distributive property of multiplication refers to the idea that either one of the two factors in a product can be decomposed into two or more parts
and each part multiplied separately and then added.
Distributive Property
Students are introduced to the distributive property of multiplication over addition as a strategy for using products they know to solve products they do not
know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16
or 56. Students should learn that they can decompose either of the factors. It is important to note that the students may record their thinking in different ways.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.7
Standard: 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication
(associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the
distributive property.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions
o Fluency Plan (FP) Lesson 3
o FP Lesson 16

http://www.ixl.com/math/grade-4/properties-of-multiplication

http://www.studyzone.org/mtestprep/math8/e/multprop_6p.cfm

http://www.aaamath.com/pro74bx2.htm definitions and examples of commutative,
associative, distributive properties

http://reviewgamezone.com/game.php?id=2646


http://www.math-aids.com/Properties/Property_Identifying.html question generator
http://www.glencoe.com/sec/math/brainpops/00112039/00112039.html
BrainPop Scroll down to “Chapter 1” and click on Commutative Property

http://www.lessonplanspage.com/MathArtCommutativeProperty35.htm lesson plan

BrainPop Click on ”Distributive Property” under Chapter 1.

http://illuminations.nctm.org/Lesson.aspx?id=1820 NCTM Illuminations:
Commutative Rectangle

http://www.glencoe.com/sec/math/brainpops/00112040/00112040.html
BrainPop Scroll down to “Chapter 1” and click on Associative Property

http://studyjams.scholastic.com/studyjams/jams/math/multiplicationdivision/distrib-property.htm Scholastic online tutorial and quiz

Harcourt School E-lab with visual models


http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-andmultiples/cc-6th-distributive-property/v/the-distributive-property Khan Academy
videos
https://www.mathscore.com/math/practice/Distributive%20Property/
Distributive property practice online

http://www.quia.com/ba/15357.html Battleship

http://www.quia.com/pages/jspicer/page22 online quizzes

http://learnzillion.com/lessons/1877-use-an-area-model-to-multiply-a-three-digitnumber-by-a-one-digit-number Learn Zillion lesson (multiplication with an area
model)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.7
Standard: 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication
(associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the
distributive property.
Item Bank:
1) Choose the number that makes the number sentence true. [IPS C&I] Answer: D
1 × (3 × 5) = (1 × 3) × ____
A. 1
B. 3
C. 4
D. 5
2) Suppose you are finding 6 × 2 × 5 mentally. Which number sentence correctly shows another way to arrange the numbers to make the mental math easier?
[IPS C&I] Answer: C
A. 6 × 2 + 5 = 17
C. 5 × 2 × 6 = 60
B. 2 × 6 × 5 = 50
D. 6 + 2 × 5 = 16
3) Which number replaces the ? to make the equation true? [IPS C&I] Answer: A
7 × (5 + 3) = (7 × ?) + (7 × 3)
A. 5
B. 7
Indianapolis Public Schools
C. 8
D. 35
Curriculum and Instruction
Mathematics Pacing Resource Document
(Readiness Form II)
Indianapolis Public Schools
Curriculum and Instruction