CNPM_AM6_[068-117]
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Page 102
Unit 7
Mental multiplication
and division
Focus
B
Use understanding of place value to multiply whole
numbers and decimals by 10 or 100
NC Level 4
Vocabulary whole number; decimal; thousands; hundreds; tens; units; tenths; hundredths; thousandths; lots of; groups
of; times; multiply; multiplication; multiplied by; multiple of; product; ten times; one hundred times
Resources RCM 6 (enlarged to A3); several sets of 0–9 digit cards; large sheet of paper and marker; Discussion
Book 6 page 46; RCM 63; RCM 64 (per child); paper clip and pencil, for the spinner (per pair or group);
two 1–9 dice (per pair or group); pile of counters (per pair or group); pencil (per child)
Adapting the
This teaching sequence involves multiplying whole numbers and decimals by 10 and
teaching sequence 100. Before delivering this teaching sequence decide whether you intend to focus on
Repeat the above, asking questions to review and assess children’s ability to
multiply a decimal by 10 or 100. Ask questions such as: What is 0·4
multiplied by 10? (4) What is 0·4 multiplied by 100? (40) Multiply 3·6 by
10. (36) What is the product of 4·2 and 100? (420) What is 35·4 multiplied
by 10? (354) What is 35·4 multiplied by 100? (3540)
Teach
Multiplying whole numbers by 10 or 100
w & Asse
vie
ss
Teach
102
Practise
Apply R
e
•
Begin by asking questions to review and assess children’s ability to
multiply a whole number by 10 or 100. Ask questions such as: What is
4 multiplied by 10? (40) What is 4 multiplied by 100? (400) Multiply
36 by 10. (360) What is the product of 42 and 100? (4200)
Teach
•
w & Asse
vie
ss
Review and Assess
Apply Re
whole numbers, decimals or both.
•
•
Display the enlarged copy of RCM 6.
•
Move the 3 digit card one place value to the left into the tens column and
place a 0 digit card in the units column. Say: As we have multiplied by 10,
the 3 has got ten times bigger and become 3 tens. It moves from the units
column to the tens column. The zero has to be put into the units column to
mark the place. If the zero was not there we would not know the number
was 30. The place value of the digits becomes ten times larger.
•
•
Write: 3 × 10 = 30 on the large sheet of paper.
•
Remove the 0 digit card from the mat and move the 3 digit card back to the
units column. Ask: What is 3 multiplied by 100? (300)
•
Move the 3 digit card two place values to the left into the hundreds column
and place 0 digit cards in the tens and units columns. Say: When a number is
multiplied by 100 it moves two columns or place values to the left. It gets
10 times bigger and then 10 times bigger again. This is the same as getting
100 times bigger, as 10 times 10 is 100. So 3 moves from the units place to
the hundreds place and we put in two zeros as place markers.
•
Underneath 3 × 10 = 30 write: 3 × 100 = 300.
Practise
Place the 3 digit card in the units column. Ask: What is 3 multiplied by
10? (30)
Say: Ten is a very important number in our number system. Every time we
multiply by 10 the digits move one place value to the left.
CNPM_AM6_[068-117]
05/10/2009
15:12
Page 103
Unit 7
Mental multiplication
and division
Focus B continued
34 × 10 = 340
34 × 100 = 3400
67 × 10 = 670
67 × 100 = 6700
3·4 × 10 = 34
3·4 × 100 = 340
52·3 × 10 = 523
52·3 × 100 = 5230
7·49 × 10 = 74·9
7·49 × 100 = 749
57·62 × 10 = 576·2
57·62 × 100 = 5762
Display Discussion Book 6 page 46 and explain how the first place value mat
demonstrates the effect of multiplying 3 by 10 and 100.
•
Repeat for a selection of one- and two-digit numbers multiplied by 10, then
100, referring to the place value mat when appropriate.
Multiplying decimals by 10 or 100
•
•
Display the enlarged copy of RCM 6.
•
Move the 0 and 3 digit cards one place value to the left into the tens and units
columns respectively. Say: As we have multiplied zero point 3 by 10, the 3
has got 10 times bigger and become 3 units. It moves from the tenths
column to the units column. The zero in the tens column we do not need
so we can remove it from the mat.
•
•
Write: 0·3 × 10 = 3 on the large sheet of paper.
•
Once again use the 0 and 3 digit cards to show 0·3 on the place value mat.
Ask: What is zero point 3 multiplied by 100? (30)
•
Move the 0 and 3 digit cards two place values to the left into the hundreds
and tens columns respectively. Say: When a number is multiplied by 100 it
moves two columns or place values to the left. It gets 10 times bigger
and then 10 times bigger again. This is the same as getting 100 times
bigger, as 10 times 10 is 100.
•
Say: As we have multiplied zero point 3 by 100, the 3 tenths has got 100
times bigger and become 3 tens. It moves from the tenths column to the
tens column. The zero in the hundreds column we do not need so we can
remove it from the mat.
•
Ask: What is wrong with this number? (0 missing from the units place) Say:
A zero has to be put into the units column to mark the place. If the zero
was not there we would not know the number was 30.
•
•
Underneath 0·3 × 10 = 3 write: 0·3 × 100 = 30.
•
Repeat for a selection of decimals with up to two places multiplied by 10, then
100, referring to the place value mat when appropriate.
Use the 0 and 3 digit cards to show 0·3 on the place value mat. Ask: What is
zero point 3 multiplied by 10? (3)
Say: Ten is a very important number in our number system. Every time we
multiply by 10 the digits move one place value to the left.
Display Discussion Book 6 page 46 and explain how the third place value mat
demonstrates the effect of multiplying 0·3 by 10 and 100.
•
Play either of the paired or group games: ‘Multiply the whole number
by 10 or 100’ or ‘Multiply the decimal by 10 or 100’ on RCMs 63 and 64.
Practise
Teach
Say: I have 54 on my calculator display. What single multiplication should
I key in to change it to 5400? (× 100) What if I change it to 540? (× 10)
There are 24 eggs in this tray. How many eggs would there be in 100
identical trays? (2400) How many millilitres are there in 4·5 litres? (4500)
w & Asse
vie
ss
Apply
&
iew Asse
Teach
or
ev
ss
Practise
Apply R
9 × 10 = 90
9 × 100 = 900
•
Apply R
e
Teach continued
Practise
103