Video: Using the Commutative Property to Solve Real World Problems

Victoria buys 8 books. Each book costs $7. Mason buys 7 puzzles. Each puzzle costs $8. Use the model to figure out how much Victoria spent. Did Mason spend more, less, or the same amount? Top Tip: Draw a model if you need to.

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Video Transcript

Victoria buys eight books. Each book costs seven dollars. Mason buys seven puzzles. Each puzzle costs eight dollars. Use the model to figure out how much Victoria spent. Did Mason spend more, less, or the same amount? Top Tip: Draw a model if you need to.

In our problem, we’ve got two characters who have been shopping. Firstly, we’re told about Victoria, who buys eight books at a cost of seven dollars each. So she spends eight lots of seven dollars. We could write this as a calculation eight multiplied by seven. And then, we’re told about Mason. He buys some puzzles. We’re told he buys seven puzzles. And they cost eight dollars each. So the amount he spends is seven lots of eight. We could write this as seven multiplied by eight.

In the first part of the problem, we’re told to use the model to figure out how much Victoria spent. The model shows a number line. It starts at zero, and it shows lots of jumps of seven. Why would we need to skip count in sevens to find the answer? Well, if we go back to Victoria’s calculation, we know that we needed to find eight lots of seven dollars. And so, the model shows eight jumps of seven. We can count in sevens eight times to find the answer. The first three jumps are done for us. So let’s start counting in sevens and see how many eight sevens are worth: seven, 14, 21, 28, 35, 42, 49, and 56. We skip counted in sevens eight times to find the answer. Eight lots of seven dollars equals 56 dollars in total.

In the second part of the problem, we’re asked to concentrate on Mason. Did Mason spend more, less, or the same amount? Well, the multiplication that we need to use to work out Mason’s amount is interesting. It involves the same numbers that we have in Victoria’s multiplication. Instead of eight times seven, we need to calculate seven times eight. The numbers are the other way around. What happens if we swap the numbers around in a multiplication? Well, we’re then given a tip to draw a model, if we need to. So perhaps, it might be helpful for us to do this. We’ll start off at zero. And this time, we’re going to make seven jumps of eight dollars. We’re going to skip count in eights seven times.

To begin with, let’s draw our seven jumps. So now, let’s skip count in eights seven times: eight, 16, 24, 32, 40, 48. And one more lot of eight dollars takes us to 56 dollars. The amount of money that Mason spent is the same as the amount that Victoria spent. So we can say that if we swap the numbers around in a multiplication, the answer remains the same. Eight multiplied by seven is 56 and seven multiplied by eight equals 56 too.

If Victoria buys eight books and each book costs seven dollars, she’ll spend 56 dollars altogether. And if Mason buys seven puzzles and each puzzle costs eight dollars, the amount that Mason will spend will be the same.

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