Video Transcript
Multiplicative Comparisons
In this video, we will learn how to
model multiplicative comparison problems with bar models and equations and solve the
problems by multiplying numbers up to 10 times 10.
Multiplicative comparison means
comparing two things that need multiplying. For example, if I need two meters
of fabric to make one bag, how many meters of fabric will I need to make five
bags? We know that for one bag we’ll need
one lot of two meters. And to make five bags, we will need
five times that amount. To calculate how much fabric we
need for one bag, we just need to calculate one times two meters. And so, to calculate the amount of
fabric we will need for five bags, we would need to calculate five times two
meters.
Using a bar model in this way to
compare the amount of fabric we need helps us to think about the multiplication
equation we need to write to solve the problem. If one bag needs two meters of
fabric, then five bags will need five times the amount of fabric. We would need 10 meters of fabric
to make five bags.
Let’s try another example. Peaches are sold in packs of
four. How can we tell who has the most
peaches? We could use a bar model to
compare. This girl has one pack of four
peaches, and her friend has three packs of four peaches. By using a bar model in this way,
we can easily see who has the most peaches. One times four is less than three
times four. So, if one friend has one pack of
peaches and another has three, then the friend with three packs of peaches has three
times more. We don’t even need to calculate the
multiplication expression because the bar model helps us to see that three times
four is greater than one times four. Let’s try some practice questions
now.
The snake is five times as long as
the caterpillar. Pick the model that shows how long
the snake is.
In this question, we’re being asked
to compare two things, the length of the snake and the length of the
caterpillar. And we’re going to need to use
multiplication to solve this problem. We know this because the question
tells us the snake is five times as long as the caterpillar. When we compare two things using
multiplication, we call this a multiplicative comparison problem. We have to use multiplication to
calculate how long the snake is.
When we’re trying to solve
multiplicative comparison problems like this, it helps to sketch a bar model. We’re not told how long the
caterpillar is. We could use this bar to represent
the caterpillar. And we know the snake is five times
longer than this. So, the bar representing the length
of the snake would look like this: five times the length is the bar representing the
caterpillar.
Now, we have to pick the model
which shows how long the snake is. Let’s look closely at the first
model. Did you notice that this cube train
has been made using groups of three cubes? How many groups of three are
there? One, two, three, four, five, five
groups of three or three multiplied by five. So, if the caterpillar is three
cubes long, then each of the bars would be worth three cubes. And the length of the snake would
be five lots of three. So, this is the model that shows
how long the snake is.
If the length of the caterpillar is
one times three, the length of the snake must be five times three. This model shows three plus five,
not three times five. And this model shows two plus
three, which equals five. We picked the model which is five
times as long as the caterpillar.
Find the missing number. 18 is what times greater than
three.
In this question, we’re being asked
to compare two numbers, the numbers 18 and three. And we’re being asked to calculate
how many times greater 18 is than number three. When we see the words “how many
times greater,” we know this is a multiplicative comparison problem. We’re being asked to compare two
numbers using multiplication. Let’s use a bar model to help us
think about how to calculate the answer.
We’ve drawn our two bars to
represent the numbers 18 and three. To work out how many times greater
18 is than three, we could see how many threes there are in the number 18. We know that one three is three,
two threes are six, three times three is nine, four times three is 12, five times
three is 15, and six times three is 18. Three is equal to one times
three. 18 is equal to six times three. The missing number is six. 18 is six times greater than
three. We found the missing number using a
bar model and multiplication equations. 18 is six times greater than
three.
Select the statement that matches
the following equation: 72 equals nine times eight. Is it 72 is eight times as many as
eight, eight is nine times as many as 72, 72 is nine times as many as nine, 72 is
nine times as many as eight, or nine is 72 times as many as eight?
In this question, we have to find
the statement that matches the given equation, 72 is equal to nine times eight. Well, we know that the equation
begins with the number 72. And we have three statements which
begin with 72. So, we can eliminate the other two
statements we know they’re not correct.
Let’s look at the second part of
our equation, 72 is nine times eight. That means we can eliminate this
statement because it says 72 is eight times. Which of the remaining two
statements is correct, 72 is nine times as many as nine or 72 is nine times as many
as eight? It’s this one; 72 is nine times as
many as eight. We found the statement that matches
the equation. 72 is nine times as many as
eight.
Emma has eight balloons. Benjamin has 32 balloons. Complete the equation what times
eight equals 32 to find how many times more balloons Benjamin has than Emma.
This is a multiplicative comparison
problem. We’re being asked to compare two
things, the amount of balloons Emma has with the amount of balloons Benjamin
has. And to solve the problem, we have
to use multiplication. We have to calculate how many times
more balloons Benjamin has than Emma.
We’re told to complete the equation
what times eight equals 32 to solve the problem. In other words, how many eights are
there in 32? Let’s sketch a bar model to help us
think about how to calculate the answer. We know that Emma has eight
balloons and Benjamin has 32 balloons. We need to work out how many eights
there are in 32. We know that one times eight is
eight, two eights are 16, three eights are 24, and four eights make 32.
Emma has one group of eight
balloons. Benjamin has four groups of eight
balloons. One lot of eight equals eight, and
four times eight equals 32. So, Benjamin has four times as many
balloons as Emma. The missing number is number
four. Four times eight equals 32.
So, what have we learned in this
video? We have learned how to use bar
models and multiplication equations to solve multiplicative comparison problems.
