Grade 3
Tips for Helping at Home
•
Questions to ask:
What is it that you don’t understand (have
the student be specific)?
What about putting things in order?
Could you try it with simpler numbers?
Can you guess and check?
Does this make sense?
What can you do to explain your answer to
show others what you are thinking?
Does your answer seem reasonable?
•
Play the number games that come home with
your child
•
Look for things that
come in equal groups
such as eggs, soda,
and shoes.
•
Discuss what “facts”
mean and what their
relationships are - for example, that 6 x 4 is four
more than 5 x 4 or that 4 x 8 is double 2 x 8.
Mathematical Emphasis
Investigation 1: Things that Come in Groups
•
Finding things that come in groups
•
Using multiplication notation
•
Using multiplication to mean groups of groups
•
Writing and illustrating multiplication sentences
Investigation 2: Skip Counting and 100 Charts
•
Recognizing that skip counting represents multi-
ples of the same number and has a connection to
multiplication
•
Looking for patterns in multiples of 2 - 12 on the 100
chart
•
Understanding that the patterns numbers make can help
us multiply those numbers
Investigation 3: Arrays and Skip Counting
•
Recognizing that finding the area of a rectangle is one
situation where multiplication can be used
•
Using arrays to skip count
•
Using arrays with skip counting to multiply and divide
•
Finding factor pairs
•
Making connections between number and shape
Investigation 4: The Language of Multiplication and Division
•
Understanding relationships between multiplication and
division
•
Identifying whether word problems can be solved using
division and/or multiplication
•
Using multiplication and division notation to write num-
ber sentences
Investigation 5: Problems with Larger Numbers
•
Multiplying and dividing in real-life situations and using
patterns to solve multiplication and division problems
•
Organizing and presenting data in tables and line plots
•
Sorting out complex problems that require both multipli-
cation and addition
•
Making up division and multiplication story problems
from real data
Website
http://cms.everett.k12.wa.us/math/Third Grade
Multiplication
and Division
Vocabulary
Factor - a number that is multiplied by another
number to find a product.
4 x 5 = 20
Multiple - the product of a given whole number
and another whole number
4 x 5 = 20
Array - a set of objects or numbers arranged
in rows or columns
2 x 6 array
Notation - using standard forms and symbols
for multiplication and division.
12
3 x 12 12 ÷ 3
3
)12
X 3
Glossary
http://www.amathsdictionaryforkids.com/
Game
Multiplication Pairs
Materials:
•
Set of Array cards
•
Paper and pencil
Players: 1 or 2
How to Play:
1. Spread out all of the cards in front of
you. Some should be turned up, show-
ing the dimensions. Others should be
turned over to show the total or product.
2. Choose a card and put your finger on it.
(Don’t pick it up until you say the an-
swer.) If the dimensions are showing
then you must give the total. If the total
is showing, you must say the dimen-
sions of the grid. The shape of the array
will help you.
For example: Suppose you pick an array
with the total 36 showing. The dimensions
could be 6 x 6, or 9 x 4, or 12 x 3. You must
decide which is right. The shape of the ar-
ray is a good clue.
3. Turn the card over to check your an-
swer. If your answer is correct, then pick
up the card.
4. If you are playing with a partner, take
turns choosing and identifying cards.
Play until you have picked up all the
cards.
While you are playing, make lists for your-
self of “pairs that I know” and “pairs that I
don’t know yet.” Use these lists to help you
learn all the pairs.
Talking and Writing About Division
Various division symbols are using as standard
notation in our society:
4)24
24 ÷ 4
24/4
24
4
In this unit, we use only the form 24 ÷ 4. However,
we want students to recognize the other forms
(which they may have seen on tests and in other
textbooks) as having the same meaning as 24 ÷ 4.
They will use the fractional form in the Fractions units
of the Investigations curriculum.
There are many different ways to “read” or speak of
these notations:
Four goes into 24
24 divided by 4
How many 4’s are in 24?
When 24 is shared among 4 people, how
many does each person get?
So many symbols and so many different ways of
reading can be very confusing to young students,
especially because the numbers and symbols appear
in different positions, depending on which notation
you are using. We would like students to read divi-
sion notation with as much meaning as possible, so
that they connect the symbols to the situations they
represent.
Sometimes a problem does not divide evenly. Rather
than teaching students to write “R” for the remainder,
have them describe the remainder in a way that
makes sense to them for that problem. For example,
how many groups of 3 can be formed with 26 stu-
dents? Some students may decide they can make 8
groups of 3 and one group of 2. Others may decide
to make 6 groups of 3 and two groups of 4. If the ex-
ample was 26 cookies to share among 3 children,
they might give 8 to each and leave the remaining 2
cookies on the plate, or break them up to share.
Tierney, C. Investigations in Number, Data, and Space:
Things That Come in Groups. Dale Seymour Publications,
1998.
