6th Grade Extension Menu

Name______

Date______Section ______

Unit, Concepts, and/or Topic:

Term 2 Unit 4 – Understanding Algebraic Relationships

Term 3 Unit 5 – Using Algebraic Relationships

Term 3 Unit 6 - Ratio & Proportional Relationships (Box 9 Only)

Choose a learning activity from one square to complete. Circlethe number of the learning activity you choose. Turn inthis paper with your work.

1. Analyze the following equation:
a + =g
Solve the equation above for c.
Solve the equation above for d.
Devise a graphic organizer that would serve as an aid to students in solving for any variable in the equation above. / 2. Compose a real-life situation that could be modeled with an equation that contains variables on both sides. Show the steps for solving the equation and justify in context. / 3. A triangle has a perimeter of 10x+12, with sides that equal 4x, 3x+8, and 5x-2. Determinethe value of x. Show your work.
The perimeter of a rectangle is 16m+4, with a length of 6m-4. Identify the expression that will represent the width of the rectangle. Show your work.
4. Invent and compose three real-life situations that could be modeled by the inequalities graphed below. Modify the graphs to include numbers that fit the real-life situations that you have invented.


/ 5. Holly has a pile of nickels, dimes, and quarters. There are 3 times as many dimes as nickels. The number of quarters is twice the number of dimes. The pile has a total value of $27.75. Using algebraic expressions and equations, distinguishhow many of each coin is in the pile. / 6. Mick was working as a clerk in a clothing store. He made a mistake and charged the wrong sales tax. He should have charged 5%, but he charged 8% instead. The total amount of money he collected for the day, including sales tax, was $459.00. Determine how much money he would have collected if he had charged the correct sales tax.
Generalize the steps you took to solve this problem and create an instruction sheet for solving similar tax-related problems.
7. For each situation below, determine the equation you would use to solve the problems and apply it to find the missing lengths and widths.
  • A rectangle has a length that is 6 times longer than its width. If the area of the rectangle is 1014 square feet, what are the length and width of the rectangle?
  • The length of a rectangle is 8 times its width. The perimeter of the rectangle is 216 inches. What is the algebraic equation you would use to solve this problem?
Adapted fromChallenge Math,
Edward Zaccaro / 8. Investigate the statement below.
Four consecutive numbers add up to 1850. What is the smallest number?
Outline an algebraic plan and solve the problem.
Createand solve a problem similar to the one above with the following criteria:
  • Consecutive odd numbers
  • Negative answer
/ 9. Mark’s family bought 4 pounds of ice cream. Mark suggested that the fair way to split it was to give people their share based on their weights. If Mark weighs 80 pounds and there are three other people in his family who weigh 120, 150, and 162 pounds, how many ounces of ice cream should Mark get? (Hint: 1 pound equals 16 ounces)
Re-evaluate the problem for each change in circumstance below and explain how each change affects the solution.
  • Mark weighs 87 lbs.
  • There is an additional family member that weighs 191 lbs.
  • The family bought 5.5 lbs of ice cream.

Teacher Resource Page

6th Grade Extension Menu

Unit, Concepts, and/or Topic:

Term 2 Unit 4 – Understanding Algebraic Relationships

Term 3 Unit 5 – Using Algebraic Relationships

Term 3 Unit 6– Ratio & Proportional Relationships (Box 9 Only)

Intended Purpose: Culminating activity for units 4 & 5 or alternative activities for students who have mastered curricular indicators

Indicators Addressed:

Extension Menu Box / CCSS / Standard
Box 1 / 6.EE.A.2 / Write, read, and evaluate expressions in which letters stand for numbers
a. Writing expressions that record operations with number and with letters standing for numbers
b. Identifying parts of an expression using mathematical terms, viewing one or more parts of an expression as a single entity,
c. Evaluating expressions for specific values for their variables – even expressions that arise from formulas in real-world problems)
Box 2
/ 6.EE.B.7 / Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
Box 3 / 6.EE.B.6 / Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Box 4 / 6.EE.B.8 / Write an inequality of the form or to represent a constraint or condition in a real-world or mathematical problems. Recognize that inequalities of the form or have infinitely many solutions; represent such solutions on a number line diagram.
Box 5 / 6.EE.C.9 / Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity (dependent variable) in terms of the other quantity (independent variable). Analyze the relationships between the dependent and independent variable using graphs and tables, and relate these to the equation.
Box 6 / 6.EE.B.7 / Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
Box 7 / 6.EE.B.7 / Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
Box 8 / 6.EE.B.7 / Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
Box 9 / 6.RP.A.3 / Use ratio and rate reasoning to solve real-world and mathematical problems by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios
b. Solve unit rate problems with unit pricing and constant speed
c. Find a % of a quantity as a rate per 100; solve problems involving finding the whole given a part and the %
d. Use ratio reasoning to convert measurement units; manipulate and transform unit appropriately when multiplying or dividing quantities.