Algebra Learning Strategies. What should students be able to do within this interactive?

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Joanna Morris
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1 Algebra Learning Strategies What should students be able to do within this interactive? Select grid intro and read the sample problem. Understand the meaning of the problem. Understand that the problem can be solved by performing the operations of addition or subtraction on the grid. Understand how to move on the grid to solve the problem. Understand the written form of the problem and the solution. Select expression and read the problem. Understand that increased by a factor of means multiplied by. Understand that increased by means plus. Understand how to create the expression defined by the problem. Understand that the problem is solved when the given amount is substituted into the defined expression. Understand how to use the grid to solve the problem. Understand the written form of the expression, the substitution and the result. Select equation and read the problem. Understand how to create the equation from the given information. Understand that the first step to solving the equation is to subtract the amount of the increase from the end result. Understand that the second step to solving the equation is to divide the result of step 1 into the number of groups of the factor. Understand the written form of the equation, the solution and its verification. Understand how to use the grid to solve the equation. Understand how to change the problem for any expression or equation. Understand that an equation is a mathematical statement equating two expressions. Common mistakes made by students: Not understanding how to move along the grid. Not understanding how to translate the words of the problem into algebraic symbols. Not understanding how to create the expression or equation from the problem. Not recognizing the steps on the grid that perform the operations needed for substitution. Not recognizing the steps on the grid that perform the operations needed for solving an equation. Not understanding the written steps for substitution. Not understanding the written steps for solving an equation. Junior High Math Interactives Page 1 of 9

2 Curriculum Connections: Please note all of the following correlations match outcomes in the new Mathematics Kindergarten to Grade 9 Program of Studies (2007). Grade 6 Patterns and Relations SO4: Express a given problem as an equation in which a letter variable is used to represent an unknown number. Grade 6 Patterns and Relations SO5: Demonstrate and explain the meaning of preservation of equality, concretely and pictorially. Grade 7 Patterns and Relations SO1: Demonstrate an understanding of oral and written patterns and their equivalent linear relations. Grade 7 Patterns and Relations SO3: Demonstrate an understanding of preservation of equality by: modeling preservation of equality, concretely, pictorially and symbolically applying preservation of equality to solve equations. Grade 7 Patterns and Relations SO4: Explain the difference between an expression and an equation. Grade 7 Patterns and Relations SO5: Evaluate an expression, given the value of the variable(s). Grade 7 Patterns and Relations SO6: Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form, where and are integers. Grade 7 Patterns and Relations SO7: Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form: where, and are whole numbers. Grade 8 Patterns and Relations SO2: Model and solve problems, concretely, pictorially and symbolically, using linear equations of the form: Junior High Math Interactives Page 2 of 9

3 where and are integers. Grade 9 Patterns and Relations SO1: Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution. Grade 9 Patterns and Relations SO3: Model and solve problems, using linear equations of the form: where are rational numbers. Print Activity notes: *Note: The Print Activity is not intended to be an assessment piece It is necessary for students to use the Explore It mode to work through the Print Activity. They will be expected to select the grid intro and be able to move along the grid to solve a problem. The student will be expected to translate a problem into an algebraic expression. They will be expected to use the grid to perform the substitution of a value into the expression. The student will be expected to translate a problem into an equation. They will be expected to understand that the equation is an expression equal to a given amount. They will be expected to solve the equation by using the grid. They will be expected to understand the written solution for the expression or equation. The Print Activity may be opened in Word Format instead of PDF so that changes to questions can be made. Junior High Math Interactives Page 3 of 9

Algebra Print Activity Key Use the Explore It mode to answer the following questions. 1. Select and click. Use the diagram below to answer the following questions: 1. a. The in the grid area above represents the bank account balance in the problem.

4 Algebra Print Activity Key Use the Explore It mode to answer the following questions. 1. Select and click. Use the diagram below to answer the following questions: 1. a. The in the grid area above represents the bank account balance in the problem. b. The problem states that there are 4 transactions to be performed. c. To perform the $1 deposits you must move right on the grid. (left/right) d. Perform the following transactions in order: i. deposit $1, account balance = $_76_ ii. deposit $1, account balance = $_77_ iii. deposit $10, account balance = $ _87_ iv. deposit $10, account balance = $ _97_ e. To perform the $10 deposits you must move up on the grid. (down/up) Junior High Math Interactives Page 4 of 9

5 f. Move the slider to answer the following questions. Place a on all transactions needed for the results pictured below: deposit of $1 _ _deposit of $1 deposit of $10 deposit of $10 deposit of $1 deposit of $1 deposit of $10 deposit of $10 g. The solution to the problem can be written as: $75 + $_1 + $ _1_ + $_10_ + $ _10_ h. The new account balance will be $ _ Select and click to answer the following questions: a. The on the grid represents x the original number in the problem. b. The problem states the original number is increased by a factor of 7. c. As the second part of Step1, the diagram below shows the original number 4 increased by a factor of 2. d. In the result of Step 1 below, the original number 4 is increased by a factor of 7 which can be written as 7 (4) = _28. Junior High Math Interactives Page 5 of 9

e. In Step 2 below, 28 is increased by 8 representing a final solution total of 36. f. The expression for the problem is 7x + 8. g. The substitution for the problem is _7(4) +8_. h.

6 e. In Step 2 below, 28 is increased by 8 representing a final solution total of 36. f. The expression for the problem is 7x + 8. g. The substitution for the problem is _7(4) +8_. h. The solution total for the problem is Select and. a. In this problem the original number x is 6. b. The problem states the original number is increased by a factor of _4. c. Move the slider to Step 2. Step 2 shows the result from Step 1 is increased by 24. d. The expression representing the problem is 4_ x + _5. e. The substitution for the problem is 4_(_6_) + _5_. f. The solution total for the problem is Select and click until you get a weekly allowance question. Then move the change problem sliders to the following values: a. The original allowance is $ 9. Junior High Math Interactives Page 6 of 9

Identify the results of Step 1 and Step 2 on the grid below: d.

7 b. Step 1: Your weekly allowance is increased by a factor 3. Identify the result of Step 1 on the grid below: c. Step 2: The result of Step 1 is then increased by 4. Identify the results of Step 1 and Step 2 on the grid below: d. The expression representing the problem is _3_x + _4. e. The substitution for the problem _3 ( 9 ) + _4. f. The solution total for the problem is 31. Junior High Math Interactives Page 7 of 9

8 5. Select and click to answer the following questions: a. The original number in the problem is unknown and defined by the variable x. (known/unknown) b. The original number is increased by a factor of 4. c. This value is then increased by 2. d. The result of these operations is 30. e. The equation that describes this problem can be written as: 4 x + 2 = 30 f. Move the slider to Step 1. Fill in the blanks below that represent Step 1: 30-2 = 28 g. Move the slider to Step 2. The values 28, 21, 14 and 7 show that 28 can be divided into 4 groups of 7. h. The solution for the original number in the problem is 7. i. To verify, the original number 7 increased by a factor of 4 is 28 and then increased by 2 is 30. This final number matches the rhs of (lhs/rhs) the equation verifying the solution. 6. Select and click until you get a number question. Then move the change problem sliders to the following values: Junior High Math Interactives Page 8 of 9

9 a. Fill in the blanks below to write the equation representing this problem. The unknown number x is:, and 6x + 5 = 53 b. Move the slider to Step 1. Step 1 of the solution below shows 53-5 = 48. c. Move the slider to Step 2. Step 2 of the solution shows 48 factored into 6 groups of 8. d. The solution for the original number in the problem is 8. e. Fill in the blanks below that the solution: 6 x + 5 = 53 6 ( 8 ) + 5 = = Select and click until you get an age problem. Change the values of the age problem to match the problem below: a. The question asks to find your age. b. Let the variable _x represents the unknown. c. Write the equation representing the problem: 7 x + 8 = 29 Junior High Math Interactives Page 9 of 9

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best