Download Algebra Math Help

Algebra Math Help
Learning Objective:
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Understand how to use a grid to solve algebraic problems.
Understand what an expression is.
Understand how to write an expression from a problem.
Understand how to substitute a given value into an expression.
Understand the written steps for the substitution into the expression.
Recognize the steps to the solution on the grid.
Understand what an equation is.
Understand how to write an equation from a problem.
Understand how to solve the equation using the grid.
Recognize the steps to the solution on the grid.
Understand the written steps for the solution and verification to the equation.
Understand that an equation is a mathematical statement in which two expressions
are equal.
Helpful Hints:
Using the Grid Intro
• The grid is used to count out the values defined in the problem.
Bank Transactions:
1. Deposit: money added to the initial balance.
Eg. Initial balance is $47 and there are two transactions: deposit $1, deposit $1.
Move 1 space to the right for each $1 deposit.
Result: $49
Eg. Initial balance is $16 and there is 1 transaction: deposit $10.
Move one space up for each $10 deposit.
Result: $26
Junior High Math Interactives
©2007 Alberta Education (www.LearnAlberta.ca)
Patterns and Relations/ Algebra/ Object Interactive / Math Help
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2. Withdrawal: money subtracted from the balance.
Eg. Initial deposit is $67 and there are three transactions:
withdraw $1, withdraw $1, withdraw $1.
Move 1 space left for each $1 withdrawal.
Result: $64.
Eg. Initial deposit is $65 and there are two transactions:
withdraw $10, withdraw $10.
Move one space down for each $10 withdrawal.
Result: $45.
3. Balance Owing: occurs when more money is withdrawn then the amount of the
initial balance.
Step 1: Withdraw $1 from the $15 initial balance.
$15 - $1 = $14.
Step 2: Withdraw $10
$14 - $10 = $4
Step 3: Withdraw $10
$4 - $10 = -$6
Result: a balance owing of $6.
Junior High Math Interactives
©2007 Alberta Education (www.LearnAlberta.ca)
Patterns and Relations/ Algebra/ Object Interactive / Math Help
Page 2 of 5
Mathematical Expression
• is made up of variables and/or numbers joined by operations.
Eg. 3 x + 5
• is used to define a situation or problem.
• can be evaluated by substituting in a defined amount for the variable.
Eg.
Define the Expression: Translate the words into mathematical symbols.
“A number”
“increased by a factor of 3”
“increased by 5”
What is the total if x is 6
Æ
Æ
Æ
Æ
let x represent the number.
x is multiplied by 3 Æ 3x
add 5
Æ+5
substitute 6 in for x Æ 3(6) + 5
Expression: 3 x + 5
Total: Substitute 6 for x.
3(6) + 5 = 18 + 5
Total = 23
Steps on the Grid:
Step 1: The values 6, 12, 18 are highlighted to show 3 groups of 6.
The number 6 increased by a factor of 3:
3(6) = 18.
Step 2: 18 is then increased by 5.
Result: 18 + 5 = 23.
Junior High Math Interactives
©2007 Alberta Education (www.LearnAlberta.ca)
Patterns and Relations/ Algebra/ Object Interactive / Math Help
Page 3 of 5
Equation
• is a mathematical statement in which two expressions are equal.
• always contains an equal sign.
Solving an Equation
• work backwards
• use the opposite operation to make x stand alone
• subtract the “increased by” value
• divide the “by a factor of “ value
Verify
• prove that the solution for x is correct
• substitute the solution for x back into the equation and show that both sides are
equal
Eg.
Define the Equation: Translate the words into mathematical symbols.
“your age”
“increased by a factor of 5”
“increased by 4”
“you will be 54”
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Æ
Æ
Æ
let x represent your age
x is multiplied by 5 Æ 5x
add 4
Æ+4
equals 54
Æ = 54
Equation: 5 x + 4 = 54
5x = 50
Æ subtract 4
x = 10
Æ divide by 5
You are 10 years old.
Solution:
Verify: Show that 10 is the correct solution.
5(10) + 4 = 54
50 + 4 = 54
54 = 54
Junior High Math Interactives
©2007 Alberta Education (www.LearnAlberta.ca)
Patterns and Relations/ Algebra/ Object Interactive / Math Help
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Steps on the Grid:
Step 1: Subtract 4
The total 54 is reduced by 4.
Result: 54 – 4 = 50
Step 2: 50 is divided into 5 groups.
The values 50, 40, 30, 20, 10 are highlighted to show 50 divided into 5 groups of
10.
Result: Your age is 10 years.
Verify: When 10 is increased by a factor of 5 it equals 50.
When this is then increased by 4 it equals 54.
Junior High Math Interactives
©2007 Alberta Education (www.LearnAlberta.ca)
Patterns and Relations/ Algebra/ Object Interactive / Math Help
Page 5 of 5