Download Module 3

Grade 3: Module 3 – Parent Letter
What’s It All About?
This 25-day module extends the study of factors from 2, 3, 4, 5, and 10 to include
all units from 0 to 10, as well as multiples of 10 within 100.
New or Recently Introduced Terms:
 Even: numbers that divide equally into 2 groups
o Example: 2, 4, 6, 8, 10, 12, etc.

Odd: numbers that can’t be divided equally into 2 groups
o Example: 1, 3, 5, 7, 9, 11, etc.

Multiples: the result of multiplying a number by a given number; particularly
the multiples of 9 and 10
o Example: 20, 30, 40, etc. are multiples of 10
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Multiplier: the factor representing the number of units
Product: the quantity resulting from multiplying two or more numbers
together
o 4 x 5 = 20

The product is 20.
Array : a set of numbers or objects that follow a specific pattern
o An array with 3 rows and 4 columns

Commutative Property: the order property; the order in which you multiply
numbers does not change the sum of those numbers
o Rotate a rectangular array 90 degrees to demonstrate that factors in
a multiplication sentence can switch places.

Distribute: break apart a larger number into 2 parts to make the
multiplication easier; multiply each of the 2 parts by the other factor
o Example: 12 × 3 = (10 × 3) + (2 × 3)

Divide/Division: partitioning a total into equal groups to show how many equal
groups add up to a specific number

o Example: 15 ÷ 5 = 3 so 15 is broken into 5 groups of 3.
Equal groups: with reference to multiplication and division; one factor is the

number of objects in a group and the other is a multiplier that indicates the
number of groups
Equation: a statement that two expressions are equal

o Example: 3 × 4 = 12
Factors: numbers that are multiplied to obtain a product
o Example: 4 x 2 = 8
Factors
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Multiply/Multiplication: an operation showing how many times a number is
added to itself
o Example: 5 × 3 = 15 is the same as 5 + 5 + 5 = 15
Number bond: model used to show part–part–whole relationships
Parentheses: the symbols ( ) used around a fact or numbers within an
equation to show what to do first

Example: (3 x 4) + (2 x 4) = 12 + 8 = 20
Quotient: the answer when one number is divided by another
o Example: 15 ÷ 5 = 3
The quotient is 3.

Row/Column: in reference to rectangular arrays
o
Rows
Columns

Tape diagram: a method for modeling problems

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Unit: one segment of a partitioned tape diagram
Unknown: the “missing” factor or quantity in multiplication or division

Value: how much
Topic A: Students will begin by revisiting the commutative property. Students
apply the commutative property to relate 5 × 8 and 8 × 5, and then add one more
group of 8 to solve 6 × 8 and 8 × 6. The final lesson in this topic builds fluency with
familiar multiplication and division facts.
Topic B: Students will be introduced to units of 6 and 7 as they learn to compose
up to, then over the next decade. For example, to solve a fact using units of 7 they
might count 7, 14, and then mentally add 14 + 6 + 1 to make 21. Students apply the
distributive property as a strategy to multiply and divide. They break apart larger
unknown facts into smaller known facts to solve. For example, 48 ÷ 6 becomes (30 ÷
6) + (18 ÷ 6), or 5 + 3.
Topic C: Students will be introduced to the associative property. Rewriting 6 as
2 × 3 or 8 as 2 × 4 makes it easier for students to group numbers together (see
example below). The following strategy may be used to solve a problem like 8 × 5:
8 × 5 = (4 × 2) × 5
8 × 5 = 4 × (2 × 5)
8 × 5 = 4 × 10
Students also relate division using units up to 8 with multiplication. They
understand division as both a quantity divided into equal groups and an unknown
factor problem.
**Mid-Module Assessment:
 Write and solve equations for multiplication and division word problems.
 Use letters to stand for unknown numbers.
o 6 x n = 24
 Explain and label arrays relating to multiplication and division word problems.
 Use and explain a table showing a pattern of multiplication.
 Use a number bond to solve multiplication and division word problems.
 Relate multiplication and division problems to each other.
o If 5 x n = 20, then 20 ÷ 5 = n.
Topic D: Students will be introduced to the nines and its patterns. They will also
find the unknown factor to solve multiplication and division problems.
Topic E: In Topic E, students begin by working with facts using units of 0 and 1.
These are simple facts that require little time for students to master; however,
understanding the concept of nothing (zero) is among the more complex as it
relates to division. This unique combination of simple and complex explains the late
introduction of 0 and 1 in the sequence of factors. Students study the results of
multiplying and dividing with those units to identify relationships and patterns. The
topic closes with a lesson devoted to two-step problems involving all four
operations.
Topic F: In Topic F, students multiply by multiples of 10. To solve a fact like 2 ×
30, they first model the basic fact 2 × 3 on the place value chart. Place value
understanding helps them to notice that the product shifts one place value to the
left when multiplied by 10: 2 × 3 tens can be found by simply locating the same
basic fact in the tens column.
Students then model place value strategies using the associative property.
2 × 30 = 2 × (3 × 10) = (2 × 3) × 10.
**End-of-Module Assessment:
 Write, solve, and explain equations for multiplication and division word
problems.
 Use letters to stand for unknown numbers.
 Relate multiplication and division problems to each other.
 Take a multiplication and division fact timed test (80 facts in 100 seconds).