By the  en d  of grade 3 all students should know from memory, all products of two 1-digit numbers.

Students move to building larger arrays (also called the area model of multiplication

The most important division
concept is the understanding	20
of equal shares.	−	5
15
20 ÷ 5	−	5

Parent
Roadmap

10	10

3

2	10
Students explore division	−	5
using strategies. One such	5
strategy involves	−	5

A student has shaded an array, 3 x 22, on grid paper.

repeated subtraction.

0	Grade	3

Third graders progress to diagrams that explain the area model of multiplication with

This third grader has used the multiplying up

larger numbers.

10	+	3

strategy. This involves finding the solution
to a division problem through multiplication.
45 ÷ 3

4	4 x 10	4 x 3

Familiarity with the area model above, allows students to move to working with

3  x 10 = 30
3  x   5	= 15
30 + 15 = 45

10 + 5 = 15 so 3 x 15 = 45

partial products.

4 x 13

(4 x 10) + (4 x 3)

Third graders begin division by sharing.

Three students need to share 12 trapezoids equally.

Another strategy a third grader may use is

3  45
− 30	10
15
− 15	5
0

Schools
Strategies for addition, subtraction, multipKliecyatCioonncaenpdtsdivision
trategies
Geometry

2013-2014

Math

236 – 79 =

Multiplication and Division
Strategies

Addition and Subtraction
Strategies

248 + 345 =

248

4 x 9

9 + 9 + 9 + 9 = 36

500 + 80 + 13
500 + 80 = 580
580 + 13 = 593

+ 345
500
80
 	13
593

1 + 20 + 100 + 36 = 157

This third grader used an open number line and added up in chunks starting at 79 and counting up to 236 in order to subtract.

9 + 9 = 18	OR	9 + 9 = 18
18 + 9 = 27	9 + 9 = 18
27 + 9 = 36	18 + 18 = 36

Students have opportunities to show their thinking in multiple ways that make sense

Here, two students used the partial sums
strategy, and recorded their thinking in two different ways. Breaking apart the numbers helps make it easier to compute.

− 3	+ 3
326  + 247 =
323 +  250 = 573
This example shows how a student could use compensation to solve an addition problem.

Third graders	216 + 149 =
can also use the

Students are encouraged to use this strategy
in a way that makes sense to them.

Students choose to use friendly numbers to make it easier when doing mental computation.

Students may solve a subtraction problem by keeping a constant difference.

236 – 79 =

(236 + 1) – (79 + 1) =
237	–	80	= 157

to them.

									

									

									

Once students understand the concept of repeated addition, they move to understanding how arrays represent multiplication facts.

This grid shows an
8 x 9 array. Students soon recognize that facts can be made
up of smaller facts

strategy adding up in chunks.

One number is kept whole and

216 + (100 + 40 + 4 + 5)
216 + 100 = 316
316 + 40 = 356
356 + 4 = 360
360 + 5 = 365

By adding 1 to 236 and making 237, as well as adding 1 to 79 to make 80 (keeping the difference constant) this student makes it easier to subtract.

Here a student

																		

																		

																		

has split 8 x 9 into two arrays, namely; 8 x 5 and
8 x 4. This helps to make the

the second number is broken into easy-to- use chunks.

computation
easier.