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Mental Math
SUGGESTIONS FOR INSTRUCTION
Sheets have been developed for teacher use. It is important to note that it is up to individual
teacher to decide how many questions to present each day. While there is a suggested time
frame for activities, it can be modified according to the needs of your classroom.
Day 1: Strategies for Zeros to Tens
On the first teaching day, you should introduce the topic of mental mathematics and explain
what it will look like in your classroom. It would be beneficial to start reviewing the strategies
for recalling the multiplication facts. Distribute Multiplication Fact Learning and discuss these
strategies as well as others the students may have. Stress to students that it is important for
them to review multiplication facts regularly
At the end of this activity, students can be told that next class, they will answer 30 randomly
selected facts from the strategies discussed today. Students should already have a 3 second
response to the facts; therefore, the activity should be timed.
Days 2: Strategies for 3s, 4s and the last nine
Begin with a timed quiz of 30 randomly selected facts (refer to Sheet 2) on the work from the
previous day. The teacher will judge the length of time, but it should not exceed 3 minutes. Have
students exchange papers and correct their partner’s work. Distribute Multiplication Facts
Graph to each student. Each student will record their own mark on this graph. This graph will be
used for the next 4 days. Both the teacher and the students will see the progress.
Review the strategies for the 3s, 4s, and the last nine. Have students complete the
Multiplication Grid for these facts. At the end of this activity, students can be told that next
class they will answer 30 more randomly selected facts for the whole grid. Tell students that this
will be a timed activity.
Days 3-6: All strategies
Each day the student will do a quiz (refer to Sheets 3-6). Have students exchange papers and
correct their partner’s work. Each student will record their own mark every day on the graph.
At the end of day six, the teacher can quickly record the highest mark achieved by the student,
as shown on the graph. Graphs and quizzes should remain in the student’s mental math
scribbler.
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Day 7: Multiplication by 10, 100, and 1000
Investigate (by recall, by pen and pencil, by calculator or manipulatives):
3x10
42x10
60x100
782x10
782x100
782x1000
Draw conclusions and give 20 to be done in 1 minute (refer to Sheet 7).
Day 8: One or more factors are multiplied by 10, 100, 1000
Investigate (by recall, by pen and pencil, by calculator or manipulatives):
3x20
4x30
6x400
70x50
800x200
900x6000
Draw conclusions and give 20 to be done in 1 minute (refer to Sheet 8).
Day 9: Products of 10, 100 and 1000
Investigate ways to make 10, 100 and 1000 making multiplication sentences. Ask students to
make multiplication sentences for 10, 100 and 1000.
10: 2x5, and reverse 5x2
100: 5x20, 10x10, 4x25, 2x50, 2x5x10 and reverses and expansions such as 2x2x5x5
1000: 2x500, 5x200, 4x250, 10x10x10 and reverses and expansions
Investigate the most efficient way to multiply 2x7x5 and 25x37x4
Give 20 to be done in 2 minutes (refer to Sheet 9)
(Additional Resource: Lesson 37, Mental Math in Junior High, p.125)
Day 10: Products and factors of 10,100, and 1000
Have students do Sheet10 (20 questions in 2 minutes). Have partner correct questions. Teacher
records results.
Day 11 Finding Products using decomposition of numbers
Similar to rearranging numbers, decomposing numbers to multiply compatible factors to make
multiples of 10 will help students further develop this strategy. Investigate the most efficient
way to multiply 16 x 25 or 45 x 8 by using the strategy—making compatibles using commutative
property. Complete Sheet 9. (Additional Resource: Lesson 37, Mental Math in Junior High,
p.125).
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16 x 25 could look like 4x 4 x25
44  25
4100  400
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36 x 25 could look like 4x9x25
94  25
9100  900
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45x8 could look like 45x2x4
445  2 
490   360
Day 12: Multiplication Sentences
Investigate the number of possible multiplication sentences for a given number.
Ask students to list all the possible multiplication sentences for 24 (1x24, 2x12, 3x8, 4x6, and
reverses). Give 10 to be done in a timed period (Sheet 12). Note that at this point, we are only
working with whole numbers, but if a student proposes a multiplication sentence with a fraction
(ex. ½ x 48), it would be useful to explore this concept with the student.
Additional Resource: Lesson 36 in Mental Math in the Middle Grades, p. 111-112
Day 13: Connecting Division “Facts”
Write this statement on the board. “For every multiplication sentence, there are two related
division sentences and one related multiplication sentence.”
Example:
has 3 related facts:
Have students do Sheet 13 (30 questions in 3 minutes). They should be thinking about related
multiplication facts to help them with these division questions.
Day 14: Division by 10, 100, 1000
Investigate: 3500/ 7; 3500/ 70, 3500/ 700; 4200/ 60;
Problem: If a group of (3,30,300,3000) people won $30000, how much would each person
receive provided the money was shared equally? Have students do Sheet 14 (20 questions).
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Day 15: Review Division
Have students do Sheet 15 (20 questions).Teacher records results.
Day 16: Multiplying and dividing by 10, 100, and 1000
Introduce multiplying and dividing by 10, 100 and 1000 with one factor or the dividend having
decimals.
EXAMPLES:
1. Investigate $25.60 divided by 10 people.
2. Find the total cost of 100 bars at $1.59 a bar.
Have students do Sheet 16. (20 questions)
(Additional Resource: Mental Math in Junior High, Lesson 38 p.127 and Lesson 39 p.129)
Day 17: Multiplying by 0.1, 0.01, and 0.001
Investigate:
2 x 0.1
2 x 0.01
2 x 0.001
2.34 x 0.1
2.34 x 0.01
2.34 x 0.001
34.5 x 0.01
3.45 x 0.1
Have students do Sheet 17. (20 questions)
Day 18: Dividing by 0.1, 0.01, and 0.001
Investigate:
2÷ 0.1
2 ÷ 0.01
2 ÷ 0.001
2.34÷0.1
2.34 ÷ 0.01
2.34 ÷ 0.001
34.5 ÷ 0.1
3.45 ÷ 0.01
Have students do Sheet 18. (20 questions)
Day 19: Review multiplying and dividing by 0.1, 0.01 and 0.001
Have students do Sheet 19 (10 questions).Teacher records results.
Day 20: Multiplication Strategies for 2-Digit Numbers
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Recall decomposition strategies from day 11. Ask students how they could multiply 16 by 25
without a calculator. Discuss strategies that may include:
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Making Compatibles/ Using Commutative Property: 16x25=4x(4x25)
Making Compatibles /Using Commutative Property: 16x25=(4x5)x(4x5)=20x20
Using Distributive Property: 16x25=10x25+6x25
Halving and Doubling Twice 16x25=8x50=4x100
Quartering and Quadrupling: 16x25=¼(16)x25x4=4x100
It would be valuable to discuss each strategy individually for the next few days. Although a
student may have a preferred strategy, ask the student to try the strategy you are discussing
that day. When you have finished the strategies, give the students some questions to do (Sheet
20). Allow them to choose any strategy. Record the results.
Conclusion: By the end of this period of mental math, most students should have a working
knowledge of their multiplication facts. At this time, teachers should proceed with the
concepts found in Mental Math Yearly Plan Grade 7, from the Nova Scotia Department of
Education. Mental Math in the Middle Grades and Mental Math in Junior High are also
excellent resources.