Algebra Teacher's Activities Kit,
Algebra lays the groundwork for every math class that comes after it, so it's crucial that students master the material and gain confidence in their abilities. The Algebra Teacher's Activities Kit helps you face the challenge, well-armed with effective activities that help students become successful in algebra class and beyond. Judith A. Muschla has taught mathematics in South River, New Jersey, for over twenty-five years. Along with teaching and writing, she has been a member of the state Standards Review Panel for the Mathematics Core Curriculum Content Standards in New Jersey. Gary Robert Muschla taught at Appleby School in Spotswood, New Jersey, for more than twenty-five years; his specialties include mathematics at the middle school level, reading, and writing. Judith and Gary have coauthored several successful math activity books, including Teaching the Common Core Math Standards with Hands on Activities , Grades 9-12, Hands-On Math Projects with Real Life Applications , The Math Teacher's Book of Lists , and Math Starters . Erin Muschla-Berry teaches 8th grade math at Monroe Township Middle School in Monroe, New Jersey, and has collaborated with Judith and Gary on eight previous math books.
Algebra Teacher's Activities Kit,
Ratios and Proportional Relationships
Teaching Notes for the Activities of Section 1
1-1: (6.RP.1) Understanding Ratios
For this activity, your students will read statements that describe ratios. They will be given choices of ratios and must select the ratio that matches each statement. Answering a question at the end of the worksheet will enable students to check their answers.
Explain that a ratio compares two numbers or quantities. For example, if you have 5 markers and 2 are green and 3 are red, you can write a ratio comparing green markers to red markers as 2 to 3. You may instead write a ratio comparing the red markers to green markers as 3 to 2. Ratios can also be written with a colon, 2:3, or as a fraction, .
Discuss the directions on the worksheet, emphasizing that students are to choose the ratio that matches each statement. Remind students to answer the question at the end.
(1) O, 5:7 (2) A, 32:8 (3) H, 12 to 5 (4) T, 6 to 10 (5) E, (6) O, (7) T, 5 to 6 (8) P, (9) W, 8 to 2 (10) L, 3:2 (11) R, 2:25
The answer to the question is "whole to part."
1-2: (6.RP.2) Unit Rates and Ratios
For this activity, your students are to determine if statements that describe unit rates associated with ratios are true or false. Answering a question at the end of the worksheet will enable them to check their answers.
Explain that a ratio that has a denominator of 1 is a unit rate. Examples of unit rates include: 4:1, , or 3 to 1. Unit rates may also be expressed as a quantity of 1, for example: 30 miles per gallon of gasoline or $3 per pound. Ratios such as 6:3, , and 2 to 9 do not represent unit rates. However, any ratio that compares two different quantities can be converted to a unit rate by writing the ratio as a fraction and dividing both numerator and denominator by the denominator. For example, or 2:1.
Discuss the directions on the worksheet with your students. After deciding whether a statement is true or false, they are to use the letters of correct answers to answer the question at the end.
(1) R, true (2) O, true (3) O, false (4) I, false (5) O, true (6) N, false (7) R, false (8) T, true (9) P, false (10) P, true The answer to the question is "proportion."
1-3: (6.RP.3) Equivalent Ratios and the Coordinate Plane
For this activity, your students will complete tables of equivalent ratios and then plot the pairs of values in the coordinate plane. They will need rulers and graph paper.
Discuss the example on the worksheet. Explain that equivalent ratios can be found by writing the ratio as a fraction, and then multiplying or dividing the numerator and denominator by the same nonzero number. Note that the process is the same as finding equivalent fractions.
Explain that ratios can be expressed as ordered pairs in the coordinate plane. If necessary, review the coordinate plane, ordered pairs, and how students can plot points. Instruct them to place the origin of their coordinate plane near the center of their graph paper to ensure that they will have enough space to plot all of the points.
Go over the directions with your students. Emphasize that after completing the tables they must use the first value of each ratio as the x -coordinate and the second value as the y -coordinate. They are then to plot the ordered pairs and use their rulers to connect the points.
Table 1: 1:2, 2:4, 3:6, 4:8, 5:10 Table 2: 2:3, 4:6, 8:12 Table 3: 12:8, 6:4, 3:2
1-4: (6.RP.3) Finding the Percent of a Number and Finding the Whole
For this activity, your students will have two tasks: Find the percent of a number and find a whole, given the percent and a part.
If necessary, review that to find the percent of a number students should change the percent to a decimal or f