Download Associative property of multiplication.

PS/IS 276 Grade 3 Parent
Math Workshop
Models for Multiplication
February 28, 2013
Welcome!
 While you’re getting settled, please help us figure something
out:
 Rebecca has 26 students in her class. If they count by fives
around the class, what number will the 26th student say?
Here’s how Rebecca’s kids solved the
same problem
Ben said:
“I know that 20 groups of 5 is 100, and 6 groups of 5 is 30, so I put the
100 and the 30 together to make 130.”
(Ben is making sense of the distributive property. He may not know
that he is doing this, but he just solved the problem like this:
5(20 + 6) = 130
5 x 20 = 100
5 x 6 = 30
100 + 30 = 130
Here’s how Rebecca’s kids solved the
same problem
Nate said that he knew that when we count by tens 26 times, we
land on 260. Since 5 is half of 10, we can cut the 260 in half to
get 130.
Nate knows that skip-counting and multiplication are related.
This is the equation he is actually solving:
10 x 26 ÷ 2 = 130
Here’s how Rebecca’s kids solved the
same problem
Tate knew that 26 x 10 =260, so to figure out a “x5 combo”
instead of a “times 10 combo,” he halved the 260. First he
halved 200 to make 100, and then he halved 60 to make thirty,
then he added them together to make 130, so 26 x 5 =130.
26 x 10 =260
260 x ½ = 130
The Common Core Standards for
grade 3 and 4 state:
 Students develop fluency with efficient
procedures for multiplying and dividing whole
numbers; understand and explain why the
procedures work based on place value and
properties of operations; and use them to solve
problems.
 The beginning activity is an activity to promote
the grade 3 and 4 fluency of multiply and divide
within 100
 Grade 5 fluency is multi-digit multiplication
Fluency
 Having efficient and accurate methods for computing
 Flexibility in computational methods
 Understand and explain methods
 Produce accurate answers efficiently
 Understands base 10 number system
 Understands number relationships
The Common Core Standards
for grade 3 state:
 Students develop an understanding of the
meanings of multiplication and division of whole
numbers through activities and problems
involving equal-sized groups, arrays, and area
models;
 Students use properties of operations to
calculate products of whole numbers, using
increasingly sophisticated strategies based on
these properties to solve multiplication and
division problems involving single-digit factors.
The Common Core Standards
for grade 4 state:
 Students use properties of operations to
calculate products of whole numbers, using
increasingly sophisticated strategies based on
these properties to solve multiplication and
division problems involving multi-digit factors.
 Student find whole-number quotients and
remainders with up to four-digit dividends and
one-digit divisors, using strategies based on
place value, and/or the relationship between
multiplication and division.
The Common Core Standards
for grade 5 state:
 Students use properties of operations to
calculate products of whole numbers, using
increasingly sophisticated strategies based on
these properties to solve multiplication and
division problems involving decimals to
hundredths.
 Student find quotients and remainders with
two-digit divisors, using strategies based on
place value, and/or the relationship between
multiplication and division.
Using the rectangular array as a model
for multiplication
 Use multiplication when you want to combine groups of the
same size.
 Rectangular arrays of objects can be used to model same-size
groups.
Common Core Focus – Multiplicationgrades 3-5
 Apply properties of operations as strategies to multiply and
divide.
 If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication.)
 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 =
10, then 3 × 10 = 30. (Associative property of multiplication.)
 Knowing that 8 × 5 = 40 and 8 × 2 = 16 One can find 8 × 7 as 8 × (5
+ 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Breaking some (arrays of) eggs
 Arrays can be broken up to help students use multiplicative
relationships as they develop fluency
Don’t know 7 x 6?
 You can use combinations you know to get there, such as 7x3
 7x6 = (7x3)x2
“Go with what you know!”
 How about 5x6 and 2x6?
7x6 =(5x6) + (2x6)
From arrays of objects to grids
 Let’s take the stuff out and leave the “boxes”
 A geometric model for area
Tricks of the Trade - Doubling
 Use your 2 times table to figure out your fours and your
eights (Doubling)
 4 x 7 = 2 x (2 x 7)
 8 x 7 = 2 x (4 x 7)
 Use your threes to figure out your sixes
 6 x 7 = 2 x (3 x 7)
Tricks of the Trade – Doubling (4th grade)
 Use your 2 times table to figure out your fours and your
eights (Doubling)
 40 x 7 = 2 x (20 x 7)
 80 x 7 = 2 x (40 x 7)
 Use your threes to figure out your sixes
 60 x 7 = 2 x (30 x 7)
Assessments include showing
mathematical proficiency
 Standards for mathematical practices are integrated into
daily tasks and assessments. Students must be able to:
 Illustrate and explain by using equations, rectangular arrays,
and/or area models.
 Represent problem situations in multiple ways and explain
the connections
 Use clear and precise language in their reasoning
 Notice repetitive actions in computations to make
generalizations
Shift in Perspective
 Seeing math as a study of relationships enables us to see
structural logic rather than just a series of random facts and
procedures.
What can parents do at home?
 Have conversations that relate to everyday life and
incorporate math questions (eg. How tall is that tree?)
 Become familiar with the new math standards
 Practice counting objects and money
 Practice telling time everyday
 Reason through questions with your children.
 Play board games