Multiplication as Scaling Worksheets
We always attribute the concept of multiplication to growing bigger, but it can also go in the other direction. When you are multiplying a fraction, the value actually decreases, at least the whole number portion. When we are making a fixed amount larger or smaller this is called scaling. You may have heard of the concept of a scale model. When architects are creating buildings, they will often create a model that is mathematical equivalent just at a much smaller scale. This means that the dimensions are in in the same exact proportion, just a lot smaller. When we look at the atomic level, we often find scientist building larger scale models to explain the unique properties of these atoms. This topic will help students learn the relationship between multiplication operations and the concept of scaling.
Aligned Standard: Grade 5 Fractions - 5.NF.5
- Fraction of Tennis Cards Step-by-step Lesson- Tennis cards... Did I lose my mind? Many parts of Europe enjoy tennis cards.
- Guided Lesson - Shade to show that you understand. This is a cool activity.
- Guided Lesson Explanation - It took me forever to make this one because it was very difficult to think up how to best explain it.
- Practice Worksheet - Bogart elementary teachers requested this one. I hope It worked out for you guys.
- Matching Worksheet - Match the shaded rectangles to the problems that shaded them this way. I agree it is a bit easy, but it's a nice conclusion to a lesson.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
It is always helpful to start out with helping them along with visuals like divided rectangles.
- Homework 1 - Dennis has 6 pieces of burger. He gives to Emmy 1/3 of the pieces of burger. Draw the number of pieces that Emmy has in the space below.
- Homework 2 - Caleb has 8 strawberries. He gives Marcus 1/4 of the strawberries. Draw the number of strawberries that Marcus has in the space below.
- Homework 3 - Mitchell has 8 sandwiches. He gives Finn 2/4 of the sandwiches. Draw the number of sandwiches that Finn has in the space below.
Practice Worksheets
This time there are slightly different shapes. I'm trying to wean them off of the concept of squares or rectangles.
- Practice 1 - Shelley has 8 cookies. She gives Erin 2/4 of the cookies. Draw the number of cookies that Erin has in the space below.
- Practice 2 - Charles has 12 parrots. He gives Gabriel 2/4 of the parrots. Draw the number of parrots that Gabriel has.
- Practice 3 - Elijah has 15 toffees. He gives Zac 4/5 of the toffees. Draw the number of toffees that Zac has in the space below.
Math Skill Quizzes
Yes, you will even find hearts and happy faces in the mix too!
- Quiz 1 - Three friends buy 12 glasses of chocolate shake so that they can share. Copper for paid 1/2 of the chocolate shake. Max and Joshua paid for 1/4 of the chocolate shake. How many of the glasses of chocolate shake does Max directly own?
- Quiz 2 - James has 10 color bottles. He gives Jaxon 2/5 of the color bottles. Draw the number of color bottles that Jaxon has.
- Quiz 3 - Beau has 12 pair of socks. He gives Jai 2/4 of the pair of socks. Draw the number of pair of socks that Jai has.
Visual Examples of Scaling
As we talked about earlier, just about any quantity can be scaled either up (bigger) or down (smaller) as long as the fixed proportions stay intact. The only thing that changes is the magnitude of the object. As we said before architects often will model the building they are about to construct or erect with scaled model. All the measures of this model are in exact proportion to what will be on the constructed building, just at a much smaller scale. Take a look at this model building being both scaled up (2 times) and scaled down (halved).
Scaled up 2x:
Scaled down 1/2x:
How to Find the Fraction of a Whole Number
When we look at the concept of scaling a fraction it is simply the multiplication between a fraction and an integer. Finding the fraction for a whole number is like multiplying a fraction with a whole number. There is a simple method where any number can be represented in different formats such as percentage, decimal, mixed number, and fraction. These conversions are far easier with whole numbers. In order to solve the problem, you need to be familiar with the basic concept of fraction division and multiplication. Here are the steps that you should run through to complete this process. We will run through an example problem while we are at it. We will solve the problem: (1/3) x 7
Step 1- Write Both as Fractions
In this case we can make the whole number a fraction by placing it as the numerator over the denominator of 1. It would therefore be restated as: (1/3) x (7/1)
Step 2- Multiply Fractions
When multiplying fractions, the product is the product of the numerators over the product of the denominators. So in this it would be (1x7) / (3 x 1) or 7/3.
Step 3- Simply and Create a Mixed Number
Divide the numerator by the denominator of the fraction (7/3). The fraction in this step might seem like an improper fraction, which means that the numerator will be larger than the denominator or be reduced. The answer you will get will be: 2 1/3