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**Math 5 Unit Review and Test Taking Strategies**

Instructor: Mrs. Tew Turner

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**In this lesson we will review the information from this unit, as well as test taking strategies.**

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**Math Warm-up = = = = In your Math Notebook Multiply across**

Multiply down Multiply your results across and down. Put these answers in the triangles 8 4 3 5 = = = = What do you notice about your results?

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**Math Warm-up 32 = = 15 480 = = 24 20 480 In your Math Notebook**

Multiply across Multiply down Multiply your results across and down. Put these answers in the triangles 32 8 4 3 5 = = 15 480 = = 24 20 480 What do you notice about your results?

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Vocabulary Review estimation - to give an approximate value rather than an exact answer

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Vocabulary Review factors - numbers that are multiplied to get a product product - the number that is the result of multiplying two or more factors

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Vocabulary Review round - 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

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

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

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

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

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**Estimation in Multiplication**

Take the example 36 x 6 = ? Step 1: Round 36 to the nearest 10 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 = 240 The estimate answer for 36 x 6 = 240!

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**Estimation in Multiplication**

Take the example 43 x 8 = ? Step 1: Round 43 to the nearest 10 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 = 320 The estimate answer for 43 x 8 = 320!

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

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**STEP 1: Multiply by the ONES place. **

Multiplying 2-digit x 2-digit STEP 1: Multiply by the ONES place. (partial product with ones factor) 98 x 12 196 2 x 8 ones = 16 Regroup 16 as 1 ten and 6 ones 2 x 9 tens = 18 tens or 1 hundred & 8 tens + 1 ten carried = 19 tens or 1 hundred 9 tens.

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**STEP 2: Multiply by the TENS place.**

(partial product with tens only) 98 x 12 196 980 10 x 8 ones = 80 ones or 8 tens 10 x 9 tens = 90 tens or 9 hundred

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**STEP 3: Add the partial products.**

1 98 x 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.

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**Check your answer with estimation!**

x x 12 ~1200 +980 1176 (Estimated answer is very close the exact answer and let's us know if our answer is reasonable.)

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**How do you multiply by 2-digit numbers?**

REVIEW the STEPS Step 1: Step 2: Step 3: Multiply by the ONES place. Regroup if necessary. Multiply by the TENS PLACE. Regroup. Add the PARTIAL PRODUCTS. Easy as ....

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

Multiplying 3-digit x 2-digit STEP 1: Multiply by the ONES place. (partial product with ones factor) MULTIPLY 17 x x 17 7 x 2 = 14 ones 7 x 40 = zero = 280 7 x 200 = zeros = 1400 NOW we add = ? (line them up by place value)

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

2 8 0 1, is the multiplication by the ones factor x 17 1,694

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**STEP 2: Multiply by the TENS place.**

(partial product with tens factor) MULTIPLY 17 x x 17 10 x 2 = 20 ones = 20 10 x 40 = zero = 400 10 x 200 = zeros = 2000 = (line them up by place value)

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**(line them up by place value)**

= ? 4 0 0 2, is the multiplication by the tens factor x 17 2,420

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**STEP 3: Add the partial products.**

242 x 17 11,1694 + 2, 420 4, 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.

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**Estimation in Division**

Estimating is like asking “about how much?” There are two ways you can estimate in division.

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**Estimation in Division**

One way is to round to the nearest tens or hundreds. Ex. 258 ÷ 6 Step 1: Round the dividend to the nearest tens or hundreds.

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**Estimation in Division**

One way is to round to the nearest tens or hundreds. Ex. 258 ÷ 6 Step 2: Divide using the rounded dividend. 300 ÷ 6 = 50

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**Estimation in Division**

One 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.

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**Estimation in Division**

Another way is to use compatible numbers. Ex. 258 ÷ 6 Step 1: Find a compatible number. For this problem you would replace 258 with 240.

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**Estimation in Division**

Another way is to use compatible numbers. Ex. 258 ÷ 6 How do you know what number is a compatible number?

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**Estimation in Division**

Another 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.

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**Estimation in Division**

Another 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.

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**Estimation in Division**

Another way is to use compatible numbers. Ex. 258 ÷ 6 240 and 6 are compatible numbers, since 24 ÷ 6 = 4.

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**Estimation in Division**

Another way is to use compatible numbers. Ex. 258 ÷ 6 Step 2: Use mental math to solve the problem. 240 ÷ 6 = 40

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**Estimation in Division**

Another 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.

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**Rounding to Estimate the Quotient**

Follow the Steps! Rounding to Estimate the Quotient Step 1: Round the dividend to the nearest tens or hundreds. Step 2: Divide using the rounded dividend. Easy as ....

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**Using Compatible Numbers to Estimate the Quotient**

Follow the Steps! Using Compatible Numbers to Estimate the Quotient Step 1: Find a compatible number. Step 2: Use mental math to solve the problem. Easy as ....

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**Guided Practice for 1 Digit Divisors**

Listen 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

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**Guided Practice for 1 Digit Divisors**

Step 1: Find 432 ÷6. Estimate first. Decide where To place the first digit in the Quotient. Use COMPATIBLE numbers. 420 ÷ 7 = 70 (42 and 7 are fast facts for division so they are compatible.) 432 candles 6 n boxes

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**Guided Practice for 1 Digit Divisors**

Step 2: Divide the tens. Multiply and subtract. 7 6 432 -42 1 Divide. 43/6 =~7 Multiply. 7x6 = 42 Subtract = 1 Compare. 1 is less than 6, so we have to BRING down the 2. 432 candles 6 n boxes

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**Guided Practice for 1 Digit Divisors**

Step 3: Bring down the ones. Divide the ones. Multiply and subtract. 7 6 432 -42 12 -12 Divide. 12/6 =2 Multiply. 2x6 = 12 Subtract = 0 There is nothing left over! It is done! 432 candles 6 72 boxes filled!

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**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.

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

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!)

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**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.

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**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.

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**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.

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**Ex. 864 ÷ 76 Dividing Larger Numbers**

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.

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**Dividing Larger Numbers**

Ex. 864 ÷ 76 = 11 r. 28 Step 2: Divide, multiply and subtract for the exact answer. 1 1 r. 28 -7 6 91 014 -7 6 2 8 Bring down the ones. Divide the ones. Multiply and subtract.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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 ten thousands, so the exponent would be ×104

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**× move the decimal to the left ÷ move the decimal to the right 65,000. **

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? ×104 4 321

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**Step 3: Drop the zeros from the number. 6.5000 6.5 × 104**

What about writing 65,000 as an exponential equation? Step 3: Drop the zeros from the number. 6.5000 6.5 × 104

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**What about writing 0.78 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

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**× move the decimal to the left ÷ move the decimal to the right 0.78 **

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? ÷102 1 2

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**Step 3: Drop the zeros from the number. 078 78 ÷ 102**

What about writing 0.78 as an exponential equation? Step 3: Drop the zeros from the number. 078 78 ÷ 102

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**Test Taking Strategies**

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

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**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.

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**Good Work with this lesson.**

Today you reviewed for the unit assessment.

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