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Grades 6-8 Activities
Station 1
6A3 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Handout to cut out
Students will use the definitions of the Commutative and Associative laws to maneuver
cards into equivalent equations. This activity is meant to show students that the
Commutative Law changes order; the Associative Law maintains the order but changes
the sequence in which the steps are completed.
Grades 6-8 Activities
Station 2 6A4 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Walk-on Number Line, Large x on paper
Two students will volunteer to demonstrate equations using a walk-on number line.
One student will hold a large x and the other will go first by standing on the number that
the equation equals. For instance, x + 4 = 10, the first student will stand on the 10. The
student holding the x will float around until they find the answer. The students will fill out
their sheet while volunteers show the answers to the equations.
Grades 6-8 Activities
Station 3 6A6 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Deck of cards
Students will use the black cards to indicate the x-value. They will substitute this value
into each equation shown to find the y-value. This point (x,y) is on the line shown.
Each student will solve 3 points per equation.
Grades 6-8 Activities
Station 4 7A4 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Walk-on Number Line, Large x on paper
Two students will volunteer to demonstrate equations using a walk-on number line.
One student will hold a large x and the other will go first by standing on the number that
the equation equals. For instance, x + 4 = 10, the first student will stand on the 10. The
student holding the x will float around until they find the answer. The students will
identify the INVERSE operation being used: - 4.
They will do this again, using 3 volunteers to use the INVERSE operations. First, they
will use the +/- INVERSE, then the multiply/divide INVERSE. All problems will be
shown on the walk-on number line and on paper.
Grades 6-8 Activities
Station 5 7A5 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Wikki Stick
Students will use a T Chart and substitution to find 2 points on a line. They will place
the Wikki Stick so that it is straight and touches both points. This is to show that 2
points determine a line.
Grades 6-8 Activities
Station 6 7A6 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Number Line and ray/dot cut-outs
Students will graph each inequality by first choosing the correct dot (open or closed)
and then determining which way to face the ray.
Grades 6-8 Activities
Station 7 8A6 – Teacher Copy
Linear Equations
Activity 1
Materials Needed: Graphs & Equation Cut outs
Students will match the graph to the correct equation playing the game of Memory. A
brief reminder about positive/negative slope and the y-intercept is shown. This game
focuses on the student’s ability to see the slope as positive or negative and the yintercept.
Activity 1 Station 1
Linear Equations
6A3
Commutative Law – when adding OR multiplying numbers, order doesn’t
matter (you may switch the order)
Examples:
3+4=7
8 x 3 = 24
4+3=7
3 x 8 = 24
Associative Law – numbers may be regrouped IN THE SAME
SEQUENTIAL ORDER and the result will be the same (do not switch the
order – switch the parenthesis)
Examples: 24 = (2x3)x4
(2+7)+3 = 12
24 = 2x(3x4)
2+(7+3) = 12
Cut out the cards and show each law. Write down each answer.
Demonstrate the Commutative Law on each of the following.
1) A = ½ bh
2) V = lwh
3) P = a + b + c
4) C = 2πr
Demonstrate the Associative Law on each of the following.
5)
6)
A = (½ b) h
V = (lw)h
7)
8)
P = (a+b)+c
C = (2π)r
A=
H V
+ +
c 2
( )
½ b
l w
Pa
π r
C
Activity 1 - Station 2 Linear Equations
6A4
Two students will volunteer to use the walk-on number line. One student
will hold a large piece of paper with an x on it. This person is the answer.
The first person will stand on the number that the equation is equal to. For
instance,
x + 4 = 10
The first person will stand on the 10, because the equation is equal to 10.
The person holding the x will float around trying to find the answer to this
equation. What does x have to be if you add 4 to it and get 10?
Try several equations.
1) x + 3 = -2
2) x + 6 = 8
3) x + 5 = 0
4) x + 7 = 2
5) On a piece of paper, write a rule that you could use to
find x. What are we really doing?
Last, try these equations.
6) x – 4 = 3
7) x – 2 = -5
8) x – 6 = 3
9) x – 8 = -3
10) On a piece of paper, write a rule that you could use to
find x. What are we really doing?
x
Activity 1 - Station 3 Linear Equations
6A6
Create 2 piles with your playing cards: red and black. Discard all face
cards.
The black cards will represent the x-component of a point. The red cards
will represent the y-component of the point. Distribute three black cards to
each of the players at the table. Spread the red cards out on the table so
all can be seen.
Each person will substitute their value of x into each equation. Find the y
answer and place it next to each x value. This point (x,y) is a point on that
line.
1) y = x
2) y = x + 1
3) y = x - 1
Activity 1 - Station 4 Linear Equations
7A4
Two students will volunteer to use the walk-on number line. One student
will hold a large piece of paper with an x on it. This person is the answer.
The first person will stand on the number that the equation is equal to. For
instance,
x+3=7
The first person will stand on the 7, because the equation is equal to 7.
The person holding the x will float around trying to find the answer to this
equation. What does x have to be if you add 3 to it and get 7? If we start
with the 7 what are we really doing to the 7 in order to get to the answer?
Subtracting 3 from both sides is an example of using INVERSE operations.
Try these equations and note the INVERSE operation.
1) x + 5 = -2
2) x + 3 = 8
3) x + 4 = 0
4) x + 9 = 2
Next, we need 3 volunteers. The first volunteer stands at the answer of the
equation. The second volunteer completes the first + or – INVERSE
operation. The steps are shown below.
2x + 3 = 9
The first person stands at 9. The second person finds the INVERSE OF +3
which is -3. So this person stands on 9-3=6. The person holding the x is
now solving
2x = 6
This means that 2 equal pieces of x length stretch from 0 to 6. How big is
each piece? The person holding x will stand on the answer. Note: 2x
means 2 times x. Using the INVERSE operation would mean dividing both
sides by 2. Everyone write the following on their paper.
2x + 3 = 9
-3 -3
2x
2
=6
2
x
=3
Now try these on the walk-on number line and show each step on paper.
5) 2x + 1 = 9
6) 2x – 4 = 6
7) 2x - 4 = -2
8) 2x – 1 = 3
Activity 1 – Station 5 Linear Equations
7A5
Use a T chart and substitution to find 2 points on each line shown below. Using a Wikki
stick, connect both points to create a straight line. This shows that it only takes 2 points
to create a line.
1) y = x
x y
2) y = x + 2
x y
3) y = x – 2
x y
Activity 2 – Station 6 Linear Equations
7A6
When graphing inequalities on a number line, there are 2 steps.
1) Determine the type of dot and place it on the number (open or
closed). Use an OPEN dot if it DOES NOT INCLUDE the number
itself. Use a CLOSED dot if it DOES INCLUDE the number.
2) Determine which way to point the ray. Greater than is always to
the right; less than is always to the left.
Use the cut-out dots and ray on the number line shown for each example.
1) x > 2
5) x < 3
2) x ≤ 1
6) x ≥ 4
3) x < -2
7) x > -3
4) x ≤ -1
8) x ≥ -4
LESS
THAN
AN
GREATER TH
-4-3 -2 -1 0 1 2 3 4
Activity 1 – Station 7 Linear Equations
8A6
The slope-intercept form of a line focuses on 2 main parts of a line: the
slope (or incline) and the intercept (or where the line crosses the y-axis).
First, you need to focus on the y-intercept. This will tell you the number for
b, when using y = mx+b. Next, look at the slope. There are 2 types of
slope: positive and negative. Here are examples.
Positive Slope (m = positive number)
Negative Slope (m = negative number)
In mathematics, we read a line from left to right. So from left to right the
first graph is going UP. This means it has a positive slope. Therefore, in
the equation y = mx + b, the m will be a positive number.
Reading the second line from right to left, it is going DOWN. This means
that it has a negative slope. Therefore, in the equation y = mx + b, the m
will be a negative number.
Using this knowledge, play Memory by cutting out the graphs and
equations, mix the pile, and then choose one of each to find a match.
y = 3x – 2
y = 3x + 2
y = -3x + 2
y = -3x - 2