## Tuesday, 4 November 2014

Solve the problems below. Try to use the strategy explained in the box above each question. Make sure you show all the steps you use to solve it.

 Stage 7: Advanced Multiplicative I can choose appropriately from a broad range of mental strategies to estimate answers and solve addition and subtraction problems involving decimals, integers, and fractions. I can also use multiplication and division to solve addition and subtraction problems with whole numbers.

 Stage 7: Advanced Multiplicative I can split decimal numbers in parts to solve addition and subtraction problems. e.g.a)  6.03 – 5.8 = __   as 6.03 – 5 – 0.8 = 1.03 – 0.8 = 0.23 (standard place value partitioning)  or b)2.36 + 1.27 = 2 + 1 = 3,  and .3 + .2 = .5,  and .06 + .07 = .13  So 3 + .5 + .13 = 3.63

1. Shona needs a length of wood for some shelves. Her first shelf needs to be 1.27m long and the second shelf needs to be 1.86m long. How much timber does need altogether?
1.27 + 1.86 = 3.13
1+ 1 = 2
0.27 + 0.86 = 1.13
2 + 1.13 = 3.13

2. She ends up finding 2 lengths of timber that are long enough but will have to cut them to the right length. The first piece is 1.5m. How much does she need to cut off it for the first shelf?
2 - 1.5 = 0.5
2 - 0.5 = 1.5
1.5 - 1 = 0.5

 Stage 7: Advanced Multiplicative I can solve addition and subtraction problems with decimal numbers by rounding and compensating. e.g.  a) 3.2 + 1.95 = (3.2 - .05) +  (1.95 + .05) = 3.15 + 2 = 5.15 Or b) 4.31 - 2.98 = 4.31 - 3 = 1.31 + .02 = 1.33

3. Dane was 1.46m tall when he last measured himself. He has since grown a further 0.47m. What is is height now?
1.46 + 0.47 = 1.93
-0.03     +0.03
1.43 + 0.50 = 1.93

4. When Dane was 1.46m tall his little sister was only 0.98m tall. How much taller was Dane than his sister?

1.46 - 0.98 = 0.48
+0.02 +0.02
1.48 - 1 = 0.48

 Stage 7: Advanced Multiplicative I can solve subtraction problems with decimal numbers by reversing to an addition equation then jumping up tidy numbers on a numberline (reverse and jump) e.g. 6.03 - 5.8 =  5.8 + __ = 6.03 5.8 + 0.2 = 6,  6 + 0.03 = 6.03    .2 + .03 = .23       So 6.03 - 5.8 = 0.23

5. Tiana has a container with 2.75 litres of juice in it. She uses it to fill a smaller container of juice that holds .985 litres. How much juice is left in the larger container?
2.75 - .985 = 1.765
0.985 +  = 2.75
0.985 + 0.015 = 1
1 + 0.75 = 1.75
0.015 + 0.75 = 0.765
1 + 0.765 = 1.765

 Stage 7: Stage 7: Advanced Multiplicative I can solve problems involving the addition and subtraction of unlike fractions by finding common denominators and partitioning e.g. ¾  + ⅝  =  (¾  +  2/8) + ⅜ =  (¾ + ¼) + ⅜ = 1 ⅜

6. Allanah has 3/4 of a one pizza left and 5/8 of another.  How much pizza has she got altogether?
3/4 + 5/8 = 1 3/8
3/4 + 2/8 = 5/8
5/8 + 3/8 = 1
3/4 + 1/4 = 1
1 + 3/8 = 1 3/8

 Stage 7: Advanced Proportional: I can use a range of mental partitioning strategies to estimate answers and solve problems that involve adding and subtracting fractions, including decimals. I am able to combine ratios and proportions with different amounts. The strategies include using partitions of fractions and “ones”, and finding equivalent fractions.

 e.g. 2 ¾ - 1 ⅔ = 2 - 1 and ¾ - ⅔ = 1 and 9/12 - 8/12 = 1 1/12  (finding equivalent fractions)

1. Tom knows that for every 20 newspapers he delivers he gets \$1.60.  How many papers does he need to deliver to earn \$20
20 - 1.6
40 - 3.2
60 - 4.8
80 - 6.4
100 - 8
120 - 9.6
140 - 11.2
160 - 12.8
180 - 14.4
200 - 16
220 - 17.6
240 - 19.2
250 - 20
1. Hana has a cup that hold .275 litres and a container that holds 2.2 litres.  How many cupfuls does she need to fill the container.
2.2 -  .275 = 1.925
.275 +   = 2.2
.275 + 0.725 = 1
1 + 0.2 = 1.2
0.725 + 0.2 = .925
1 + 0.925 = 1.925