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Unit Rates Word Problems

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Aligned To Common Core Standard:

Grade 6 Proportional Relationships - 6.RP.A.3b

What is a Unit Rate? A rate is a comparison or ratio that defines how many of one you have compared to another. Unit rates are just a little more specific. A unit rate distinguishes the quantity of the first type of item compared to a single unit of the second type of item. Students often across this in cars. The speedometer tells unit rate of speed of the vehicle. In the Imperial measurement system, it tells you how many miles the car will travel in one hour. In the metric system it tells you how many kilometers the car will travel in an hour, if it were to maintain that speed for an hour. Every time you go shopping whether it be online or in a store you can use your knowledge of unit rates to determine the best deal. In this case you look on the pricing shelf a unit price is often displayed this indicates the cost of one unit of the item you are buying. The lowest unit price is the best deal every time.

Printable Worksheets And Lessons

  • Kneading Dough Step-by-step Lesson- Sally is making some sweets. She has a lot of dough to knead. How long do you think it will take Sally to knead 36 kilograms of flour? Solve using unit rates.

  • Guided Lesson - I really got you covered here. A standard unit rate problem, price problem, and what would be complete without a speed problem.

  • Guided Lesson Explanation -I start using visible ratios in favor of standard proportions this is the grade level to do that at.

  • Practice Worksheet - A nice solid arrangement of concrete word problems to tackle.

  • Unit Rates Five Pack - These are incomplete rates that you need to work on.

  • Matching Worksheet - Match the problem to the outcome. Units of measure are found on this one.

Homework Sheets

I was baking during the week that I was creating these. See if it shows...

  • Homework 1 - Lucky is making cake. Lucky took 4 hours to knead the dough. The dough was made up of 8 kilograms of flour. How long do you think it will take Lucky to knead 40 kilograms of flour?
  • Homework 2 - Albert makes 20 kg of sweets in 5 weeks. If he continued to make sweets, how much would he have after 10 weeks?
  • Homework 3 - Oddie sells 25 bags in 5 days. After 20 days how many bags should he sell?

Practice Worksheets

These are critical problems for students to fully understand.

  • Practice 1 - Steve runs 8 kilometers in 2 hours. He runs for another hour. How many kilometers can Steve run in that time, if he maintains his pace?
  • Practice 2 - Joseph makes 20 muffins in 1 hour. After 5 hours, how many muffins should Joseph have been able to make?
  • Practice 3 - Joe is making lunch for his crew. Joe took 3 hours to prepare the vegetables. The vegetables were made up of 9 kilograms. How long do you think it will take Joe to prepare 30 kilograms of vegetables?

Math Skill Quizzes

Most of the problems are focused in story form. This is commonly how you will see them.

  • Quiz 1 - Mark is making jackets. Mark took 2 hours to make a jacket. The jacket was made up of 50 kilograms of wool. How long do you think it will take Mark to use 500 kilograms of wool for all the jackets?
  • Quiz 2 - Maria flies her helicopter 600 kilometers in 2 hours. She flies for another 6 hours. How many kilometers can Aria fly in that time, if she maintains her pace?
  • Quiz 3 - Erin is making sweaters. Erin took 8 hours to make a sweater. The sweater was made up of 80 kilograms of wool. How long do you think it will take Erin to make sweaters from 800 kilograms of wool?

What is a Price Unit Rate?

We had studied the unit rate before, where we defined the ratio for comparing different quantities. A price unit tells us the cost per 1 unit of any object. For instance, you want to know the per liter cost of milk from your local milk shop. You learned that the milkman is selling milk at $15 per liter. So, if you want to buy 6 liters of milk, you have to multiply $15 and 6 together, you will get an answer of $90. Now, let us compare other unit prices and learn which is the best bargain. There are two stores on the street near your house, named Store A and Store B. One of them sells sugar at $10 per 3 kg, and the other one sells it at $8 per 2 kg. Now, we need to calculate from which shop you can get sugar at a lowered cost. First, let’s calculate the per-unit cost from Store A, where we divide $10 by 3 kg; then, we get a per kg cost of $3.33. Now, we find out the per kg cost of the sugar from Store B; so, we divide $8 by 2kg; then, we get a per kg cost of $4. Therefore, we can conclude that the sugar at the lowest price is available at Store A. These worksheets and lessons show students how to approach word problems that include unit rates, speed, and/or price.