Illustrative Mathematics
Ratio of Boys to Girls
How many boys are in the class? Here is an introductory exercise describing ratios. The commentary shows different ways learners can approach the problem, using a tape diagram of boys to girls and using a table. The activity includes...
Illustrative Mathematics
Price per Pound and Pounds per Dollar
Help learners understand the concept of unit rate as it is applied to buying beans at a grocery store. The objective is to determine the unit rate in two ways, and then apply each ratio to an additional problem. The attached commentary...
Illustrative Mathematics
Voting for Three, Variation 1
This is an opportunity for young mathematicians to apply reasoning to solve real-world problems with ratios. Even though there are three candidates for class president, students will only consider two at a time, making the first problem...
Illustrative Mathematics
Voting for Three, Variation 2
Here is another opportunity for math students to apply reasoning to solve real-world problems with ratios. The ratio of the number of votes for two candidates is provided. Your class is asked to use this ratio and information given about...
Illustrative Mathematics
Voting for Three, Variation 3
Get your learners to think outside the box. Young scholars require a good understanding of ratios and their relationship to fractions to complete the problem. The only quantities given in the problem are the ratio of the number of votes...
Illustrative Mathematics
Jim and Jesse's Money
Jim and Jesse started their road trip with the same amount of money. Your class must find the amount of money each one had given, the amount of money spent, and the ratio of money at the end. This is a comprehensive problem that takes...
Curated OER
Art Class, Variation 1
Student statisticians calculate ratios to determine how many shades of green were mixed by Ms. Baca's art class. They graph the number of blue parts against the number of yellow parts for each combination and discover that some produce...
National Research Center for Career and Technical Education
Business Management and Administration: Compound Interest - A Millionaire's Best Friend
Many math concepts are covered through this resource: percentages, decimals, ratios, exponential functions, graphing, rounding, order of operations, estimation, and solving equations. Colorful worksheets and a link to a Google search for...
Illustrative Mathematics
Computing Volume Progression 3
Learners are given a volume of a rectangular tank and are asked to find the water height. Because the total volume of the tank is given in liters, your geometers will need to use a unit ratio to convert to centimeters cubed. The exercise...
Illustrative Mathematics
Overlapping Squares
The objective of this activity is to find the percent of the area of a two squares overlapping. Mathematicians find the ratio of area for the part that overlaps to the rectangle formed. The final answer is a percent as a rate per 100....
Virginia Department of Education
Field Goals, Balls, and Nets
Score a resource on ratios. Young mathematicians learn about different ways to express ratios. Using sports data, they write statements about the statistics in ratio form.
Curated OER
Art Class, Variation 2
Given a set of six paint mix ratios, artistic mathematicians produce an equation that relates the number of parts for blue paint to parts for yellow paint resulting new shades of green.
Curated OER
Candy Machine
Using the concept of a candy vending machine, young mathematicians explore the sugar ratios found in different types of candy. Using the provided information, class members calculate and compare different ratios in order to find the...
Curated OER
7.RP Music Companies, Variation 1
We've got the beat! And your musically-minded mathematicians will tap their toes as they determine which music company would be getting a better deal based on their offers to buy out TunesTown. The topic is extended in an additional task...
Curated OER
How Fast is Usain Bolt?
Revisit the 2012 Summer Olympics by having seventh graders calculate the unit rate sprinting speed of the 100-meter gold medal winner.
Curated OER
Stock Swaps, Variation 2
If Microsoft wanted to take over Apple, how many shares would they need to break even? This is an ideal task for seventh graders who are studying proportional relationships and applying them to real-world scenarios. Use it as an...
Illustrative Mathematics
Currency Exchange
Take your class on a North American adventure with a currency conversion problem. Pupils are asked to change US dollars into Canadian dollars and then to Mexican pesos. The commentary includes two solutions, converting by unit rates and...
Illustrative Mathematics
Running at a Constant Speed
The learner must use the given constant speed to find the unit rate. A table is made in order to relate the speed to the time and the distance. From the table, learners are able to see the unit rate in miles per minute and miles per...
Illustrative Mathematics
Converting Square Units
Jada has a rectangle board that is measured in inches. Young learners confirm their understanding of converting inches to feet. Then they find the area in square feet. Jada thinks she has a short-cut to convert inches square to square...
EngageNY
Multi-Step Problems—All Operations
Harness the power of algebra to solve problems. Young mathematicians learn to work out multi-step problems by applying algebraic techniques, such as solving equations and proportions. They use tape diagrams to model the problem to finish...
Illustrative Mathematics
Anna in D.C.
The amount of tax and tip on a restaurant bill is a common example used in percent problems. Here, learners only know the total amount paid, and they need to figure the itemized amounts. Solutions using a ratio table, using knowledge of...
Virginia Department of Education
Going the Distance
Estimate the value of one of the most famous irrational numbers. The hands-on lesson instructs classmates to measure the circumference and diameters of circles using yarn. The ratio of these quantities defines pi.
National Research Center for Career and Technical Education
Health Science: Back to Basics
This lesson focuses on unit conversion, proportions, ratios, exponents, and the metric system. Discuss measurement with your math class and demonstrate how to solve several health-science word problems. Give learners a chance to visit an...
Education Development Center
Logic of Fractions
Before diving into operations with fractions, learners discover the foundation of fractions and how they interact with one another. Exactly as the title says, logic of fractions is the main goal of a resource that shows pupils how...
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