# 3 7 = + 5 1 3 x 3 7 = + 5 1 3 x 02 6 = 5 x2 1 7 = 0 6 + 1 1 0 4 0 3 1 +1 0 3 4 0 + +1 10 0

1 6 10 3 7 1 6 =1 = 11 + 3 10 1 0 3 07 3 0 =1 + 1 5 10 13 10

Addition and Subtraction 30 Fractions and Decimals 33 2 + 27 1 = 12 3 2x 4 8 = 3x4 1 2 7 18 + 2 = 1 1 2 4 2 3 1 +1 2 +2 7 2

12 1 37 12 3 +1 2 5 +1 2 4 3 4 1 2 Addition and Subtraction 30 Fractions and Decimals 33

2 + 27 1 = 12 3 1+2=3 + = + = =1 = 15 12 = 1 1 + 3 =4 1 +2 = 4 Addition and Subtraction 30 Fractions and Decimals 33 4 Factors of 3: 1, 3 12: 1, 2, 3, 4, 6, 12 Circle the common factors, factors of 3: 1, 3 factors of 12: 1, 2, 3, 4, 6, 12 3 3

1 12 3 = 4 4 = 4 Addition and Subtraction 30 Fractions and Decimals 33 2 7 = 10 5 2x 2 4 = 5x 10 2 7 4 = 10 10 4 -1 0 3 7

1 10 0 7 4 3 = 10 10 10 7 2 10 5 = 3 10 Addition and Subtraction 30 Fractions and Decimals 33 3 2

- 1 = 4 12 3 8 2x 4 = 3 X 4 12 8 3 4 - 1 1 1 2 32 5 1 + 12 12 + 5 1 7 2

3 2 1 2 3 -1 2 -1 3 3 1 2 3 4 1 2 Addition and Subtraction 30 Fractions and Decimals 33 8 1

8 3 - 1 4 - 1 = 35 1 12 1 12 2 2 31 = 2 15 8 7 = 1 1 1 2 2 2 7

7 2 2 + = 12 1 2 3 4 - 12 = 2 7 1 12 3 2 Addition and Subtraction 30 Fractions and Decimals 33 Investigation: 1. Select cards to make 2 fractions or mixed numerals with related denominators that are neither too easy nor too challenging to add. 2. Record the fractions in an addition number sentence. 3. Add the fractions using place value. Reflection: How can we add fractions and mixed numerals using

place value? Problem Solving Sarah was paving a path. She used of a bag of sand on Saturday, and 1 bags of sand on Sunday. How much sand did she use altogether? Addition and Subtraction 30 Fractions and Decimals 33 Investigation: 1. Select cards to make 2 fractions or mixed numerals with related denominators that are neither too easy nor too challenging to subtract. 2. Record the fractions in a subtraction number sentence. 3. Subtract the fractions, using place value. Reflection: How can we subtract fractions and mixed numerals using place value? Problem Solving Sarah is paving 2 paths. She has 2 bags of sand. She needs of a bag of sand for the first path and 1 bags of sand for the second path. How much more sand will they need? Addition and Subtraction 30 Fractions and Decimals 33

Addition and Subtraction 30 Fractions and Decimals 33 Investigation: 1. Use playing cards to make non-unit fractions (fractions where the numerator is not 1, for example, ) that is neither too easy nor too challenging. 2. Name the fraction needed to make 1. 3. Name an equivalent fraction needed to make 1. Reflection: How can we add fractions and mixed numerals using place value? Addition and Subtraction 30 Fractions and Decimals 33 Investigation: 1. Use playing cards to make a mixed numeral. 2. Name the fraction needed to add to get to the nearest whole number. 3. Name an equivalent fraction needed to make the next whole number. Reflection: How can we add fractions and mixed numerals using place value?

Addition and Subtraction 30 Fractions and Decimals 33 Investigation: 1. Sit with a friend. 2. Have some paper circles. 3. Each of you divide 1 circle in halves, 1 circle in quarters, 1 circle in eighths, 1 circle in thirds, 1 circle in sixths, 1 circle in twelfths, 1 circle in fifths, 1 circle in tenths. 4. Use your understanding of measuring and constructing angles with a protractor and the number of degrees in a circle (revolution). 5. Using both sets of fractions, join fractions with the same denominators together. Record in an addition number sentence. 6. For example, join 3 fifths with 4 fifths, and record + = 7. Reflection: How can we add fractions and mixed numerals using place value? Addition and Subtraction 30 Fractions and Decimals 33