Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

CONTENTS OF CURRICULUM UNIT 23.03.06

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Content Objectives
  4. Teaching Strategies
  5. Teaching Implementation
  6. Lessons
  7. Classroom Activities
  8. Resources
  9. Appendix
  10. Implementing District Standards
  11. Works Cited

Division of Fractions in Algebra, from real-life applications to abstract equations

J. Ulises Reveles

Published September 2023

Tools for this Unit:

Resources

Interactive online number line generator https://helpingwithmath.com/generators/numberlinegenerator01/

Solutions to selected problems from Problem Set I.

(1) Let x be the price of a container of ice cream in dollars; then,

4x + 10 = 20

4x = 20 - 10

x = (20 – 10) / 4 = 10 / 4 = 2.5 $

(3) Let x be the number of notebooks that Roger bought, then,

3x + 2 = 20

3x = 20 -2

x = (20 - 2) / 3 = 18 / 3 = 6 notebooks.

(7) Let x be the number of pages in the sticker book.

5x + 2 = 62

5x = 62 – 2

x = (62 – 2) / 5

x = 60 / 5 = 12 pages

(10) Let x be the number of bulbs in each row, then,

7x + 4 = 5(12)

7x + 4 = 60

7x = 60 – 4

x = (60 – 4) / 7

x = 56 / 7 = 8 bulbs in each row. 

Solutions to selected problems from Problem Set II.

(1) Let x be the number of persons who will get some cake, then,

2/3 x + ¼ = 25 /4

2/3 x = (25 /4) – (1/4)

2/3 x = 24 /4

x = (24 /4) * (3/2) = 72 / 8 = 9 people.

(4) Let x be the price of one pound of grapes.

4/5 x + 2 = 10

4/5 x = 10 – 2

4/5 x = 8

x = 8 / (4/5) = (8 /1) / (4/5) 

x = (8 /1) * (5/4) = 40 /4 = 10 $ / b

(6) Let x be the number of miles Peter swam.

And, time = speed * distance, then,

4/3 x + ½ = 3

4/3 x = 3 – ½ = 6 /2 – 1 /2

4/3 x = 5/2

x = (5/2) / (4/3) 

x = (5/2) * (3/4) = 15/8 miles

(8) Let x be the number of tables Carlos set up, then,

(2/3) 4x + 20 = 60

8/3 x = 60 - 20

8/3 x = 40

x = (40/1) / (8/3)

x = (40/1) * (3/8) = 120 / 8 = 15 tables

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