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Sample Answers
2. a)
d)
b)
c)
17
, 0.017
1000
314
1000
2, 2.314
4.
Hundreds Tens Ones Tenths Hundredths Thousandths
6
, 0.006
1000
407
, 0.407
1000
4
358
1000
209
1000
1
1000
48
1000
2
4
0
0
8
5
5
0
3
2
2
4
0
8
8
4
8
2
7.564
2.412
7.564
6.943
0.015
0.015
Practice
Ask:
• For which numbers did you use more than
41
1000
1062
1000
one grid? (1 and ) Why? (The numbers
are greater than one whole.)
1062
• How did you colour grids to show ?
1000
(I coloured 1 whole grid and 62 small squares on
1062
a second grid.) How else can you write 1000
62
as a fraction? (1)
1000
Use the numbers in the place-value chart to
introduce the expanded form of decimals (for
example, 0.732 7 tenths 3 hundredths 2 thousandths).
Provide students with Base Ten Blocks and
thousandths grids to complete the questions.
Assessment Focus: Question 10
Students understand that they must combine
the 4 digits in as many ways as they can to
form decimal numbers. Students realize that
since the numbers must be greater than one but
less than 5, the whole number part must be 2.
Some students may use a systematic, organized
approach to find all the combinations while
others may use a random approach.
Discuss the equivalent decimals 0.700 and
0.70. Elicit the third equivalence, 0.7. Invite
a volunteer to demonstrate on a thousandths
grid how they know they are equivalent.
Repeat with 0.3, 0.30, and 0.300.
Unit 4 • Lesson 2 • Student page 121
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5. a) 0.5 0.07 0.003 b) 80 6 0.09 0.003
c) 6 0.2 0.04
d) 20 000 9000 200 70 3
e) 0.1 0.02 0.004 f ) 0.1 0.007
7. a) three hundred forty-one thousandths
b) twenty-five and sixteen-thousandths
c) two and three-thousandths
d) nine hundred sixty-four and twenty-four thousandths
8. 5.407
407
1000
5 Quit
425.032
48.48
0.085
2.408
0.341
25.016
964.024
2.003
five and four hundred seven thousandths
5 and 407 thousandths
5 0.4 0.007
5 ones 4 tenths 7 thousandths
10. I know that the number has to have 2 in the ones place so
that the number is greater than 1 and less than 5. So I started
with 2 each time. Then I wrote 2 numbers with a zero in the
tenths place, 2 with a 5 in the tenths place, and 2 with an 8
in the tenths place.
256
1000
365 , 365.256
REFLECT: 0.2, 0.20, and 0.200 are equivalent decimals because
2
20
10
100
2
200
, of the grid, and 0.200 is of the grid, which is the
10
1000
2
20
same as and of the grid.
10
100
on a thousandths grid, 0.2 is of the grid, 0.20 is , or
2.058, 2.085, 2.508, 2.580, 2.850, 2.805
Numbers Every Day
Students may find it helpful to record the factors in pairs, one of
which is a prime, then continue to factor the composite number
until all the factors of the original number are prime numbers.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand that decimals are
another way of writing fractions with
tenths, hundredths, and thousandths.
✔ Students understand that equivalent
decimals name the same amount.
Extra Support: Model decimals such as 3.7, 0.28, and
1.047 with Base Ten Blocks. Have students write the decimal,
then read it aloud.
Students can use Step-by-Step 2 (Master 4.14) to complete
question 10.
Accuracy of procedures
✔ Students model decimals with tenths,
hundredths, and thousandths.
✔ Students write a fraction or mixed
number for a decimal and vice versa.
✔ Students write decimals in expanded
form.
Extra Practice: Have students write the lengths in the table
in question 3 in as many ways as they can.
Students can complete Extra Practice 1 (Master 4.27).
Extension: Have students use a decimal to write each of the
following distances in kilometres:
27 m, 869 m, 3 m, 998 m.
(Answers: 0.027 km, 0.869 km, 0.003 km, 0.998 km)
Recording and Reporting
Master 4.2 Ongoing Observations:
Decimals
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Unit 4 • Lesson 2 • Student page 122
2,
2,
2,
2,
2,
3
3
7
3, 11
3, 13