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Explorations in Core Math - Grade 6: Online Textbook Help10 chapters | 118 lessons

Instructor:
*Cassandra Cook*

Cassandra Cook has taught grades K-8 and has a Specialist degree in Curriculum and Instruction

In this lesson, we will discuss how to estimate the sums, differences, products, and divisors of a whole number. You will learn about strategies to estimate the sums, differences, products, and divisors of a whole number using a real-life problem.

**Estimation** is an educated guess, a calculated guess of the value, number, or quantity of a problem. When you estimate, you use your best guess to provide an answer that is close to the real answer of a problem. Estimations typically include language such as about, around, close to, or maybe. Because estimations are guesses, your answer is never definite or exact. There is room for error, some wiggle room, plus or minus a few numbers.

Today you decide to go shopping, and you stop by your favorite clothing store at the mall. There is a shirt you have been wanting for some time now, and today it is 30% off the regular price of $60.00. You only have $45.00 cash. You begin to mentally do the math and make an estimation of the final price to see if you have enough money. Estimation is a calculated guess of a value, number, or quantity of something.

When adding, you can estimate the sums by rounding the addends. Let's say instead of buying one shirt that is on sale, you decide to buy three shirts that are on clearance, reduced to even less than the sale prices. Shirt one costs $12.00, shirt two costs $15.00, and the last shirt is $7.00. What a steal! Instead of adding each addend you can round them to the nearest tens place value and add from there.

$12.00 will round down to $10.00. $15.00 will round up to $20.00. $7.00 will round up to $10.00.

You can then quickly add $10.00 + $20.00 + $10.00 = $40.00.

Your total will be about $40.00. Since you have $45.00, you have enough money to buy all three shirts.

As you continue to comb the clearance rack you see a pair of jeans that are reduced to an unbelievable price of $23.00. You decide instead of buying three shirts to get the pants and one shirt instead. The shirt you decide to purchase is $12.00. You can round these prices then add to determine if you will have enough money.

$23.00 will round down to $20.00. $12.00 will round down to $10.00. $10.00 + $20.00 = $30.00.

Your total for the pants and shirt is about $30.00. Since you rounded down for both items, your total cost will be a little more than $30.00 but not by much. Since you have $45.00, you have enough to buy the pants and shirt.

While shopping you get hungry and realize you have a coupon for $5.00 off if you spend $15.00 or 30% off of any amount for your combo meal at the food court. As you decide what you want to eat you begin calculating the total cost to see what the better deal is for your discount. The #1 combo meal costs $8.75, and it has a sandwich, a bag of chips, soda, and a cookie. The #2 combo meal costs $9.00, and you get 1/2 a salad, 1/2 a sandwich, soda, and a bag of chips. Since the $5.00 discount requires you to spend $15.00, you consider purchasing two combos - one for now and one for later. Here are your options:

Two meals for $8.75 each will cost a total of $17.50. You subtract $5.00 and 30% to see what the better deal is. 30% of $17.50 is $5.25.

$17.50 - $5.00 = $12.50 is the total with $5.00 off. This meal will cost about $13.00. $17.50 - $5.25 = $12.25 is the total with 30% off. This meal will cost close to $12.00.

For combo #1 taking $5.00 is the better deal. However, you really want a salad, so you do the math for combo #2. Let's do the math:

Two meals for $9.00 is $18.00. 30% of $18.00 is $5.40.

$18.00 - $5.00 = $13.00. This meal is exactly $13.00. $18.00 - $5.40 = $12.60. This meal will cost about $13.00 as well.

As you can see, taking the $5.00 discount is best for combo #1, however getting 30% off is best for combo #2. Using subtraction to estimate the differences to see what is the better purchase is easy when you want to get more for your money.

The next time you go to the mall, you decide to buy a pair of shoes for the outfit you just purchased. As you shop in the shoe store, you decide to look at the shoes that are marked down by 30% on the sale rack. You find a pair of shoes that will go perfectly with an outfit you already have. The shoes original cost is $80.00. All you have is $60.00! You need to estimate the final costs with the percentage discount to determine if you have enough money. To do this, you need first to figure out how much 30% of $80.00 is. Convert 30% to a decimal by moving the percentage sign over two spaces to the left:

30% becomes 0.30.

Now multiply 0.30 x $80.00 or you can estimate the product with 8 x 3 = 24, so the percentage off is about $20.00

Now to estimate the total for the shoes:

$80.00 is the original cost of the shoes - $20.00 as the sales percentage = $60.00 as the total for the shoes. You have exactly enough money to buy this pair of shoes.

You buy this pair of shoes, and a friend gives you an idea to decorate them with studs. You go to the craft store and see several packs of studs that cost between $12.00 and $15.00. You have about $40.00 to spend. You estimate that one shoe will use about 75 studs to cover the whole shoe. You decide you want to use these stubs for other pairs of shoes. If you want to cover 12 pairs of shoes, that's 24 shoes with 75 studs, how many studs will you need in total? Let's estimate the product to find out!

24 shoes can be rounded to 30. Rounding up will make sure you have enough studs because if you round down, you are removing shoes.

75 can also be rounded up to 80.

Now you can multiply: 80 x 30 = 2,400 (8 x 3 = 24, add the two zeros that are in 80 and 30).

So if you cover all 24 shoes, you will need about 2,400 studs.

The $12.00 pack of studs has 989 studs, which can be rounded to 1,000. The $15.00 pack of studs has 1,079 studs that can be rounded to 1,100. If you buy three packs for $12.00 each, it will be about $36.00 for almost 3,000 studs. This is more than enough studs, and you will have $4.00 left over. Or you can buy two packs of studs for $30.00 and have about 2,200 studs which aren't quite enough studs, but you will have $10.00 left over.

You decide to buy three packs of studs, so you will have more left over to use for other crafts. When you get home, you set out all 12 pairs of shoes and begin to divide the studs. There's no way you can count out over 3,000 studs for each shoe! Instead, you decide to divide. If you have 12 pairs of shoes, or 24 shoes in total, and there are 3,000 studs, you can estimate your answer to see how many studs each shoe will get. The 24 pairs of shoes can be rounded to 20, and since 3,000 is a well-rounded number already, we can leave it as 3,000.

3,000 / 20 = 150

Each shoe will get about 150 studs.

You then decide to evenly place the studs on the four sides of the shoe. You have to estimate how many studs each side will get. A shoe has four sides - front/top, the left side, back, and the right side.

150 / 4 = 37.5

Since we cannot use decimals, each side of the shoe will get close to 38 studs.

When we use **estimation** to solve problems, you are taking an educated, realistic guess. Your answers will not always be exact. Since you are estimating, you will use language such as: about, almost, maybe, and close to. Since your estimation isn't exact, the answer cannot be exact. When finding the products, sums, and divisors with math problems, estimating helps us to solve these problems quickly. This type of mental math makes it easier for us to solve problems.

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Explorations in Core Math - Grade 6: Online Textbook Help10 chapters | 118 lessons

- Estimating With Whole Numbers
- Estimating Sums, Products and Divisors of Whole Numbers
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