NYS COMMON CORE MATHEMATICS CURRICULUM
Family Math Newsletter Gr. 3
Grade 3 • Module 1 • Topic E
Family Math Newsletter
Hey There Matey!
Some ports are so cool to explore that you just have to go back and visit them again, and that’s just what we’re
going to do in Topic E. We are going to revisit the commutative and distributive properties of multiplication, as
well as continue on with our skip-counting. We will also continue to practice using array models and tape
diagrams to model multiplication and division, all while learning our 4 facts.
Multiplication and Division: Units of 4
In Topic E, students will be shifting from simply understanding the
relationship between multiplication and division, to analyzing it.
Students will be modeling the relationships between multiplying and
dividing by units of 4 using skip-counting, the distributive property,
arrays, number bonds, and tape diagrams. Students will also explore
multiplication’s commutative property once again as well.
Array
Key Ideas

Skip-count objects in models to
build fluency with multiplication
facts using units of 4.

Model the commutative property
of multiplication using arrays and
tape diagrams

Use the distributive property as a
strategy to find related
multiplication facts.

Model the relationship between
multiplication and division.
For more information about Third
Grade in New York State, please visit
https://www.engageny.org/resource/g
rade-3-mathematics
Number Bond
How to Help at Home

Make arrays using quarters by putting 4 quarters in each group and
having your child skip count the number of quarters in the array.

Brainstorm a list of famous fours: The Beatles,
Presidents on Mt. Rushmore, The Fantastic
Four, Scooby’s Pals (Fred, Daphne, Shaggy,
Velma), Wizard of Oz (Dorothy, Cowardly Lion,
Scarecrow, Tin Man), etc. and skip count the
total number of famous finds.

Play hopscotch! There are no rules to say you
can only hop and count by ones!
Module 1:
Date:
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
Words and Key Terms
Array
Commutative Property
Distributive Property
Number Bonds
Parentheses ()
Tape diagram
Family Math Newsletter Topics A–D
8/12/15
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Family Math Newsletter Gr. 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Spotlight on Math Models
Models can help us demonstrate mathematical properties quickly and easily. Just take a look at these two
representations of the commutative property that students will be seeing in this topic: the first uses an array
and the second a tape diagram.
Fabulously Fluent
in Fours
Topic E explores multiplying
and dividing with units of 4.
Besides the suggestions listed
in “How to Help at Home,” try
this investigation to extend
your child’s learning.
Ask your child to skip count
by 4 and list their answers on
a sheet of paper.
Then, ask your child to flip
their paper over and skip
count by twos writing each of
those numbers down on the
paper as well.
Next, ask your child to
multiply each of their skip
counting numbers by two, by
two.
Together, see if your child’s
4-skip counting (front side)
matches their 2-skip counting
after they multiplied it by 2
(back). Discuss with them
why this happened.
5 + n Strategy
Children begin counting and learning that there is a 1:1 correspondence
between the objects they point to and the numbers they say. Eventually,
children develop the skill of “counting on.” For example, when taking their
turn in a board game, they no longer have to count each dot on the dice,
but recognize that one die has, let’s say, 4 dots on it and so they start with 4
and count on from there to get their total.
We can use the same principle to find the answer to a multiplication fact
as well. A student might not remember the answer to 8 x 4 (eight fours),
but they DO know 5 x 4 (five fours) is 20 and that 3 x 4 (three fours) is 12.
So if they combine the two pieces of information that they DO know (20 +
12), they can determine that the answer to 8 x 4 equals 32. A number
bond model can be used to clearly represent this strategy for solving larger
multiplication problems.
Module 1:
Date:
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
Family Math Newsletter Topics A–D
8/12/15
2
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Module 1:
Date:
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
Family Math Newsletter Gr. 3
Family Math Newsletter Topics A–D
8/12/15
3
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.