3
Mental Math
Suggestions for Instruction
The intent of this component of the support document is to provide students with activities designed to practice multiplication facts through previously learned strategies and to practice skills pertaining to radical numbers corresponding with Chapter 1 of the student text. Activity sheets have been developed; however, it is important to note that it is up to the individual teacher to decide how many questions to present each day. While there is a suggested time frame for some 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 the Multiplication Grid and have students complete the facts they can recall. Distribute Multiplication Fact Learning and discuss these strategies as well as others the students may know. Stress to students that it is important for them to review multiplication facts regularly. A practice sheet has been provided (Sheet 1).
At the end of this activity, students should prepare to 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.
Day 2: Multiplication Quiz Students will complete a timed quiz of 30 randomly selected facts (refer to Sheet 2) on the work from the previous day.
Day 3: Perfect squares
Review perfect squares from 1 to 144 and how they can be written. Examine such questions involving whole numbers and decimals. Have students complete Sheet 3.
Discuss such questions as:
· What is the area of a square with a side length of 5 cm? 7cm? 9 cm? 1.2?
· What is the side length of a square with an area of 36 square centimeters? 0 .81?
· How can we write 49 as a power with exponent of 2?
· 11 x 11=, 3 X 3 =, etc.
Day 4: Perfect squares
Examine questions involving perfect squares with whole numbers and decimals. Have students complete Sheet 4.
Discuss such questions as:
· What perfect square is located between 16 and 36? 0.36 and 0.64?
· What perfect squares are located between 1 and 36?
· The number 87 is located between what two perfect squares?
· What perfect square is located between 21 and 34?
Day 5: Square roots with whole numbers and decimals If the topic of square root has been covered, it would be a good time to introduce this concept mentally. If not, this activity may be presented when appropriate. Students should understand that since 9x9 =81, then the square root of 81 is 9. . Complete Sheet 5.
Sample questions to use:
· What is the square root of 36? ?
· 6 is the square root of what perfect square number?
· What is the square root of 0.04? ?
· What is the square root of?
Day 6: Cumulative Quiz
Students can complete a timed quiz of all 30 questions or you may choose the manner in which you would like to administer this quiz to the students. (Sheet 6)
Day 7: Multiplication by multiples of 10, 100, and 1000
Discuss whether the following products are perfect square numbers. Why or why not? Students should recognize that the number of zeros is significant. Do Sheet 7.
30 x 30 10 x 10 120 x 120 7 x 70 80 x 80 2000 x 2000
400 x 40 50 x 50
Day 8: Products of 10, 100 and 1000 using rearrangement of numbers
Examine ways to multiply 2 x 7 x 5 and 25 x 37 x 4 by investigating ways to make 10, 100 and 1000.Have students make multiplication sentences for 10, 100 and 1000. (Additional Resource: Lesson 36, Mental Math in Junior High, p.123). Complete Sheet 8.
· 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
Day 9: 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 45x8 by using the strategy—making compatibles using commutative property. Complete Sheet 9. (Additional Resource: Lesson 37, Mental Math in Junior High, p.125).
· 16 x 25 could look like 4x 4 x25
· 36 x 25 could look like 4x9x25
· 45x8 could look like 45x2x4
Students may have existing strategies such as:
· Quartering and Quadrupling: 16x25=¼(16)x25x4=4x100
· Halving and Doubling Twice 16x25=8x50=4x100
· Using Distributive Property: 16x25=10x25+6x25
These are effective strategies; therefore, encourage their use. Students will naturally use the ones with which they are most comfortable.
Day 10: Finding Products using rearrangement and decomposition of numbers
Have students do Sheet 10. (20 questions)
Day 11: Cumulative Quiz
Students can complete a timed quiz of all 30 questions or you may choose the manner in which you would like to administer this quiz to the students. (Sheet 11)
Day 12: 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 12. (20 questions)
Day 13: 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 13. (20 questions)
Day 14: Review multiplying and dividing by 0.1, 0.01 and 0.001
Have students do Sheet 14 (10 questions).
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 8, from the Nova Scotia Department of Education. Mathematics 8 Focus on Understanding: Teacher’s Resource has excellent warm up activities for mental math. Mental Math in the Middle Grades and Mental Math in Junior High are also excellent resources.