2. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10

3. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10

4. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10

5. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10

6. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths

7. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 1 4

8. 1.At least once a week, draw a multiplicative place value chart to tenths from memory. 2.Explain to a friend that you are multiplying by 10 to get the value of the column on the left. 3.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? Investigation: Problem Solving What number is missing from this place value chart? Place Value 20 Fractions and Decimals 11

9. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 1 4 1 4

10. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 1 4 1 4. decimal point dec means 10

11. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 0 4 0 4..

12. 1.Gather examples of points (dots). 2.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? Investigation: Place Value 20 Fractions and Decimals 11 Problem Solving Is this dot a decimal point? $5.25 Why?

13. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 1 0 1.. 1.

14. 1.Draw a multiplicative place value chart to tenths. 2.Select a card and place it in the tenths column. 3.Record the number with and without the zero in the ones place. 4.Explain that the number’s value is still ‘tenths’. For example, select Investigation: Place Value 20 Fractions and Decimals 11 Problem Solving Jill recorded a number as 0·7 and Jerry recorded a number as ·7 Do both numbers have the same value? What is the value?

15. 1 0 1 = 1 one 1 = 10 tenths Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10

16. 1 0 0 10 = 1 ten 10 = 10 ones 10 = 100 tenths Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10

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

18. 1.Draw a multiplicative place value chart to tenths. 2.Select a card and place it in the ones place. 3.Describe your number of ones using standard and non-standard place value as a number of ones and as a number of tenths. 4.Place your card in the tens place. 5.Describe your number of tens using standard and non-standard place value as a number of tens and as a number of tenths. 6.Place your card in the hundreds place. 7.Describe your number of hundreds using standard and non-standard place value as a number of hundreds and as a number of tenths. Investigation: Place Value 20 Fractions and Decimals 11 Reflection: How can we describe ones, tens and hundreds as tenths? Problem Solving Alex recorded a number as 5 tens. Mike recorded a number as 500 tenths. Did they both record the same number?

19. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10 1 4 1 4 = 1 one + 4 tenths... 1 4 = 14 tenths..

20. 1.Draw a multiplicative place value chart to tenths. 2.Select cards to make a number with ones and tenths. 3.Describe your number using standard and non-standard place value. 4.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? Investigation: Place Value 20 Fractions and Decimals 11 Problem Solving 6.8 is equal to: (a)68 tens68 tens (b)68 ones68 ones (c)68 tenths68 tenths Problem Solving 7.3 is equal to: (a)7 tenths and 3 ones7 tenths and 3 ones (b)7 ones and 3 tenths7 ones and 3 tenths (c)73 ones73 ones

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

22. 1.Draw a multiplicative place value chart to tenths. 2.Select cards to make a number with tens, ones and tenths. 3.Describe your number using standard and non-standard place value. 4.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 Investigation: Place Value 20 Fractions and Decimals 11 Problem Solving 46.8 is equal to: (a)468 tens468 tens (b)468 ones468 ones (c)468 tenths468 tenths Problem Solving 47.3 is equal to: (a)4 tens and 7 tenths and 3 ones4 tens and 7 tenths and 3 ones (b)4 tens and 7 ones and 3 tenths4 tens and 7 ones and 3 tenths (c)473 ones473 ones Reflection: How can we describe numbers with tenths using standard and non-standard place value?

23. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10. 0.8 x 10 = 8 onestens hundredsthousands x 10 ÷ 10 tenths x 10.

24. Place Value 20 Fractions and Decimals 11 onestens hundredsthousands x 10 ÷ 10 tenths x 10. 8 ÷ 10 = 0.8 onestens hundredsthousands x 10 ÷ 10 tenths x 10.

25. 1.Draw a multiplicative place value chart to tenths. 2.Place cards in columns to make a number. 3.Record the number. 4.Move the digits one column to the left. 5.Record the new number. 6.What happened to the value of the number when you moved the digits one column to the left? Investigation: Place Value 20 Fractions and Decimals 11 Problem Solving Alex placed a digit in the tenths column. He multiplied it by 10. Which column is the digit in now? What is the value of the digit now? Problem Solving Alex placed a digit in the ones column. He divided it by 10. Which column is the digit in now? What is the value of the digit now? Reflection: Why do digits move to the left when we multiply by 10 and to the right when we divide by 10?

26. Place Value 20 Fractions and Decimals 11

27. 1.Sit with a friend. 2.Each select cards to make a number with tenths. 3.Place your numbers in order. 4.Explain your order using place value. 5.Each of you make a number with tenths that would come between your numbers. 6.For example, Reflection: How did you use place value to order your numbers? Place Value 20 Fractions and Decimals 11 More Investigations:

28. 1.Sit with a friend. 2.Take turns to take a card and place it in either the tenths place or the ones place or the tens place. 3.Once placed it cannot be changed. 4.Read your number out loud. 5.The child who creates the highest / lowest number takes all cards. 6.Explain your number using standard place value. 7.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 More Investigations:

29. 1.Sit with a friend. 2.Take turns to flip 2 or 3 cards and each make a number with tenths. 3.Read your numbers out loud. 4.Each place your number on the same number line. 5.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 More Investigations:

30. 1.Sit with a friend. 2.2 or 3 cards are selected to be a target number with tenths. 3.Each of you flip 2 or 3 cards to make a number with tenths. 4.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 More Investigations:

31. 1.Measure lengths in millimetres. 2.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 More Investigations:

32. 1.Sit with a friend. 2.Make a place value slide: 3.Take a sheet of paper and cut slits into which you thread a strip of paper, for example, 4.Record a number onto the strip, for example, 5.Record the number’s value. 6.Move it between place value columns. 7.Record the number’s new value. 8.What number did you multiply or divide by? Place Value 20 Fractions and Decimals 11 More Investigations: 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?