2. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27

3. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation: 1.Select cards to make a fraction. 2.Use the fraction as the first term in an increasing number pattern, and repeatedly add the fraction. 3.Record the pattern on a number line. 4.Identify the part that repeats. 5.Describe a rule to describe the way the pattern repeats. 6.Use the rule to find the next term. Reflection: How did you determine a rule to describe the way your pattern increases?

4. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27

5. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation: 1.Select cards to make a fraction. 2.Record a whole number as the first term in a decreasing number pattern, and repeatedly subtract the fraction. 3.Record the pattern on a number line. 4.Identify the part that repeats. 5.Describe a rule to describe the way the pattern repeat. 6.Use the rule to find the next term. Reflection: How did you determine a rule to describe the way your pattern decreases?

6. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Repeatedly add 0.3.

7. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Start at 0.4 and Repeatedly add 0.3.

8. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation: 1.Select cards to make a decimal. 2.Use the decimal as the first term in an increasing number pattern, and repeatedly add the decimal. 3.Record the pattern on a number line. 4.Identify the part that repeats. 5.Describe a rule to describe the way the pattern repeat. 6.Use the rule to find the next term. Reflection: How did you determine a rule to describe the way your pattern increases? Problem Solving 2.75, 3.0, 3.25, 3.5, 3.75,... What is the rule to continue this decimal number pattern? (a) increase by 0.5 (b) increase by 0.25 (c) decrease by 0.5 (d) decrease by 0.25

9. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27

10. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Start at 4 and Repeatedly subtract 0.3.

11. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation: 1.Select cards to make a decimal. 2.Record a whole number as the first term in a decreasing number pattern, and repeatedly subtract the decimal. 3.Record the pattern on a number line. 4.Identify the part that repeats. 5.Describe a rule to describe the way the pattern repeat. 6.Use the rule to find the next term. Reflection: How did you determine a rule to describe the way your pattern decreases? Problem Solving The number pattern shows the height of a burning candle measured every 5 minutes. 15cm, 14.25cm, 13.5cm, 12.75cm, 12cm, … How far does the candle burn each 5 minutes? What will be the height of the candle if it burns for 5 more minutes?

12. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27

13. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation:

14. Place Value 27 Fractions and Decimals 24 Patterns and Algebra 27 Investigation: 1.Create a rule involving multiples of a decimal. For example, ‘Start with 0.4, and repeatedly add 0.4’, or ‘Record the multiples of 0.4’. 2.Record the number pattern on a number line. 3.Use the rule describing the way the pattern repeats 4.Work out further terms using the rule. Reflection: How did you determine the pattern from the rule?