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REACHING ALL LEARNERS
Common Misconceptions
➤ Students consistently round to the nearest whole number
when estimating.
How to Help: Have students use a calculator to find the
exact answers to some questions and compare them with
their estimates; for example, 25.47 19.49. This should
help them to see that rounding to the nearest whole number
does not always produce a close estimate.
Numbers Every Day
To find the target sum for each row, column, and diagonal,
students can add the numbers from 17 to 25, then divide the sum
by 3. Because each number appears once in the square, adding
them gives the sum of all 3 rows. Since all rows have the same
sum, dividing by 3 gives the sum for one row. Once the target
sum of 63 is known, a good step in completing the square is to
place the 3 middle numbers, 20, 21, and 22, along a diagonal.
9.36
5.213
6.67
13.351
6.9
4.689
6.58
6
9.204
12.82
3
2.737
3.07
1.593
0.25
2.104
Sample Answers
24 17 22
19 21 23
20 25 18
1. Estimates may vary. For parts a, b, c, e, g, and h, I rounded
2.5 m 0.6 m 1.9 m
one decimal to the nearest whole number. For parts d and j,
I rounded each decimal to the nearest hundredth. For part f,
I rounded each decimal to the nearest whole number.
For part i, I rounded each decimal to the nearest tenth.
• Suppose you want to round only 1 of the
numbers to find the difference in masses of
2 fruits. Which number would you round?
(I would round the decimal being subtracted because
it is easy to subtract a number that ends in zeros.)
AFTER
Connect
Have volunteers share their estimates and
describe the strategies they used. Use Connect to
illustrate some estimation strategies. Encourage
discussion about how to decide whether to round
to whole numbers for the ease of calculating or
to tenths or hundredths for greater precision.
Ask questions, such as:
• Which strategy is easiest? Why?
(Rounding both numbers to the nearest whole number;
it is easy to add and subtract whole numbers.)
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Unit 4 • Lesson 5 • Student page 132
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36
50
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• Which strategies produce a closer estimate?
(Rounding both decimals to the nearest tenth
or hundredth)
• What might help you decide whether to round
to whole numbers, to tenths, or to hundredths?
(How the estimate will be used; how much time I
have to make my estimate; how precise I need my
estimate to be)
Practice
Assessment Focus: Question 5
Students recognize that they must estimate the
combined mass of the 2 pianos. Some students
may round both numbers to the nearest whole
number and add to find the combined mass,
then subtract 650 from the sum. Other students
may round 396.696 to 400 and 267.728 to 268
and add, then subtract 650 from the sum.
Home
No
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2. Estimates may vary.
a) Round each number to the nearest whole number.
b) Round 4.991 to 5.
c) Round 5.837 to 6.
d) Round each number to the nearest hundredth.
e) Round 1.245 to 1.25.
f) Round 0.892 to 1.
4. a) 2.225 is a little more than 2 and 6.95 is almost 7;
7 2 9.
b) 83.1 is a little more than 83; 34.016 is a little more than 34;
About 2.89 km
83 34 49.
c) 58.37 rounds to 58.4; 22.845 rounds to 22.8;
58.4 22.8 35.6.
About 6.14 m
d) 19.531 rounds to 19.5; 19.5 16.8 36.3.
5. a) 396.696 rounds to 397; 267.728 rounds to 268;
397 268 665; this is greater than the limit of 650 kg.
b) The combined mass is about 15 kg over the limit;
665 650 15.
9. a) Tyrel may have added 2.8 and 1.
Jordana may have added 2.853 and 1.
A little more than $2
b) Jordana’s estimate was closer to the sum. Both Tyrel and
Jordana rounded 0.986 to 1. Jordana did not round
2.853 but Tyrel rounded this decimal down.
REFLECT: I might estimate the difference of two decimals when
I spend part of my money and I want to know about how
much I have left.
At Home
My family members estimate sums and differences when
shopping, cooking, travelling, and when playing golf. Their
favourite strategy is rounding to the nearest whole number.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand there are different
ways to estimate decimal sums and
differences and that some ways
produce better estimates than others.
Extra Support: Provide students with practice in using one
method of estimating at a time, starting with rounding both
decimals to whole numbers, and progressing to more
sophisticated methods.
Students can use Step-by-Step 5 (Master 4.17) to complete
question 5.
Accuracy of procedures
✔ Students use various rounding
strategies to estimate decimal sums
and differences.
Communication
✔ Students describe their estimation
strategies clearly and concisely.
Extra Practice: Have students use different strategies to estimate
the differences in questions 6 and 7. Students decide which
strategies gave the estimates closest to the actual differences.
Students can complete Extra Practice 3 (Master 4.29).
Extension: Have students suggest 2 sets of digits that could be
used in the blanks to make 38 a reasonable estimate for this
sum: 23.84 1.136
Recording and Reporting
Master 4.2 Ongoing Observations:
Decimals
Unit 4 • Lesson 5 • Student page 133
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