Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8

Judith A. Muschla, Gary R. Muschla, Erin Muschla

• Publisher: Jossey-Bass
• Year: 2012
• ISBN:
  9781118237281
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

Helpful advice for teaching Common Core Math Standards to middle-school students

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. Hands-on Activities for Teaching the Common Core Math Standards is designed to help teachers instruct their students so that they will better understand and apply the skills outlined in the Standards.

This important resource also gives teachers a wealth of tools and activities that can encourage students to think critically, use mathematical reasoning, and employ various problem-solving strategies.

• Filled with activities that will help students gain an understanding of math concepts and skills correlated to the Common Core State Math Standards
• Offers guidance for helping students apply their understanding of math concepts and skills, develop proficiency in calculations, and learn to think abstractly
• Describes ways to get students to collaborate with other students, utilize technology, communicate ideas about math both orally and in writing, and gain an appreciation of the significance of mathematics to real life

This practical and easy-to-use resource will help teachers give students the foundation they need for success in higher mathematics.

Section 1

Standards and Activities for Grade 6

Ratios and Proportional Relationships: 6.RP.1

“Understand ratio concepts and use ratio reasoning to solve problems.”

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1. “Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.”

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Background

A ratio is a comparison of two numbers. A ratio can compare a part to a whole, a whole to a part, a part of a whole to another part, or a rate (a comparison of two different quantities).

Ratios may be expressed in three ways: with “to,” by a colon, or by a fraction bar. For example, a ratio that compares the value of a quarter to a dollar can be expressed as 1 to 4, 1:4, or

.

Activity: Ratios All Around Us

Working in groups of three or four, students will select a topic and write ratios that compare numbers associated with their topic. They will then create a poster, illustrating the meaning of select ratios.

Materials

Math, science, and social studies texts; reference books, particularly almanacs and atlases; poster paper; markers; rulers; scissors; glue sticks. Optional: computers with Internet access.

Procedure

1. Explain that numbers are constantly compared. Provide examples such as 1 inch on a map equals 50 miles, 1 pound of chopped meat makes 4 hamburgers, and a team's record of wins to losses is 2 to 1. These are all examples of ratios.

2. Explain that each group is to select a topic and write at least ten ratios associated with their topic. They are to then choose five of their ratios and create a poster that illustrates the meanings of these ratios.

3. To help your students get started, offer a broad list of topics and examples of possible ratios they may consider, such as:

• Transportation: distance between cities, gas mileage, amount of luggage per person, costs per trip.
• Cooking and baking: servings per person, cooking times per pound of food, ratios of ingredients.
• Sports: per-game averages for individual players and teams, won-loss records, attendance.
• Amusement parks: admission prices, types of attractions, roller-coaster statistics.
• Information about their state, town or city, or school.

4. Encourage your students to brainstorm other possible topics.

5. After students have selected their topics, they should research the topics. Along with using books, they may also find the Internet helpful, especially for finding statistics on various topics. Remind them that they are to write at least ten ratios associated with their topics. From these they should select five that they will illustrate on a poster.

6. Encourage your students to be creative, neat, and accurate with their posters.

Closure

Have each group of students present their poster to the class, explaining their selections of ratios. Display the posters in the room.

Ratios and Proportional Relationships: 6.RP.2

“Understand ratio concepts and use ratio reasoning to solve problems.”

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2. “Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.”

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Background

A ratio is a rate that compares two quantities. A unit rate compares a quantity to 1.

To find a unit rate, divide the numerator and denominator of a ratio expressed as

by b where b ≠ 0. For example, if Milo ran 1 lap in

minutes, the ratio of laps to minutes is

. The unit rate is found by dividing the numerator and denominator by

so the denominator is equal to 1. Milo ran

of a lap in 1 minute.

Activity: Unit Rate Tic-Tac-Toe

This activity is best implemented in two days. Students will first work individually and then in groups of four or five, with each group divided into two teams. Each team will create problems about finding unit rates that the other team will solve. As they solve, or fail to solve, the problems, the teams will complete a tic-tac-toe board.

Procedure

1. On the first day of the activity, explain that each student is to create five unit rate problems. They should make an answer key for their problems on the back of the sheet. Caution them not to show their problems to other students. After students have finished their problems, collect them and check that the answers to the problems are correct.

2. The next day, return the problems to their owners and divide students into groups.

3. Within each group, students should form two teams: One team will be the “X” team and the other will be the “O” team. One student should draw a tic-tac-toe board.

4. Explain the rules of the game:

• A member of the X team will read a unit rate problem, which the members of the O team must solve. If the O team solves the problem correctly, they may place an O on any square of the tic-tac-toe board. If their answer is incorrect, they must place an X on any square of the board.
• A member of the O team now reads a unit rate problem, which the members of the X team must solve. If the X team solves the problem correctly, they may place an X on any square of the tic-tac-toe board. If their answer is incorrect, they must place an O on any square of the board.
• The object of the game, of course, is to get three Xs or three Os in a row. The game continues until there is a winner or there is a draw. If a second game is played, a member of the O team reads the first problem. To play more games, students may need to create more unit rate problems.

5. As students play, you may find it necessary to assume the role of referee and provide an explanation for answers that students challenge.

Closure

Announce the wi...