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Expressions/Equations/Variables

Learn Alberta - video

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell08.swf

Expressions/Equations/Variables

3 + 4 = 7

v + 4 = 7, what must v =

s + 4, if s = 10 what is the answer?

w – 12, if w = 20 what is the answer?

b x 3, (b3, 3b) if b = 7 what is the answer?

Y ÷ 6, ( y )if y = 30 what it the answer?

6

Describe Patterns (Unit 10)

Student Outcome: Describe patterns using words, tables and diagrams.

Patterns can be made of shapes, colours, number, letters,

words and more. Some patterns are quite easy to

describe. Others can be more difficult.

Find the Pattern

How many hexagons are in the next 3 diagrams?

How will you do this?

Describe Patterns (Unit 10)

Student Outcome: Describe patterns using words, tables and diagrams.

Patterns can be made of shapes, colours, number, letters,

words and more. Some patterns are quite easy to

describe. Others can be more difficult.

Find the Pattern

How many cubes are in the 4th and 7th shape?

How will you do this?

Describe Patterns (Unit 10)

Student Outcome: Describe patterns using words, tables and diagrams.

Patterns can be made of shapes, colours, number, letters,

words and more. Some patterns are quite easy to

describe. Others can be more difficult.

Find the Pattern

How many squares are in the 48th diagram?

How will you do this?

Describe Patterns (Unit 10)Student Outcome: Describe patterns using words, tables and diagrams.

Make a T – Chart

Fill in chart

3. Pattern Rule

Figure 1

Figure 2

Figure 3

Describe Patterns (Unit 10)Student Outcome: Describe patterns using words, tables and diagrams.

Make a T – Chart

Fill in chart

3. Pattern Rule

Describe Patterns of shapes…

Pattern: an arrangement of shapes, colours, #’s, letters,

words…etc, which you can predict what comes

next.

Create a T - chart which includes…Figure # and Pattern

Describe Patterns of shapes…

Using your description above…predict the

number of squares in… (show your work)

Figure # 7:

Figure # 12:

Use the chart to help describe the pattern in words…

Hint: Use the figure #’s in your answer…

Describe a Number Pattern…

Student Outcome: Describe patterns with repeating decimals.

Find the pattern of “ninths” changed to decimals.

Example: 1/9 = 0.111111111 repeated

__

This can be changed to 0.1called a repeating decimal

Change the ninths below to repeating decimals!

2/9 = 5/9 = 8/9 = 3/9 =

Describe a Number Pattern…

Student Outcome: Describe patterns with repeating decimals.

Answer: when you change the ninths to a decimal

number, the numerator of the fraction

becomes the digit used as a repeating decimal.

What is the pattern of ninths?

Repeating Decimal:

we use a bar notation to illustrate the a number has

repeated one ore more times continuously.

Describe Patterns of shapes & numbers…

Page 354: # 5ab, 6 (Draw & Create a chart)

Page 355: # 7, 9ac

Page 356: # 13 (Good Luck!)

Exploring Variables & Expressions…

Student Outcome: I can write an expression to represent a pattern.

A kitchen floor is being covered with red & white tiles.

- Try to figure our in “words” what the pattern(s) are…

Write the “expression” to represent the pattern…

Exploring Variables & Expressions…

Student Outcome: I can write an expression to represent a pattern.

A kitchen floor is being covered with red & white tiles.

Create a chart for your information (to help find the expressions)

Write the “expression” to represent the pattern…

Exploring Variables & Expressions…

Student Outcome: I can write an expression to represent a pattern.

Use your data to find expressions for patterns…

Write the “expression” to represent the pattern…

- Red Tiles = W ÷ 2 or W/2

White Tiles =

Exploring Making Predictions…

Student Outcome: I can write an expression to represent a pattern.

- White Tiles = 2 x R or 2R

- Red Tiles = W ÷ 2 or W/2

- How many red tilesif there are…
- a. 10 white tiles? b. 22 white tiles?
- How many white tiles if there are…
- a. 24 red tiles? b. 110 red tiles?

Use your expression to “predict” the amount of red or white tiles for

the examples below.

Describing patterns using EXPRESSIONS

Student Outcome: Identify constant, numerical coefficient and variable.

Label the “terms” above to the arrows in the example below…

Learn Alberta

http://www.learnalberta.ca/content/memg/index.html?term=Division02/Variable/index.html

Variable: a letter that represents an unknown number (x, a, b, etc…)

Expression: a number or variable combined with an operation (+, -, x…)

Value: a known or calculated amount

Equation: a mathematical statement with 2 expressions ( = )

Constant: a number that does NOT change. It increases or decreases the value.

Numerical Coefficient: a number that multiplies the variable.

3c x 4 = 36

Describing patterns using EXPRESSIONS

Student Outcome: I can write an expression to represent a pattern.

Use your knowledge of the terms to answer the questions below:

Everyday three employees work at the food bank with some

volunteers. What is the variable, constant and expressionfor the statement above.

2. The following diagrams are made up of toothpicks. Find the expression for this pattern. How will you do this?

Describing patterns using EXPRESSIONS

Student Outcome: I can write an expression to represent a pattern.

Find the pattern(s)…put into words

Create a T-chart

Find an expression for the diagrams and number of toothpicks.

Predict the number of toothpicks for diagrams 10, 22 and 35.

Do you see another pattern? HINT “use the base” Can we create an expression based on the base and total number of toothpicks?

Describing patterns using EXPRESSIONS

Student Outcome: I can write an expression to represent a pattern.

Complete #4 on page 361 (squares made from toothpicks)…you

may work with a partner and discuss.

Find the pattern(s)…put into words

Create a T-chart

Find the expressions comparing the “base” and the “totalnumber of toothpicks”

Predict the total number of toothpicks (perimeter) if the base is 10, 22 and 35?

Predict the # of toothpicks on the base if the perimeter is

40, 60, and 120?

Student Outcome: I will be able to model an expression.

Model an expression: draw a picture for an expression

Let “c” represent the unknown number of pennies in the cup(s)…then add 4 more pennies. If you where to Place 6 pennies in the cup. Write the expression, draw a model for the expression, what is the value of “c” and find the value of the expression?

Evaluate Expressions…Student Outcome: I will be able to model an expression.

Student Outcome I can make and solve equations with adding and subtracting

Let “c” represent the unknown number of pennies in the cup(s)…then add 4 more pennies. If you place 6 more pennies in the cup. Write the expression, what is the value of “c” and find the value of the expression?

+

Evaluate Expressions…Student Outcome: I will be able to model an expression.

Student Outcome I can make and solve equations with adding and subtracting

Let “c” represent the unknown number of pennies in the cup…then add 4 more pennies. Place 6 more pennies in the cup. Write the expression, what is the value of “c” and find the value of the expression?

+

Student Outcome: Understand how to make a table of values for an expression.

A table show two sets of related numbers.

In your table have the picture # replace value of “n” and then complete the equation. For example…

Model

Student Outcome: Understand how to make a table of values for an expression.

Your Turn!

In your table have the picture # replace value of “n” and then complete the equation. For example…

Model

Use the model below to complete the following…

- What is the expression?
- Show a “table of values” from 0-5 as your variables.
- How many pennies in the 13th picture? Show Work!
- What is the expression to find the picture #?
- What is the picture # of 77 pennies? Show Work!

Page 368: # 5 (mode as a class)

Page 369: # 8, 9, 10, 11,12

Page 370: # 15, 18

Extend: 19, 20

Graph Linear Relations …

Student Outcome: I will be able to graph a linear relation.

- What can we do to make the data on the grid make more sense?
- What is the pattern?
- What is the “expression?”

Linear Relation:

a pattern made by two sets of numbers that results in points

along a straight line (pattern) on a coordinate grid.

Plot Points From a Given Data…

Student Outcome: I will be able to graph a linear relation.

Take the data from the chart and complete the following…

Find the Expression(s) using the first 3 sets of data.

Complete the rest of the chart.

Then Label the data onto a coordinate grid.

Remember, the 1st number of the coordinates is always the x-axis!

Plot Points From a Given Data…

- What is the pattern?
- What is the expression to find “p”
- What is the expression to find “f”

Describe a Graph to Solve a Problem

- Armand is four years
- old. His allowance
- starts at $2 per
- week. Each year he
- will get a $1 per
- week increase. The
- graph shows what
- his total allowance
- will be after
- the increase each
- year.

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