Unit Rate

Read through the lesson below on ratios and unit rates. Print off the worksheets and then work through the lesson with your child.

Introduction/ Warm-up

Students normally learn best when they can associate what they are learning with what they already know. This introduction will provide your child with an opportunity to do this and help prepare them for what is to be learned later in this lesson.

This introduction should take around 10-15 minutes. Do not worry if it takes longer.

Materials Needed: Worksheet #1

Steps

Together with your child, complete worksheet #1 which is about word problems.
Remind them to cross out the information that is not needed first and to only look at the most important information in the problem.
This worksheet is designed to draw on your child's problem solving skills. Problems with ratios in them usually require good word problem-solving skills.
Ensure that your child has a solid understanding of how to solve word problems before exploring ratios in more depth.

Lesson Explanation

This part should take around 20 to 30 minutes but you can take as long as necessary.

Step 1: Ratios

Explain to your child that a ratio is just a comparison of two things using numbers. Tell your child that if they want to compare two different quantities it is important to use a ratio to compare it.
For example, if they want to know how many books they have compared to toys they can use a ratio to do so.
Before they can write the ratio they must identify what they are comparing. Use the example below to illustrate this concept to your child.
Example: Sally has 10 toys. She has 7 dolls and the rest are stuffed animals. What is the ratio of dolls to stuffed animals?

To complete this you must write a ratio. The most common way to write a ratio is in number notation. To do this write the ratio as follows:

7:3 (7 dolls to 3 stuffed animals)
Tell your child that the first number in a ratio is always the first item stated to compare. For example in this problem it was stated to compare dolls to stuffed animals so the number of dolls is first.

Show your child the alternative ways to write ratios.To write a ratio you may write them in the following manner. Write these examples on the board or on a sheet of paper.

Word notation: 4 to 6
Number notation: 4:6
Fraction notation: 4/6

Complete the following example with your child.
- Jack wants to compare the number of boys in his class to the number of girls. There are 25 kids in his class and 12 of them are girls. What is the ratio of boys to girls.
- Discuss with your child the need to first find out how many boys are the class?
- Having found that there are 13 (25 - 12) boys, ask your child to write the ratio with number notation.
- The ratio of boys to girls is 13:12
- Reinforce the need to write the numbers in the correct order as stated in the question. i.e. boys to girls.
- Ask your child what the ratio of girls to boys is. They should be able to tell you that it is 12:13.

Step 2: Rates

Now that your child understands how to compare numbers with ratios, demonstrate how they can use ratios to determine rates in a problem.
Use the example below to show how to solve rates. Remind your child that to solve problems with rates they must look at the entire word problem.

Jackie bought three equally-priced dresses at the store. She paid $150.00 for all three dresses. How much did she pay per dress?

To solve this you must know how much was paid in total and how many items were purchased. In this case she purchased 3 dresses (the quantity) for $150.00 (the total amount).
Discuss with your child and show on the board that you must divide 150.00 by 3
Ask your child to do the division and find the rate (amount of each dress)
When they complete this they will know that the dresses were purchased at a rate of $50 per dress.
Solve the following question with your child to practice this concept again.
- Johnny’s dad bought pizza for his hockey team. The team ate 8 pizzas and the total for all of the pizzas was $72.00. What is the rate (amount) per pizza?

Guided Practice

Step 3:

Together complete worksheet #2 to practice solving ratios and proportions. Work through each type of problem with your child to help them master concepts from the lesson.
Review concepts that they may not completely understand or have questions with.

Independent Practice/ Lesson Closure

Use Worksheet #3 to assess your child’s learning of the lesson.
Have them complete worksheet#3 individually.
Grade the worksheet to determine how well they understand the material.
When grading the worksheets consider the following:
- Students who get all answers correct are ready to move forward to the next lesson
- Students who get two out of three correct may move forward, but may need additional review.
- Students who do less well need to repeat the lesson or have additional instruction on the concept.

Lesson Variations

Children who struggle with this lesson may benefit from reviewing basic ratio concepts again.
Children who excel with this lesson are ready from more complicated problems.
If your child is advanced, have him/her help you with solving the examples on the board to keep them engaged with the lesson.
If your child is struggling, have them help with reading the problems, working out components to the problem that they excel in to keep them engaged.

Word Problems, Ratio, & Rate Worksheets

The 3 worksheets listed above are grouped below:

Ratio & Proportion 4 Direct Proportion Simplifying Ratios Using Ratios Ratios and Rates