Rates of Change I am learning to solve

Rates of Change I am learning to solve rate problems.

You can buy 16 apples for $12. How many apples can you buy for $9? There a few different ways we can work this out. First lets try using pictures. apples $1 $1 $1 You can see it takes $3 to buy 4 apples If you can buy 4 apples for $3 you must be able to buy 12 apples for $9 Dollars Apples $3 4 $6 8 $9 12 $12 16 $1 Dollars

Now let’s use a table to answer the same question. You can buy 16 apples for $12. How many apples can you buy for $9? Divide the $12 by 4 so we can work out how many Apples we will get for $3 Dollars Apples $12 16 $9 $12 …. . $3 4 Divide the 16 by 4 so we can work out how many Apples we will get for $3 Note: I chose to divide by 4 because I knew both numbers (12 and 16) are divisible by 4. To change $3 into $9 I must multiply by three. That means I must also multiply the number of apples by three.

A bottling machine can fill 24 bottles very 60 seconds. How many can it fill every 15 seconds? Seconds 15 seconds is of 60 seconds We can simplify that to So . ÷ 4 Bottles 60 seconds 24 bottles 6 15 seconds …. . bottles of 60 is 15 seconds. That’s the same as saying 60 ÷ 4 = 15 So if we divide 24 by 4 we will find how many bottles can be filled in 60 seconds. ÷ 4

We solved the last question by using a ‘within’ strategy. Identifying how the 60 seconds was changed into 15 seconds. Now we are going to answer the same problem using a ‘between’ strategy (comparing the 60 seconds to the 24 bottles). 24 is of 60. Seconds Bottles 60 seconds 24 bottles 6 15 seconds …. . bottles We can simplify this to So of 60 is 24. That’s the same as saying 60 ÷ 5 =12 then multiplying this by 2 because we have two fifths, not one fifth. Now we need to find of 15 is 3 so must be 6.

Now try these questions on your own. Solve the following problems. Click again when you have worked out all the answers. 1) A newspaper company can print 84 newspaper in 12 minutes. How many newspapers can it print in 8 minutes? 56 2) A car company can make 18 cars in 4 days. How many cars can they make in 3 days? 18 Need some more practise? Try Teacher Tools Fractions, Decimals and Percentages Book Numeracy resources