Grade 3, Module 7
Core Focus
• Reviewing and extending the tens multiplication facts in order to learn strategies
for the nines multiplication facts
• Working with the eights multiplication facts in order to divide
• Working with the ones and zeros division facts
• Solving word problems involving multiplication
• Representing data (many-to-one picture graphs, bar graphs, and line plots)
Ideas for Home
Multiplication and Division
• In this module, students continue to work on making sense of various multiplication
and division facts, including extending their knowledge of tens, nines, eights, and
ones facts in ways that build on what they have already learned about multiplying
with these numbers.
• Of the range of strategies that can be used for the ×9 facts, the most useful strategy
involves starting with a tens fact and building down from it. Students use the more
familiar ×10 facts, to solve less familiar ×9 facts.
• For example, an array that has 10 rows with 4 columns in each row equals 40. When
one row is covered or folded back (see below) it leaves 9 rows of 4. The folded-back
array shows or 40 − 4 = 36, so 9 × 4 = 36. Making these connections builds number
sense and reasoning.
10 × 4 =
so
so
10 × 4 =
9
4
×
4
=
×
=
9×4=
• Another interesting pattern in the multiples of 9 is that when the digits in each multiple
are added, they equal 9.
7.3
Reinforcing the Nines Multiplication Facts
Look at each of these nine facts.
What do you notice about each product?
9 × 3 = 27
9 × 4 = 36
• Practice the ×10 and ×9 facts
together. Encourage your
child to explain how knowing
the ×10 fact makes the 9 fact
easier to solve. “I know that
5 × 10 is 50, and 50 − 5 is 45,
so 9 × 5 is 45.”
• Create arrays with pennies to
illustrate 10 × __ and then cover
one row to illustrate 9 × __ .
• Visualizing the array prevents
confusion about which group
to subtract from the ×10 total.
E.g. instead of 9 × 6 is the
same as 10 × 6 − 6 = 54, your
child may solve 10 × 6 − 9,
which equals 51.
• If your child knows their
facts, ask them to elaborate by
explaining a strategy.
Glossary
An array models the
build down strategy for ×9
facts, e.g. 10 × 3 − 3 = 27.
9 × 5 = 45
What happens when you add the two digits in each product?
© ORIGO Education.
When working with the nines
multiplication facts, the digits
in each product total 9.
Write three more nines facts that you know.
Then check to see if the digits in each product total 9.
In this×lesson,= students explore
to reinforce× the nines
facts.
× patterns
=
=
Step Up
a.
180815
I know that my nines fact
is incorrect if the digits in
the product do not total 9.
1. Loop the facts that are incorrect.
Write the facts so that they are correct.
9×1=9
b.
9×1=9
c.
9×1=9
9 × 2 = 18
9 × 2 = 18
9 × 2 = 18
9 × 3 = 27
9 × 3 = 30
9 × 3 = 27
10 rows of 3 are 30 and then,
when one row is “folded-back,”
the array shows 9 rows of 3
are 27.
1
Introducing the Eights Division Facts
7.6
There are 32 cards in this pack.
Grade 3, Module
7
How could you share the cards into groups of equal size?
32 cannot be shared among
5 or 10 because there is a
2 in the ones place.
• Students connect what they learned about multiplication to develop strategies
How could
you doubling
share the cards
2?
to divide by eight.
Since
isbetween
convenient
in multiplication, halving makes sense
How could you share the cards among 4?
for dividing. “Thinking
multiplication”
is
another
useful
strategy.
How could you share the cards among 8?
Kana used a halving strategy.
Janice thought of the related
multiplication facts.
32
÷2
32
÷2
÷2
32
÷2
÷2
2×
= 32
4×
= 32
8×
= 32
How many cards
are in each group?
÷2
Step Up
Writebe
the number
cards in each share.because it does not follow the
• Division involving
zero 1.can
quiteofchallenging
pattern of other a.facts. Multiplication involving
0 is pretty easy because 0 groups,
b.
16 ÷ 2 =
40 ÷ 2 =
or 0 in each group will always result in 0 and it is an easy pattern to remember.
16 ÷ 4 =
40 ÷ 4 =
16 cards
40 cards
© ORIGO Education.
• Some division situations involving 0 are also easy. 0 ÷ A = 0, regardless of what
16 ÷ 8 =
40 ÷ 8 =
number we use for A, other than 0 itself, e.g. 0 ÷ 2 = 0, and 0 ÷ 17 = 0,
0 ÷ 198 = 0, 162
and so on. If we begin with nothing and divide it into groups, we still
have nothing in each group.
ORIGO Stepping Stones 3 • 7.6
281014
• Mathematicians say “division by 0 is undefined.” it simply cannot be done. For
Facts number is 3, so 6 ÷ 2 = 3. Using
example, with7.9
6 ÷ 2,Introducing
we think the
2 ×Zeros
? = 6.Division
The missing
the same thinking
with
6 ÷ it0,
we are
looking
formultiplication
a number
that makes 0 × ? = 6 true.
To divide
with zero,
is easier
to think
of the related
sentence.
Think about how you would divide 0 by a number.
It is impossible.
Whenever we multiply by 0, the answer is 0 (never an answer of 6).
What happens when you divide 0 by a number?
see
0÷6=
think
6×
The answer has to be 0.
=0
Ideas for Home
• Enter “Picture graphs for kids”
to search images online. With
this search, many types of bar,
picture and line plots will be
displayed. Choose several
to discuss and interpret.
• Notice when data is displayed
in graphs in the newspaper,
on websites, and in magazines.
Interpret the graphs together
and ask questions that can be
answered by looking at
the graph.
• Notice if any videogames your
child plays collect performance
data, and interpret the
information together.
Glossary
A graph shows the
relationships between two or
more things using lines, bars,
dots or pictures.
Think about how you would divide by 0.
3
4
2 and
2 and
3
1
4
2
4
2 and
3
4
2
1 and
1
4
Number of inches
=6
What happens when you divide 0 by 0?
Data
1 and
1
1 and
0×
3
4
think
A number multiplied
by 0 is 0, so 6 Ö 0
is not possible.
1
4
6÷0=
2
4
see
2
4
What happens when you divide by 0?
Favorite Movies
Comedy
see
0 x 9 = 0 and 0 x 194 = 0,
0÷0=
Cartoon
so 0 multiplied by
• Collecting data and displaying it in graphs
is a way to visually address questions
any number equals 0.
Therefore, the answer to
like: How many? How
much?
What
kind?
Students
learn ways to organize data and
think 0 ×
=0
0 Ö 0 cannot be decided.
to display it in charts and graphs. Lessons in this module focus on creating and
interpreting many-to-one
picture
barfacts.
graphs, and line plots.
Step Up
1. Write
numbers graphs,
to complete these
Action
Scary
Hockey
b.
c.
Many-to-One
Picture
Graphs
7.10 see Introducing
see
see
0÷7=
0÷
8=
Whatthink
do you notice
about
7×
8×
= 0this picture
think graph?
=0
168
© ORIGO Education.
281014
Type of pizza
Pizza Sales
Cheese
think
Baseball
0÷4=
4×
=0
means 10 pizzas
Tennis
© ORIGO Education.
a.
0
2
4
6
8
10
12
14
16
18
20
ORIGO Stepping Stones 3 • 7.9
Hawaiian
What does
represent? What does
represent?
How could you represent 25 pizza sales? Draw a picture.
In Lesson 10, students are introduced to many-to-one picture graphs where
one picture represents ten observations.
180815
Basketball
2