2. 1 half Fractions and Decimals 8

3. 1 half quarter Fractions and Decimals 8

4. 1 half quarter eighth Fractions and Decimals 8

5. 1.Create equal strips of paper by ruling rows 1 ruler width. 2.Keep 1 strip whole and place it at the top of the fraction wall as 1. 3.Divide one strip into halves by dividing into 2 equal parts. 4.Place the halves under the 1 to continue the fraction wall. 5.What fraction of 1 is a half? 6.Divide one strip into quarters by halving a half. 7.Place the quarters under the halves to continue the fraction wall. 8.What fraction of 1 is a quarter? 9.What fraction of a half is a quarter? 10.Divide one strip into eighths by halving a quarter. 11.Place the eighths under the quarters to continue the fraction wall. 12.What fraction of 1 is an eighth? 13.What fraction of a quarter is an eighth? 14.What fraction of a half is an eighth? Reflection: How can we describe multiplicative relationships between fractions? Investigation: Problem Solving Gina cut her paper into quarters, then she cut her quarters in half. What fraction did Gina create? Problem Solving Helen wanted to divide her shape into quarters. She divided her shape in half. What could Helen do to create quarters from her halves? Fractions and Decimals 8

8. Investigation: 1.Create equal strips of paper by ruling rows 1 ruler width. 2.Divide one strip into fifths by estimating a fifth at each end, then estimating the remaining 3 fifths. 3.Place the fifths under the eighths to continue the fraction wall. 4.What fraction of 1 is a fifth? 5.Divide one strip into tenths by halving a fifth, or by fifthing a half. 6.Place the tenths under the fifths to continue the fraction wall. 7.What fraction of 1 is a tenth? 8.What fraction of a fifth is a tenth? 9.What fraction of a half is a tenth? Reflection: How can we describe multiplicative relationships between fractions? Problem Solving If I cut a fifth in half, what fraction will I have? Problem Solving Mark wanted to divide his shape into tenths. He divided his shape in half. What could Mark do to create tenths from his halves? Fractions and Decimals 8

11. Investigation: 1.Create equal strips of paper by ruling rows 1 ruler width. 2.Divide one strip into thirds by estimating a third, then estimating the remaining 2 thirds. 3.Place the thirds under the tenths to continue the fraction wall. 4.What fraction of 1 is a third? 5.Divide one strip into sixths by halving a third, or by thirding a half. 6.Place the sixths under the thirds to continue the fraction wall. 7.What fraction of 1 is a sixth? 8.What fraction of a third is a sixth? 9.What fraction of a half is a sixth? Reflection: How can we describe multiplicative relationships between fractions? Problem Solving If I cut a half into thirds, what fraction will I have? Problem Solving Mary wanted to divide her shape into sixths. She divided her shape in half. What could Mary do to create sixths from her halves?

12. Fractions and Decimals 8

13. Investigation: 1.Create equal strips of paper by ruling rows 1 ruler width. 2.Divide one strip into twelfths halving a sixth and by sixthing a half and by quartering a third, and by thirding a quarter. 3.Place the twelfths under the sixths to continue the fraction wall. 4.What fraction of 1 is a twelfth? 5.What fraction of a sixth is a twelfth? 6.What fraction of a half is a twelfth? 7.What fraction of a third is a twelfth? 8.What fraction of a quarter is a twelfth? Reflection: How can we describe multiplicative relationships between fractions? Problem Solving Leo wanted to divide his shape into twelfths. He divided his shape in half. What could Leo do to create twelfths from his halves? Problem Solving Gina cut her paper into thirds, then she cut her thirds in quarters. What fraction did Gina create? Fractions and Decimals 8

15. Investigation: 1.Have identical shapes of paper, for example, squares or circles. 2.Divide the shapes into halves, quarters, eighths, thirds, sixths, twelfths, fifths and tenths. 3.Explain how you have created each fraction. 4.Explain the multiplicative relationships between the fractions. Reflection: How can we describe multiplicative relationships between fractions? Fractions and Decimals 8

16. Investigation: 1.Once you have constructed your own fraction wall, explaining multiplicative relationships between the fractions as you build it, you may use a commercially available fraction wall to continue to investigate the multiplicative relationships. 2.Build the fraction wall by: Starting with 1, identifying that all of the fractions are fractions of this sized 1. Placing a fraction on the wall that has a multiplicative relationship to the fractions already on the fraction wall. 3.For example, you may select any fraction as your first fraction because every fraction has a multiplicative relationship to 1. Let’s select thirds. 4.Explain the multiplicative relationships on the fraction wall, for example a third is a third of 1. 5.Our next fraction must have a multiplicative relationship to thirds. Let’s select sixths. 6.Explain the multiplicative relationships on the fraction wall, for example, a sixth is a sixth of 1, a sixth is half of a third. 7.Our next fraction must have a multiplicative relationship to thirds and / or sixths. Let’s select twelfths. 8.Explain the multiplicative relationships on the fraction wall, for example, a twelfth is a twelfth of 1, a twelfth is half of a sixth, a twelfth is quarter of a third. 9.Continue building the fraction wall placing fractions on the wall that have a multiplicative relationship to fraction/s already on the wall, explaining all multiplicative relationships. Reflection: How can we describe multiplicative relationships between fractions? Fractions and Decimals 8