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2. a) 24.109, 24.351, 24.762
c) 1.639, 1.7, 1.78
3. a) 3.53, 0.571, 0.538
c) 16, 15.2, 15.012
4. 6.738
Maude’s airplane flew farther.
When you discuss the third technique, you may
want to use a blank number line on the overhead
projector to demonstrate how to divide the line
to show hundredths and thousandths. To provide
extra practice ordering on a number line, you
could have the class work together to place the
heights of the mountains from Explore on a
number line.
Ask:
• How would you read the number line on
page 125 to give the lengths from shortest
to longest?
(From left to right)
b)
d)
b)
d)
0.5, 0.59, 0.598
0.4, 2.84, 2.968
1.35, 1.267, 1.002
2.76, 2.3, 2.041
I knew the number had to have more than 6 ones and
730 thousandths, but less than 6 ones and 741 thousandths.
Any number of thousandths between 731 and 740 would work.
5. 4.25 is equivalent to 4.250.
Compare the hundredths: 5 hundredths is greater than
4 hundredths.
So, 4.250 is greater than 4.247.
6. 1.513 and 1.518.
1.51 is equivalent to 1.510 and 1.52 is equivalent to 1.520.
So, I chose 2 numbers between 1.510 and 1.520. Any
number of thousandths between 510 and 520 would work.
7. a) Luis’
b) Cy’s
c) Vladimir’s and Abu’s
d) 2.438, 2.4, 2.357, 2.35, 1.943, 1.7
Assessment Focus: Question 9
Students realize that two of the numbers are
less than 6 and two are greater than 6. Some
students may order the 4 numbers on a number
line to determine which is closest to 6. Other
students may recognize that 5.91 and 6.002 are
closer to 6 than the other two numbers and
eliminate the other two as possibilities. They
then use number sense to determine which
number is closer to 6.
Practice
Have Base Ten Blocks and blank number lines
(PM 16) available for students who wish to use
them. Students can use 4-column charts (PM 19)
to make place-value charts.
Unit 4 • Lesson 3 • Student page 125
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9. Of the two numbers greater than 6, 6.002 is closer to 6.
Of the two numbers less than 6, 5.91 is closer to 6. 6.002
is 2 thousandths greater than 6. 5.91 is 9 hundredths less
than 6. 2 thousandths is less than 9 hundredths, so 6.002
is closer.
10. Answers may vary. For example:
a) 0.412
b) 5.782
c) 32.001
d) 2.367
e) 21.211
f) 0.003
11. c) A: Goliath; B: Zeus; C: Hoppy; D: Cleo; E: Ajax
12. From least to greatest: 1.2, 1.236, 1.27, 1.279, 1.284
1.2
1.2
1.236
1.27 1.279
0.482 g
0.32 g
0.44 g
6.002
1.284
1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30
Ajax
Goliath
REFLECT: The student is not correct. 7.52 is equivalent to 7.520.
Compare 7.516 and 7.520. Both numbers have 7 ones and
5 tenths. Compare the hundredths. 1 hundredth is less than
2 hundredths. So, 7.520 is the greater number, and 7.52 is
to the right of 7.516 on a number line.
Numbers Every Day
Every number has at least 2 factors: 1 and itself.
Students find numbers that have exactly 1 more factor.
Students discover that these numbers are some of the square
numbers, with the third factor a prime number.
For example: 4, 9, 25, 49, 121, 169
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students use various strategies to
compare and order decimals.
Extra Support: Dictate several decimal numbers and have
students record them in a place-value chart. Then, have students
order the decimals from greatest to least.
Students can use Step-by-Step 3 (Master 4.15) to complete
question 9.
Problem solving
✔ Students choose an appropriate
strategy and solve problems
involving the comparison and
ordering of decimals.
Communication
✔ Students describe their thinking
clearly and concisely.
Extra Practice: Students can do the Additional Activity,
Comparing Decimals (Master 4.9).
Students can complete Extra Practice 2 (Master 4.28).
Extension: Have students research the batting averages of
some members of their favourite baseball team, then order the
averages from greatest to least.
Recording and Reporting
Master 4.2 Ongoing Observations:
Decimals
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Unit 4 • Lesson 3 • Student page 126