MATHLINKS GRADE 8 STUDENT PACKET 4 PATTERNS AND LINEAR FUNCTIONS 2

Name ___________________________

Period _________ Date ___________

8-4

STUDENT PACKET

MATHLINKS GRADE 8 STUDENT PACKET 4 PATTERNS AND LINEAR FUNCTIONS 2

4.1

Growing Shapes

1

? Use variables, parentheses, and exponents in

expressions.

? Use formulas to find perimeter and area of rectangles.

? Describe geometric patterns numerically, symbolically,

graphically, and verbally.

? Plot ordered pairs that satisfy a specified condition.

? Informally connect the slope of a line to its context in a

graph.

4.2

Going to the Park

8

? Solve time-distance problems.

? Interpret time-distance graphs.

? Explore rates of change on a graph.

? Understand the meaning of the points of intersection of

two graphs.

? Informally connect the slope of a line to its context in a

graph.

4.3

Stacking Cups

17

? Use numbers, graphs, and symbols to represent data.

? Understand and estimate a line that fits the data.

? Draw conclusions based on data displays.

4.4 Skill Builders, Vocabulary, and Review

21

MathLinks: Grade 8 (Student Packet 4)

Patterns and Linear Functions 2

Word or Phrase

WORD BANK

Definition or Explanation

explicit rule (for a sequence)

Example or Picture

function

inductive reasoning

linear function

point of intersection

rate

slope (of a line)

y-intercept

MathLinks: Grade 8 (Student Packet 4)

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Patterns and Linear Functions 2

GROWING SHAPES

4.1 Growing Shapes

Summary (Ready)

We will extend square and rectangle patterns. Then we will represent geometric measures in the patterns using inputoutput tables, a graphs, symbols, and words (the "fourfold way").

Goals (Set)

? Use variables, parentheses, and exponents in expressions.

? Use formulas to find perimeter and area of rectangles.

? Describe geometric patterns numerically, symbolically, graphically, and verbally.

? Plot ordered pairs that satisfy a specified condition.

? Informally connect the slope of a line to its context in a graph.

Warmup (Go) Use inductive reasoning to complete each table. Write an explicit rule in words and symbols.

Table 1

Input (x)

Output (y)

1

1

Table 2

Input (x)

Output (y)

1

2

Table 3

Input (x)

Output (y)

1

2

2

2

2

3

2

4

3

3

3

4

3

6

4

4

4

5 Rule: If the input value is x, then the output value is:

________________ In symbols:

y = ____________

5 Rule: If the input value is x, then the output value is:

________________ In symbols:

y = ____________

5 Rule: If the input value is x, then the output value is:

________________ In symbols:

y = ____________

MathLinks: Grade 8 (Student Packet 4)

1

Patterns and Linear Functions 2

4.1 Growing Shapes

GROWING SQUARES

1. This is a pattern of growing squares built from unit squares. Continue the pattern for steps 4 and 5.

Step # 1

2

2. Complete the tables.

Table 1

Step

Length of

number

side

(n)

(L)

3

4

Table 2

Step number

(n)

Perimeter (P)

5

Table 3

Step number

(n)

Area (A)

n Rule: L = _________

n Rule: P = _________

n Rule: A = _________

3. What is the perimeter of the figure in step 4. If the perimeter of the figure is 84, what is

#10?

the step number?

rule: ___________________________

rule: ___________________________

substitute: ______________________

substitute: ______________________

perimeter: ______________________

step number: ___________________

5. Use words or diagrams to explain how the length of the side and the perimeter of a square are related.

6. Use words or diagrams to explain how the length of the side and the area of a square are related.

MathLinks: Grade 8 (Student Packet 4)

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Patterns and Linear Functions 2

4.1 Growing Shapes

GROWING SQUARES GRAPHS

1. Graph the data from the tables on the previous page. Scale the graphs appropriately.

Two Graphs on the Left (Use Tables 1 and 2)

One Graph on the Right (Use Table 3)

Lengths in units L (one color) Perimeter in units P (a second color) Area in square units A (a third color)

Step number n

Step number n

2. How is the graph on the right different from the two graphs on the left?

3. A linear function is a function whose graph is a line. Which of the rules describe linear functions? Explain.

MathLinks: Grade 8 (Student Packet 4)

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