68.25 + 58.97 = 68.25 682.5 + 58.97 = 50 + 8 + 0.9 + 0.07 40 + 10 118.25 68.25 + 10 108.25 + 40 +2 +10 +40 68.25 108.25 118.25 120.25 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32 Continue to next page.

Continued from previous page 682.5 + 58.97 = 50 + 8 + 0.9 + 0.07 40 + 10 2 + 6 0.8 + 0.1 0.05 + 0.02 +2 +10 +40 +6 68.25 108.25 120.25 126.25 118.25 +2 +10 +40 +6 +0.8 +0.1 68.25 108.25 118.25 126.25 127.05 120.25 127.15 +2 +10 +40 +6 +0.8 +0.1 +0.05 +0.02 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32 68.25 108.25 118.25 126.25 127.05 127.2 127.22 120.25 127.15 682.5 + 58.97 = 127.22

68.25 + 58.97 = 68.25 + 60 = 128.25 128.25 – 1.03 = 127.22 682.5 + 58.97 = 127.22 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32

127.22 - 58.97 = 127.22 - 58.97 = 50 + 8 + 0.9 + 0.07 - 20 107.22 127.22 127.22 - 58.97 = 50 + 8 + 0.9 + 0.07 20 + 30 - 20 - 30 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32 77.22 107.22 127.22 Continue to next page.

Continued from previous page. 127.22 - 58.97 = 50 + 8 + 0.9 + 0.07 20 + 30 7 + 1 - 1 - 7 - 20 - 30 69.22 70.22 77.22 107.22 127.22 127.22 - 58.97 = 50 + 8 + 0.9 + 0.07 127.22 - 58.97 = 68.25 20 + 30 7 + 1 0.2 + 0.7 0.02 + 0.05 - 0.7 - 1 - 7 - 20 - 0.05 - 0.02 - 0.2 - 30 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32 68.25 68.30 68.32 69.02 69.22 70.22 77.22 107.22 127.22 Continue to next page.

127.22 ̶ 58.97 = 127.22 ̶ 60 = 67.22 67.22 + 1.03 = 68.25 127.22 ̶ 58.97 = 68.25 Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32

Investigation: Select cards to make numbers with decimals to add and subtract using place value and compensation. Make digits in the numbers you add, each add to more than 10 to allow you to add using place value. Make digits in the numbers you subtract, each subtract into the decade below to allow you to subtract using place value. Add or subtract using place value. If one of the numbers is close to a place value, add or subtract using compensation. Reflection: How can we add and subtract numbers with decimals? Problem Solving Jenny showed this number on her calculator. 6.82 She changed it so that it became this number. 23.51 What did Jenny do to change 6.82 to 23.51? Problem Solving Jenny showed this number on her calculator. 8.25 She changed it so that it became this number. 6.87 What did Jenny do to change 8.25 to 6.87? Problem Solving Matt thought of a number. He added 36.8. The answer was 41.4. What number did Matt first think of? Problem Solving Matt thought of a number. He subtracted 2.75. The answer was 3.58. What number did Matt first think of? Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32

Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32

Reflection: How can we add and subtract numbers with decimals? Investigation: Sit with a friend. Flip cards to make a target number with decimals. Flip cards to make a starting number with decimals. Take turns to flip a card and decide on the value to add or subtract the number, for example, as thousands, hundreds, tens, ones, tenths, hundredths, thousandths etc. Keep a running total. When the total is within one digit of the target number, you may ‘wish’ for the digit. Keep a record of the number of turns it took you to reach the target number. NB: You may choose to add or subtract a digit as tens and your friend may choose to add or subtract a digit as hundreds. This is great! Wait to see whose strategy reaches the target number more quickly. This game is based on WISHBALL THOUSANDTHS. Other levels of Wishball are also available on the Internet and as Apps – enter ‘wishball’ into your search engine or app store. Reflection: How can we add and subtract numbers with decimals? Addition and Subtraction 29 Fractions and Decimals 32 Place Value 32