Review Mental Math Strategies
Solving with Mental Math Strategies
1.
Display the Mental Math Strategies anchor chart. Direct students toLesson 2 BUILD Mental Math Strategies.
2.
Remind students that they have already practiced front-endestimation and rounding as mental math strategies, but that thesestrategies do not provide an exact answer.
3.
Model and do a Think Aloud for the strategy
Compensate to Make aBenchmark Number
. A suggested process follows:
Review with students the definition of a benchmark numbers.Students used benchmark numbers when they studied fractions in Primary 3. Benchmarks are “friendly” numbers that are easy to add and subtract mentally and usually include multiples of 10 or100.
Record on the board. Model as follows compensating by subtracting 3 from the 8 and giving the 3 to the 37 to make a benchmark number (40):
ASK
Which benchmark number should we make for 37? In other words, what number is 37 close to that is easier to add in our heads?
(Most likely students will answer 40. If students have other ideas, let them explain their thinking, but use rounding as a strategy to guide students to choose 40 as the benchmark.)
How many Ones do we need to add to 37 to get to this benchmark?
Where could I get those 3 Ones?
Do a Think Aloud as you write the following on the board, explaining each step aloud. Be sure to remind students that this strategy makes mental computation much easier.
37 + 8
Solving with Mental Math Strategies
1. Display the Mental Math Strategies anchor chart. Direct students to Lesson 2 BUILD Mental Math Strategies.
2. Remind students that they have already practiced front-end estimation and rounding as mental math strategies, but that these strategies do not provide an exact answer.
3. Model and do a Think Aloud for the strategy
Compensate to Make aBenchmark Number
. A suggested process follows:
Review with students the definition of a benchmark numbers.Students used benchmark numbers when they studied fractions inPrimary 3. Benchmarks are “friendly” numbers that are easy toadd and subtract mentally and usually include multiples of 10 or100.
Record
on the board. Model as follows compensating by subtracting 3 from the 8 and giving the 3 to the 37 to make a benchmark number (40):
ASK
Which benchmark number should we make for 37? In other words, what number is 37 close to that is easier to add in our heads?
(Most likely students will answer 40. If students haveother ideas, let them explain their thinking, but use rounding asa strategy to guide students to choose 40 as the benchmark.)
How many Ones do we need to add to 37 to get to this benchmark?
Where could I get those 3 Ones?
Do a Think Aloud as you write the following on the board, explaining each step aloud. Be sure to remind students that this strategy makes mental computation much easier.
37 + 8
SK
What is the new problem we created and what is the sum?
Explain to students that there is sometimes more than one way to compensate in a problem. However, they must maintain balance and make sure the total does not change. In other words, if we take from one number, we have to give to another. If we give to one number, we have to take from another. For example, they could have taken 2 from the 37 to make it 35, adding the 2 to the 8 to make 10. Both strategies work because they maintain balance and provide a correct answer.
ASK
Do you think we can compensate with subtraction? Why or why not?
Record and ask students to solve the problem mentally and tell their Shoulder Partner the difference. Ask volunteers to share their thinking about the following:
ASK
Knowing that
, what would the answer be if the problem is?
How do you know?
4.Read the Break Up and Bridge strategy as a group. In this strategy, students break up numbers in addition or subtraction problems to get partial answers, then go back and add or subtract the missing quantities.
Model the strategy and do a Think Aloud:
Write the problem _______ on the board.
Explain that you are finding numbers in the problem that are easy to add in your head. For example,
(write on the board).
Then, you simply need to add the remaining 7 from 27. Write on the board:
, so
.
5.
Model and do a Think Aloud for the strategy
Add to Subtract
. In this strategy, students start with the subtrahend and add to get to the minuend. They then find the sum of the numbers they added to the subtrahend.
Write the problem
_______ on the board.
Explain that you know you can add 2 to 48 to get to 50, and then add 600 more to get to 650.
36 − 20 =
36 − 20 = 16
36 − 19
32 + 27 =
32 + 20 = 52
52 + 7 = 59 32 + 27 = 59
652 − 48 =
You added 2, 600, 2 to 48 to make 652. Answer:
So,
6. Display the Thinking Like a Mathematician anchor chart.
TEACHER NOTE: Students discussed these traits In Primary 3. This anchor chart represents eight practices that describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. The practices are applicable across subject areas and will help students become better learners.
7. Remind students that they had some practice with Thinking Like a Mathematician in Primary 3. They will continue to discuss these ideas to develop a deep and flexible understanding of math. Using mental math strategies is about noticing the structure of numbers (7)to help, as well as using rules and patterns (8).
8. Ask students to work with a partner to complete the table in their Student Materials. (If there is not enough time left, ask students to complete the problems for homework. They should be prepared to discuss the strategies they used.) Explain that they might not always
652 − 48 = ___
+ 2
−−−−−−−
50
+600
−−−−−−−
650
+ 2
−−−−−−−
652
652 − 48 = 604
652 − 48 = ___
+ 2 → 2
−−−−−−−
50
+600 → 600
−−−−−−−
650
+ 2 → 2
−−−−−−−
652
652