2. thousands hundreds tens ones x 10 x 10 x 10 ÷ 10 ÷ 10 ÷ 10
Place Value 20
Fractions and Decimals 11

3. 3 4 1 3 thousands hundreds tens ones x 10 x 10 x 10 ÷ 10 ÷ 10 ÷ 10
Place Value 20
Fractions and Decimals 11

4. thousands hundreds tens ones x 10 x 10 x 10 ÷ 10 ÷ 10 ÷ 10
Place Value 20
Fractions and Decimals 11

5. thousands hundreds tens ones x 10 x 10 x 10 ÷ 10 ÷ 10 ÷ 10
Place Value 20
Fractions and Decimals 11

6. ÷ 10 = 1 10 thousands hundreds tens ones tenths x 10 x 10 x 10 ÷ 10
÷ 10 = 1 10
Place Value 20
Fractions and Decimals 11

7. 1 4 thousands hundreds tens ones tenths x 10 x 10 x 10 x 10 ÷ 10 ÷ 10
Place Value 20
Fractions and Decimals 11

8. Investigation:
At least once a week, draw a multiplicative place value chart to tenths from memory.
Explain to a friend that you are multiplying by 10 to get the value of the column on the left.
Explain to a friend that you are dividing by 10 to get the value of the column to the right.
Reflection: Why is the value of the column to the right of the ones column, tenths?
Place Value 20
Fractions and Decimals 11

9. 1 4 1 4 thousands hundreds tens ones tenths x 10 x 10 x 10 x 10 ÷ 10
1 4
Place Value 20
Fractions and Decimals 11

10. . 1 4 1 4 thousands hundreds tens ones tenths decimal point
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths 1 4
÷ 10
÷ 10
÷ 10
÷ 10 .
1 4
decimal point
dec means 10
Place Value 20
Fractions and Decimals 11

11. . . 4 0 4 thousands hundreds tens ones tenths x 10 x 10 x 10 x 10 ÷ 104
÷ 10
÷ 10
÷ 10
÷ 10 .
0 4
Place Value 20
Fractions and Decimals 11

12. Reflection: What is a decimal point?
Investigation:
Gather examples of points (dots).
Investigate if they are decimal points.
For example,
in time, the colon is sometimes recorded as a dot. Is the dot a decimal point? Are we multiplying and dividing by 10?
the dot dividing the seconds from the fractions of seconds when timing races. Is the dot a decimal point? Are we multiplying and dividing by 10?
in AFL, scores are recorded using a dot. Is the dot a decimal point? Are we multiplying and dividing by 10?
the dot between the dollars and cents. Is the dot a decimal point? Are we multiplying and dividing by 10?
Reflection: What is a decimal point?
Place Value 20
Fractions and Decimals 11

13. . 1 . 1 . 0 1 thousands hundreds tens ones tenths x 10 x 10 x 10 x 10
÷ 10
÷ 10
÷ 10
÷ 10 . 1 .
0 1
Place Value 20
Fractions and Decimals 11

14. Draw a multiplicative place value chart to tenths.
Investigation:
Draw a multiplicative place value chart to tenths.
Select a card and place it in the tenths column.
Record the number with and without the zero in the ones place.
Explain that the number’s value is still ‘tenths’.
For example, select
Record the number as 0·4 and as ·4, explaining that the value is still 4 tenths or 𝟒 𝟏𝟎 .
Place Value 20
Fractions and Decimals 11

15. 1 0 1 = 1 one 1 = 10 tenths thousands hundreds tens ones tenths x 10
÷ 10
÷ 10
÷ 10
÷ 10
1 = 1 one
1 = 10 tenths
Place Value 20
Fractions and Decimals 11

16. 1 0 0 10 = 1 ten 10 = 10 ones 10 = 100 tenths thousands hundreds tens
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths
÷ 10
÷ 10
÷ 10
÷ 10
10 = 1 ten
10 = 10 ones
10 = 100 tenths
Place Value 20
Fractions and Decimals 11

17. 1 0 0 0 100 = 1hundred 100 = 10 tens 100 = 100 ones 100 = 1000 tenths
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths
÷ 10
÷ 10
÷ 10
÷ 10
100 = 1hundred
100 = 10 tens
100 = 100 ones
100 = 1000 tenths
Place Value 20
Fractions and Decimals 11

18. Draw a multiplicative place value chart to tenths.
Investigation:
Draw a multiplicative place value chart to tenths.
Select a card and place it in the ones place.
Describe your number of ones using standard and non-standard place value as a number of ones and as a number of tenths.
Place your card in the tens place.
Describe your number of tens using standard and non-standard place value as a number of tens and as a number of tenths.
Place your card in the hundreds place.
Describe your number of hundreds using standard and non-standard place value as a number of hundreds and as a number of tenths.
Reflection: How can we describe ones, tens and hundreds as tenths?
Place Value 20
Fractions and Decimals 11

19. .
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths 1 4
÷ 10
÷ 10
÷ 10
÷ 10 .
1 4 = 1 one + 4 tenths .
1 4 = .
1 4 = 14 tenths .
1 4 =
Place Value 20
Fractions and Decimals 11

20. Draw a multiplicative place value chart to tenths.
Investigation:
Draw a multiplicative place value chart to tenths.
Select cards to make a number with ones and tenths.
Describe your number using standard and non-standard place value.
Record tenths as both fractions and decimals.
For example,
3.2 = 3 ones + 2 tenths, 3.2 = 32/10
3.2 = 32 tenths, 3.2 = 32/10
Reflection: How can we describe numbers with tenths using standard and non-standard place value?
Place Value 20
Fractions and Decimals 11

21. .
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths 1 2 4
÷ 10
÷ 10
÷ 10
÷ 10 .
12 4 = 1 ten + 2 ones + 4 tenths .
12 4 = 1 ten + 2 ones .
12 4 = 12 ones + 4 tenths . .
12 4 = .
12 4 = 5 ones + 77 tenths .
12 4 = 124 tenths .
12 4 = 5 ones
12 4 =
Place Value 20
Fractions and Decimals 11

22. Investigation: Draw a multiplicative place value chart to tenths.
Select cards to make a number with tens, ones and tenths.
Describe your number using standard and non-standard place value.
Record tenths as both fractions and decimals.
For example,
53.2 = 5 tens + 3 ones + 2 tenths
53.2 = 53 ones + 2 tenths
53.2 = 532 tenths
53.2 = 3 tens + 12 ones + 12 tenths
Reflection: How can we describe numbers with tenths using standard and non-standard place value?
Problem Solving
46.8 is equal to:
468 tens
468 ones
468 tenths
Problem Solving
47.3 is equal to:
473
Problem Solving
47.3 is equal to:
4 tens and 7 tenths and 3 ones
4 tens and 7 ones and 3 tenths
473 ones
Place Value 20
Fractions and Decimals 11

23. . . 0.8 x 10 = 8 thousands hundreds tens ones tenths thousands
÷ 10
÷ 10
÷ 10
÷ 10 .
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths
÷ 10
÷ 10
÷ 10
÷ 10
0.8 x 10 = 8
Place Value 20
Fractions and Decimals 11

24. . . 8 ÷ 10 = 0.8 thousands hundreds tens ones tenths thousands
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths
÷ 10
÷ 10
÷ 10
÷ 10 .
x 10
x 10
x 10
x 10
thousands
hundreds
tens
ones
tenths
÷ 10
÷ 10
÷ 10
÷ 10
8 ÷ 10 = 0.8
Place Value 20
Fractions and Decimals 11

25. Draw a multiplicative place value chart to tenths.
Investigation:
Draw a multiplicative place value chart to tenths.
Place cards in columns to make a number.
Record the number.
Move the digits one column to the left.
Record the new number.
What happened to the value of the number when you moved the digits one column to the left?
Reflection: Why do digits move to the left when we multiply by 10 and to the right when we divide by 10?
Place Value 20
Fractions and Decimals 11

26. Place Value 20
Fractions and Decimals 11

27. Reflection: How did you use place value to order your numbers?
More Investigations:
Sit with a friend.
Each select cards to make a number with tenths.
Place your numbers in order.
Explain your order using place value.
Each of you make a number with tenths that would come between your numbers.
For example,
Reflection: How did you use place value to order your numbers?
Place Value 20
Fractions and Decimals 11

28. Once placed it cannot be changed. Read your number out loud.
More Investigations:
Sit with a friend.
Take turns to take a card and place it in either the tenths place or the ones place or the tens place.
Once placed it cannot be changed.
Read your number out loud.
The child who creates the highest / lowest number takes all cards.
Explain your number using standard place value.
Each place your number on the same number line, explaining your placement.
Reflection: How did you use place value to decide the values of your numbers?
Place Value 20
Fractions and Decimals 11

29. Take turns to flip 2 or 3 cards and each make a number with tenths.
More Investigations:
Sit with a friend.
Take turns to flip 2 or 3 cards and each make a number with tenths.
Read your numbers out loud.
Each place your number on the same number line.
Each suggest a number that would come between the 2 numbers, using place value to explain how you know.
Reflection: How did you use place value to find a number between your numbers?
Place Value 20
Fractions and Decimals 11

30. 2 or 3 cards are selected to be a target number with tenths.
More Investigations:
Sit with a friend.
2 or 3 cards are selected to be a target number with tenths.
Each of you flip 2 or 3 cards to make a number with tenths.
The child who makes a number closest to the target number wins.
Reflection: How did you use place value to find make a number close to the target number?
Place Value 20
Fractions and Decimals 11

31. Measure lengths in millimetres.
More Investigations:
Measure lengths in millimetres.
Convert to centimetres and millimetres, then to centimetres and a fraction of a centimetre, then to centimetres and a decimal fraction of a centimetre.
For example,
45 mm = 4 cm + 5 mm = 41/2 cm = 4.5 cm.
Reflection: How are multiplicative place value and metric measurement related?
Place Value 20
Fractions and Decimals 11

32. Make a place value slide:
More Investigations:
Sit with a friend.
Make a place value slide:
Take a sheet of paper and cut slits into which you thread a strip of paper, for example,
Record a number onto the strip, for example,
Record the number’s value.
Move it between place value columns.
Record the number’s new value.
What number did you multiply or divide by?
Reflection: Why are we multiplying by 10 when we move digits to the left and dividing by 10 when we move digits to the right?
Place Value 20
Fractions and Decimals 11