### Key Strategies for Teaching Elementary Mathematics

```Key Strategies for
Teaching
Elementary
Mathematics
Mrs. James left a tray of cookies on the counter early one
morning. Larry walked by before lunch and decided to take 1/3
of the cookies on the tray. Later that afternoon Barry came in
and ate 1/4 of the remaining cookies. After supper Terry saw the
tray of cookies and ate 1/2 of the cookies remaining at that time.
The next morning Mrs. James found the tray with only 6 cookies
left. How many cookies were on the tray when Mrs. James first
left it on the counter?
Visual representations are critical for
learning.
Mrs. James found the tray with only 6 cookies left.
6
Terry ate 1/2 of the cookies remaining.
6
Terry’s
6
6
remaining
Barry ate 1/4 of the remaining cookies.
12
Barry
remaining
Larry took 1/3 of the cookies.
16
Larry
starting
4
4
4
4
There are 338 players on a soccer team. 186 are girls and the
rest are boys. How many boys are on the soccer team?
186
?
338
Misha has 34 dollars. How many dollars does she have to earn
to have 47 dollars?
Visual representations for multiplication
Visual representations translate to symbolic (CRA)
Estimate:
1.4 x 1.3 is somewhere between 1 and 4
Distributive Property:
1.4
x 1.3
0.12
0.3
0.4
1
1.82
Knowing the reasons behind a procedure
is as important as being fluent with it.
Reason?
2
13
x8
104
13
x8
24
+80
104
10
8
8∙3 + 8∙10 = 8(3+10)
a∙b + a∙c = a(b+c)
3
Reason?
1 1
1
× =
3 4 12
What problem does this illustrate?
Students should work things out with
their hands.
Division by Partitioning
354 photos to share among 3 children
Work with manipulatives also translates to
procedures
354 ÷ 3
(300 + 50 + 4) ÷ 3 = 100 + 10 + 1 r 21
100 + 10 + 1 + 7
Try this with 251 ÷ 8. Partition base 10 blocks, then write a corresponding algorithm.
Problem-solving is enhanced by knowing
the structures of word problems.
Part-whole where a part is unknown
There are 23 players on a soccer team. 18 are girls and the rest
are boys. How many boys are on the soccer team?
18
?
23
Joining (adding to) where the change is unknown
Misha has 34 dollars. How many dollars does she have to earn
to have 47 dollars?
Equal groups
Each person on a relay race team runs 5/8 of a mile. There are 4
people on the team. How long is the total race?
5
8
5
8
5
8
5
8
+ + + =
4×5
8
Multiplicative comparison
The tree is 40 times taller than the person. If the person is 5 feet
tall, how tall is the tree?
Measurement division
Our class baked 225 cookies for a bake sale. We want to put
them in bags with 6 in each bag. How many bags can we make?
225 – 60 = 165
165 – 60 = 105
105 – 60 = 55
45 – 30 = 15
15 – 12 = 3
10 bags
10 bags
10 bags
5 bags
2 bags
37 bags with 3 cookies left over
Try this with 251 ÷ 8. What’s a corresponding word problem?
A recipe that makes 20 cookies needs ¾ cup of sugar. How much
sugar is needed to make 100 cookies?
Measurement division
How many groups of 20 are
in 100?
(repeated subtraction, or
20 x what = 100?)
Equal groups
How much is 5 groups of 3
fourths?
(Skip count on a number
line)
If a serving size for Cheerios is 3/4 cup, how many servings are
in a box that has 12 1/2 cups?
While division by a fraction is in the 6th grade
curriculum, this example shows how important
it is to understand the underlying structure of
word problems.
Alternative ways of solving a
problem should be celebrated.
T-shirts with the school logo cost \$8 wholesale. The Pep
Club has saved \$496. How many t-shirts can they buy
for their fund-raiser?
Mental Math is Important
Number Talks
32 x 15
14
64
4
-38
26
Practice and drill are essential for
developing fluency
Do these multiplication problems as quickly as
you can using the partial product method.
25 x 164 562 x 36 285 x 102
Practice makes perfect: Frequent cumulative
review is the most underused method for
ensuring long-term retention.
```