This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
solve multiplication and division problems with decimals
This activity involves decimal multiplication and division in the context of the ratio of grams of dog roll to grams (kilograms) of dog. The activity is therefore best suited for students at the advanced multiplicative stage or beyond of the Number Framework.
Question 1 asks the students to think of a short-cut method for calculating the mass of dog roll needed to feed various-sized dogs given that 100 grams is required for every 5 kilograms of a dog’s mass.
To work out the amount of dog roll needed daily by each of the 7 dogs in question 2, the students can make use of the strategy for multiplying by 20 that they have hopefully come up with for question 1. A variation on renaming 20 as 2 x 10 or 10 x 2 is the use of doubling and halving, which, in this question, ties in with multiplying by 10. For example, for Brock, the border collie that weighs 23 kilograms, 23 x 20 can be renamed as 46 x 10 to give an answer of 460 grams. Encourage the students to calculate all the answers for this question mentally. If they use the 20 = 10 x 2 strategy with the decimal numbers in particular, they will be applying their knowledge
of place value.
In question 3, the students need to add the number of grams of dog roll required daily for all 8 dogs, not just the 7 in question 2. Encourage them to use number strategies such as rounding and compensation to add these up without using a calculator.
The students should be aware that amounts larger than 999 grams are usually given in kilograms and that there are 1 000 grams in a kilogram. To convert 4 460 grams to kilograms, they just have to shift all the digits 3 columns to the right, so 4 460 grams becomes 4.460 or simply 4.46 kilograms.
Answers to Activity
1. A quicker way is to multiply by 20, which you might choose to rename as 2 x 10. (Multiplying by 20 is the same as ÷ 5 x 100.)
2. a. 560 g
b. 50 g
c. 380 g
d. 160 g
e. 460 g
f. 790 g
g. 860 g
3. 4 460 g or 4.46 kg