Weight Scales – Model
A
19
B
12
C
Find the Weight for each block.
Cylinder = __7_ pounds
Sphere = __8__ pounds
Cube = __4__ pounds
List of draw the steps you followed to find the weights of the blocks.
1. I see Scale B in Scale A
4+
-4
0
+ 12 = 19
- 12 -12
0 7
2. Scale C
4. Check for accuracy
+
2
= 12
-4
8
=8
=7
7+
-7
0
3. Scale B
=8
=4
= 15
-7
8
A. 7+8 +4 =19
B. 4 + 8 = 12
C. 7 + 4 + 4 = 15
15
Shape Grids
Columns
1
2
3
14
21
A
17
16
Step 1: Row 2
18
20
Step 3: row 1
5+
+ + = 21
21 ÷ 3 = 7
=7
Step 2: Column 1
+7 +
- 7
= 17
-7
10
+
= 10
10 ÷ 2 = 5
=5
10 +
-10
+ 5 = 14
= 14
-10
4
=4
Step 4: Row 3
5 + 5 + A = 18
10 + A = 18
- 10
- 10
8
A=8
Step 5: Check for accuracy
Columns
2
1
3
59
52
63
56
82
67
81
Step 1: I see row 3 within column 1
+
+
= 63, so 63 +
- 63
Step 2: Row 3
19 +
- 19
+
+
= 63
- 19
44
= 44
44 ÷ 2 = 22
= 22
= 82
- 63
19
Step 3: row 1
22 +
44 +
- 44
+ 22 = 59
= 59
- 44
15
= 15
Step 4: Check for accuracy.
Patterns and Algebra- Shape Equations
Solving algebraic expressions using pictures and models:
Example 1:
+
+
= 27
27 ÷ 3 = 9
9 + 9 + 9 = 27
=9
 When the shapes are the same, the values for those shapes
are the same.
Example 2:
A
+
B
Step 1: A
Step 2: B
= 36
+
36 ÷ 3 = 12
Place a 12 in all
12 +
+
= 25
When doing
EQUAtions, remember
that what you do to one
side, you have to do to
the other.
**you can’t put one
shoe on without putting
the other one**
s
= 25
25 – 12 =
13 =
Step 3: Check for accuracy
+
12 + 13 = 25
= 25
Example 3:
A
+
B
Step 1: A
+
= 48
+
= 34
Substitute
+
with 34
+ 34 = 48, so
48 – 34 =
= 14
Step 2: A
Place a 14 in all
14 + 14 +
= 48
28 +
= 48
s
= 48 – 28
= 20
Step 3: B
A
14 + 20 = 34
14 + 14 + 20 = 48
Place a 20 in all
S
Shape Equations: 2 Operations
When you have an addition AND a subtraction open sentence:
1. Change the subtraction sentence to an addition sentence.
2. Substitute the new addition sentence into the other open sentence.
Example:
(5+
)+ (5 +
A
+
B
-
)+
+
= 31
= 31
=5+
+
Step 1:
B CHANGE
-
n = 5 to
Step 2:
Go back to A and SUBSTITUTE
kh
5+
+5+
+
= 31
10 +
-10
+
+
+
+
21 ÷ 3 = 7 , so
Step 3:
B
=5+
=5+
= 31
-10
21
= 21
=7
Go back to A and B and place a 7 in all the
- 7 = 5
+ 7 +7
12, so
for all
= 12
Step 4: Go back to A and B to CHECK FOR ACCURACY.
A
12 + 12 + 7 = 31
s to solve for
s
B
12 – 7 = 5
Shape Equations: 2 Operations- Explanation in Words
When you have an addition and a subtraction open sentence:
Step 1: CHANGE- you go to the subtraction problem and move the variable
with the negative (–) symbol in front of it, to the other side of the equal
sign. To do that, you perform it’s opposite operation to cancel it out on one
side, and perform the same exact operation to the other side (remember
you have to keep your equation balanced… “what you do to one side, you have
to do to the other”).
B
-
=5+
+
=5+
Step 2: SUBSTITUTE your new addition open sentence into equation A.
(5+
)+ (5 +
A
5+
10 +
-10
+
+5+
+
+
+
+
+
21 ÷ 3 = 7, so
)+
+
= 31
= 31
-10
21
= 21
= 31
= 31
Rewrite the equation so that there is one
variable (square).
1. Combine numbers on the side of the =
with the variables (5 + 5).
2. Once they are added together (10), move
them to the other side of the equal sign.
You have to cancel them out with the
opposite operation (-10).
3. WHAT YOU DO TO ONE SIDE, YOU
HAVE TO DO TO THE OTHER, so -10
from 31 and get 21.
4. Divide the new total into the number of
like variables (3 squares). 21 ÷ 3 = 7.
=7
Step 3: plug 7 in either equation and solve for the missing variable. I picked B.
B
- 7 = 5
+ 7 +7
12, so
= 12
You want to isolate the variable, so you perform
the opposite operation of the -7 (+7), to move it
from one side of the = to the other. Do the same to
the other side and 5+7 = 12.
Cell Sums
A
Step 1: WRITE 3 Equations:
A + B = 17
A + C = 16
B + C = 15
17
16
B
15
C
Step 2: COMPARE 2 Equations
Box out 1st 2 problems with the variable A.
1. Cross out the As (they cancel each other out)
A + B = 17
A + C+1 = 16
+1
2. I know that the 1st equation is 1 more, so _B= C + 1_
Step 3: SUBSTITUTE and REWRITE for equation with B and C as variables.
Solve for C.
B + C = 15
and
B=C=1
(C + 1)+ C = 15
-1
-1
C + C = 14
14 ÷ 2= 7, so C = 7
Step 4: Solve for B. C= 7
B + C = 15
B + 7 = 15
-7 - 7
B=8
Step 5: Solve for A.
B=8
OR
A + B = 17
A + 8 = 17
A=9
Step 6: PROVE IT!
A + B = 17
9 + 8 = 17
A + C = 16
9 + 7 = 16
B + C = 15
8 + 7 = 15
C=7
A + C = 16
A + 7 = 16
A=9
Weight Scales
A
10
B
12
C
8
1. Find the Weight for each block.
Cylinder = _____ pounds
Sphere = _____ pounds
Cube = _____ pounds
2. List of draw the steps you followed to find the weights of the blocks.