6th Grade Math Textbook, Fundamentals

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Lesson 3-7 for exercise sets.

Check to make sure your answer makes sense.

You can check the result by finding a different pattern.

A 1-row design has 1 1 horizontal toothpicks.

A 2-row design has 1  2 2 horizontal toothpicks.

A 3-row design has 1  2  3 3 horizontal toothpicks; and so on.

So the number of horizontal toothpicks in a 10-row design will be

1  2  3  4  5  6  7  8  9  10 10, or 65 in all.

The number of vertical toothpicks is the same as the number

of horizontal toothpicks.

So the total number of toothpicks for a 10-row design is 2 • 65,

or 130 toothpicks.

Problem 2: Use the fact that 3^8 is 6561 to find the following sum

without using a calculator: 31  312 313 314 315 316 317 318

Read to understand what is being asked.

List the facts and restate the question.

Facts: 38  6561

Question:Find 31  312 313 314 315 316 317 318 without a calculator.

Select a strategy.

Examine sums of the first term, the first twoterms, the first threeterms, and so on.

Use the strategy Find a Patternthat would help find the sum of all eightterms.

Apply the strategy.

The “sum” of the first term is just.

The sum of the first twoterms is  .

The sum of the first threeterms is

.

The sum of the first fourterms is

.

In each case, the denominator is 3n, where nis the number of terms,

and the numerator is found by subtracting 1 from the denominator

and then dividing by 2.

If this pattern continues, then the denominator of the sum

of all eightterms will be 3^8 , which is given as 6561;

and the numerator will be (6561 1) 2, or 3280.

So 31  312 313 314 315 316 317 318 65613280.

40

81

1

81

3

81

9

81

27

81

1

81

1

27

1

9

1

3

1

34

1

33

1

32

1

3

13

27

1

27

3

27

9

27

1

27

1

9

1

3

1

33

1

32

1

3

4

9

1

9

3

9

1

9

1

3

1

32

1

3

1

3

Check to make sure your answer makes sense.

Add the terms with your calculator. The result will be 0.4999237921,

which is equivalent to^32806561.