Math 5Unit Review and Test

Taking Strategies

Instructor: Mrs. Tew Turner

In this lesson we will review the information

from this unit, as well as test taking strategies.

Math Warm-up

8 43 5

In your Math Notebook

Multiply acrossMultiply downMultiply your results across and down.Put these answers in the triangles

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What do you notice about your results?

Math Warm-up

8 43 5

In your Math Notebook

Multiply acrossMultiply downMultiply your results across and down.Put these answers in the triangles

==

==

What do you notice about your results?

3215

24 20 480480

Vocabulary Reviewestimation - to give an approximate value rather than an exact answer

Vocabulary Review

factors - numbers that are multiplied to get a product

product - the number that is the result of multiplying two or more factors

Vocabulary Reviewround - a process that determines which multiple of 10, 100, 1,000, etc. a number is closest to

compatible number - numbers that are easy to compute with mentally

Vocabularypartial product - products found by breaking one of two factors into ones, tens, hundreds, and so on, to multiply each.

Vocabulary

dividend- the number to be divided 24 ÷ 4 = 6

divisor- the number that the dividend is divided by 24 ÷ 4 = 6

Vocabulary

quotient - the number that is the result of dividing 24 ÷ 4 = 6

Vocabulary

compatible numbers – numbers that are easy to compute with mentallyEx. 21 and 3 are compatible numbers in division because 21 ÷ 3 = 7 is a fast fact.

Estimation in MultiplicationTake the example 36 x 6 = ?

Step 1: Round 36 to the nearest 10 36 40

Step 2: 40 x 6 = ?What is 4 x 6?

4 x 6 = 24 (This is a multiplication fact!) We call these FAST FACTS! Step 3: Add any zeros to the Fast Fact. 40 x 6 = 240The estimate answer for 36 x 6 = 240!

Estimation in MultiplicationTake the example 43 x 8 = ?

Step 1: Round 43 to the nearest 10 43 40

Step 2: 40 x 8 = ?What is 4 x 8?

4 x 8 = 32 (This is a multiplication fact!) We call these FAST FACTS! Step 3: Add any zeros to the Fast Fact. 40 x 8 = 320The estimate answer for 43 x 8 = 320!

Follow the Steps!Step 1: Find the product of the non-zero digits.

Easy as ....

Step 2: Count the total number of zeros in both factors.

Step 3: Place the total number of zeros after the product of the non-zero digits.

Multiplying 2-digit x 2-digit

STEP 1: Multiply by the ONES place.(partial product with ones factor) 1

98x 12196

2 x 8 ones = 16 Regroup 16 as 1 ten and 6 ones2 x 9 tens = 18 tens or 1 hundred & 8 tens + 1 ten carried = 19 tens or 1 hundred 9 tens.

STEP 2: Multiply by the TENS place.(partial product with tens only)

1

98x 12196980

10 x 8 ones = 80 ones or 8 tens 10 x 9 tens = 90 tens or 9 hundred

STEP 3: Add the partial products.

1

98x 12 1196 +980 1176

Can the computers be paid off in 12 months?(Will $1,176 be enough?)Can the principal pay $2,700 dollars in 12 months? NO, she will not be able to pay them off.

Check your answer with estimation!

98 100x 12 x 12 1196 ~1200 +980 1176

(Estimated answer is very close the exact answer and let's us know if our answer is reasonable.)

REVIEW the STEPSStep 1:

Step 2: Step 3:

How do you multiply by 2-digit numbers?

Add the PARTIAL PRODUCTS.

Easy as ....

Multiply by the TENS PLACE. Regroup.

Multiply by the ONES place. Regroup if necessary.

Multiplying 3-digit x 2-digit

STEP 1: Multiply by the ONES place.(partial product with ones factor)

MULTIPLY 17 x 242 242x

177 x 2 = 14 ones7 x 40 = 28 + 1 zero = 2807 x 200 = 14 + 2 zeros = 1400NOW we add 1400 + 280 +14 = ?(line them up by place value)

1400 + 280 +14 = (line them up by place value)

1 4 0 0 2 8 0+ 1 41, 6 9 4 is the multiplication by the ones factor. 242

x 17

1,694

STEP 2: Multiply by the TENS place.(partial product with tens factor)

MULTIPLY 17 x 242 242x

1710 x 2 = 20 ones = 2010 x 40 = 40 + 1 zero = 40010 x 200 = 20 + 2 zeros = 20002000 + 400 + 20 = (line them up by place value)

(line them up by place value)2000 + 400 + 20 = ?

2 0 0 0 4 0 0+ 2 02, 4 2 0 is the multiplication by the tens factor. 242

x 17

2,420

STEP 3: Add the partial products.242 x 17 11,1694+ 2, 4204, 114

How many bags of rice did the class sell?They sold 4,114 bags of rice. Our estimate of 5000 was more because we rounded UP on both factors.

Estimation in DivisionEstimating is like asking “about how much?”

There are two ways you can estimate in division.

Estimation in DivisionOne way is to round to the nearest tens or hundreds.

Ex. 258 ÷ 6

Step 1: Round the dividend to the nearest tens or hundreds.

258 300

Estimation in DivisionOne way is to round to the nearest tens or hundreds.

Ex. 258 ÷ 6

Step 2: Divide using the rounded dividend.

300 ÷ 6 = 50

Estimation in DivisionOne way is to round to the nearest tens or hundreds.

Ex. 258 ÷ 6

300 ÷ 6 = 50 This quotient is an estimate.It should be faster to get the estimate because 30 ÷ 6 = 5, which is a fast fact, then you add the final zero, because 0 ÷ 6 = 0.

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

Step 1: Find a compatible number.

For this problem you would replace 258 with 240.

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

How do you know what number is a compatible number?

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

Use the fast facts to help you choose a compatible number.

Think about fast facts for the 6 times table.

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

6 x 4 = 24

So, 24 ÷ 6 = 4

This fast fact will help to solve the problem mentally.

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

240 and 6 are compatible numbers, since 24 ÷ 6 = 4.

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

Step 2: Use mental math to solve the problem.

240 ÷ 6 = 40

Estimation in DivisionAnother way is to use compatible numbers.

Ex. 258 ÷ 6

240 ÷ 6 = 40

40 would be an underestimate since 258 was replaced with a smaller compatible number.

Follow the Steps!Rounding to Estimate the

QuotientStep 1: Round the dividend to the nearest tens or

hundreds.

Easy as ....

Step 2: Divide using the rounded dividend.

Follow the Steps!Using Compatible Numbers to

Estimate the Quotient

Step 1: Find a compatible number.

Easy as ....

Step 2: Use mental math to solve the problem.

Guided Practice for 1 Digit DivisorsListen to this problem. Then let’s try

to solve it together for practice. Students are selling candles to raise money. A shipment arrived yesterday. The candles are sold in boxes of 6. How many boxes can be filled? A Diagram can help you decide what operation to use.

n boxes

432 candles

6

Guided Practice for 1 Digit DivisorsStep 1: Find 432 ÷6.

Estimate first. Decide whereTo place the first digit in theQuotient.Use COMPATIBLE numbers.420 ÷ 7 = 70 (42 and 7 are fast facts for division so they are compatible.)

432 candles

6 n boxes

Guided Practice for 1 Digit DivisorsStep 2: Divide the tens.

Multiply and subtract. 7 6 432 -42 1

432 candles

6 n boxes

Divide. 43/6 =~7Multiply. 7x6 = 42Subtract. 43-42 = 1Compare. 1 is less than 6, so we have to BRING downthe 2.

Guided Practice for 1 Digit DivisorsStep 3: Bring down the ones.

Divide the ones. Multiply and subtract. 7 6 432 -42 12

-12 0432 candles

6 72 boxes filled!

Divide. 12/6 =2Multiply. 2x6 = 12Subtract. 12-12 = 0There is nothing left over!It is done!

Using compatible numbers will help you to estimate division using a 2-digit divisor.

Ex. 159 ÷ 75

Step 1: Find compatible numbers for 159 and 75.

Ex. 159 ÷ 75

Think 16 can be divided evenly by 8.

160 and 80 are close to 159 and 75.

So, 160 and 80 are compatible numbers. (8 & 16 are fast facts!)

Ex. 159 ÷ 75

Step 2: Divide with compatible numbers.

160 ÷ 80 = 2

This is the estimate answer for the problem 159 ÷ 75 = ~ 2

75 fits into 159 about 2 times.

Ex. 412 ÷ 84

Step 2: Divide with compatible numbers.

400 ÷ 80 = 5

This is the estimate answer for the problem 412 ÷ 84 = ~ 5

84 fits into 412 about 5 times.

Ex. 288 ÷ 37

Step 2: Divide with compatible numbers.

280 ÷ 40 = 7

This is the estimate answer for the problem 288 ÷ 37 = ~ 7

37 fits into 288 about 7 times.

Dividing Larger NumbersEx. 864 ÷ 76

Step 1: Estimate with compatible numbers first.

880 ÷ 80 = ~11

This is the estimate answer for the problem 864 ÷ 76 = ~ 11

76 fits into 864 about 11 times.

Dividing Larger Numbers

Ex. 864 ÷ 76 = 11 r. 28

Step 2: Divide, multiply and subtract for the exact answer.

1 1 r. 28 76 8 6 4 -7 6

91 014 -7 6

2 8

Bring down the ones.Divide the ones.Multiply and subtract.

Writing a number in standard form from an exponential equation:

Step 1: Look at the order of operation to see which direction you are moving the decimal point. × move the decimal to the right÷ move the decimal to the left**Note: This is the opposite of writing a number as an exponent.

Writing a number in standard form from an exponential equation:

Step 1: Look at the order of operation to see which direction you are moving the decimal point. × move the decimal to the right÷ move the decimal to the left

Ex. 3.5 × 103 This is ×, so the decimal will move to the right.

Writing a number in standard form from an exponential equation:

Step 2: Look at the power of ten to see how many places you will move the decimal point.

Ex. 3.5 × 103 This is to the power of 3, so you would move the decimal three places.3.500.

Writing a number in standard form from an exponential equation:

Step 1: Look at the order of operation to see which direction you are moving the decimal point. × move the decimal to the right÷ move the decimal to the left**Note: This is the opposite of writing a number as an exponent.

Writing a number in standard form from an exponential equation:

Step 1: Look at the order of operation to see which direction you are moving the decimal point. × move the decimal to the right÷ move the decimal to the left

Ex. 5 ÷ 102 This is ÷, so the decimal will move to the left.

Writing a number in standard form from an exponential equation:

Step 2: Look at the power of ten to see how many places you will move the decimal point.

Ex. 5 ÷ 102 This is to the power of 2, so you would move the decimal three places.0.05.

Step 1: Figure out what the exponent would be, using the

place value chart you copied in your Math Notebook

This is to the ten thousands, so the exponent would be ×104

What about writing 65,000 as an exponential equation?

Step 2: Move the decimal place the number of places of the exponent.

The × or ÷ will tell you the direction.× move the decimal to the left

÷ move the decimal to the right

65,000.

What about writing 65,000 as an exponential equation?

4 321×104

Step 3: Drop the zeros from the number.

6.50006.5 × 104

What about writing 65,000 as an exponential equation?

Step 1: Figure out what the exponent would be using the

place value chart you copied in your Math Notebook

This is to the hundredth, so the exponent would be ÷102

What about writing 0.78 as an exponential equation?

Step 2: Move the decimal place the number of places of the exponent.

The × or ÷ will tell you the direction.× move the decimal to the left

÷ move the decimal to the right

0.78

What about writing 0.78 as an exponential equation?

1 2÷102

Step 3: Drop the zeros from the number.

07878 ÷ 102

What about writing 0.78 as an exponential equation?

Test Taking Strategies

•Read each problem twice•Underline key words•Underline the information you need to solve a problem.•Circle the data given.

Test Taking Strategies

•Solve the problem•Show your work as you solve the problem.•Check your work•Use estimation to check if your answer is reasonable.

Today you reviewed for the unit assessment.

Good Work with this

lesson.