Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Insights Into Algebra 1 - Teaching For Learning
algebra home workshop 1 workshop 2 workshop 3 workshop 4 workshop 5 workshop 6 workshop 7 workshop 8
Topic Overview Lesson Plans Student Work Teaching Strategies Resources
Workshop 1 Variables and Patterns of Change Lesson Plans
Lesson Plans:


Lesson Plan 1: Miles of Tiles - The Pool Border Problem

Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives
Download the Workshop 1 Guide

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NCTM Standards

Lesson Plan 1: Miles of Tiles - The Pool Border Problem

Overview Procedures For Teachers Related Standardized Test Questions Materials

The questions below dealing with translating words into symbols have been selected from various state and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other standardized assessment questions.

  • Taken from the Maine Educational Assessment, Mathematics, Grade 11 (2002):
    Carl needed to rent a car for one week. He collected the following information.
    • Hillbrook Car Rentals charges $230/week plus 20 per mile.
    • Bridge Car Rentals charges $210/week plus 25 per mile.
    a. Write an equation for the cost, c, to rent from Hillbrook Car Rentals if Carl drives the car x miles.

    b. Write an equation for the cost, c, to rent from Bridge Car Rentals if Carl drives the car x miles.

    c. For what number of miles will it cost the same to rent a car from the two companies? Show or explain how you found your answer.

    Solution: For Hillbrook Rentals, c = 230 + 0.2x. For Bridge Car Rentals, c = 210 + 0.25x. The cost will be the same when the value of c is equal for both companies, which occurs when
    230 + 0.2x = 210 + 0.25x, or when x = 400 miles.

  • Taken from the Maryland High School Algebra Exam (2002):

    Lydia has $200 in her bank account at the beginning of the year. Each month, she deposits $40 into her account. She does not withdraw any money from her account, and the account pays no interest. Which of these equations could Lydia use to find the total amount (T) in her bank account at the end of m months?

    A. T = 40m
    B. T = 240m
    C. T = 200m + 40
    D. T = 40m + 200 (correct answer)

  • Taken from the New York Regents High School Examination (January 2003):
    The equation P = 2L + 2W is equivalent to

    A. (correct answer)
  • Taken from the Mississippi Algebra I Test, Version 2 (2003):

    Jan took a taxi to visit the Petrified Forest northwest of Jackson, Mississippi. The taxi fare for the trip was $14.80, based on a fixed charge of $2.00 plus a charge of $0.80 for each mile. Which of these could be used to determine m, the number of miles that Jan rode in the taxi?

    A. 14.80 = 2 + 0.80m (correct answer)
    B. 14.80 = 2m + 0.80
    C. 14.80m = 2 + 0.80m
    D. 14.80m = 2m + 0.80

  • Taken from the Colorado State Assessment, Grade 5 (2002):

    Which problem can be solved using the number sentence shown below?

    6 2 = __

    A. There are 6 children in a swimming pool. Two more children are getting in. How many children are in the pool?
    B. There are 6 children eating lunch. Each child ate 2 slices of cheese. How many slices of cheese were eaten? (correct answer)
    C. There are 6 children playing basketball. Two left to get a drink of water. How many children are left playing basketball?
    D. There are 6 children walking to the library. They are walking in groups of 2. How many groups of 2 are there?
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