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- Estimation

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Get Started Now- Intro Lesson: a5:58
- Intro Lesson: b6:20
- Intro Lesson: c7:33
- Intro Lesson: d11:41
- Intro Lesson: e7:12
- Intro Lesson: f6:01
- Lesson: 1a6:00
- Lesson: 1b6:15
- Lesson: 1c6:15
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- Lesson: 1e5:23
- Lesson: 2a4:03
- Lesson: 2b4:34
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- Lesson: 3a8:36
- Lesson: 3b8:24
- Lesson: 47:23
- Lesson: 5a4:43
- Lesson: 5b1:20
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- Lesson: 5d3:20
- Lesson: 5e1:28
- Lesson: 5f5:15
- Lesson: 6a4:03
- Lesson: 6b4:55
- Lesson: 6c5:17

In this lesson, we will learn:

- How to estimate the answer to multiplication statements
- The three methods for estimating products: estimation by rounding, estimation by clustering, and estimation with compatible numbers
- How to check and compare your estimated products with the exact answer

- An
**estimation**is a rough calculation of what the**exact answer**could be around. It is less exact but easier (faster) to calculate! - When
**estimating**, it is helpful to remember the rules for**rounding**numbers: - If the number to the right of the digit you are rounding to is $\geq$ 5, round UP; if the number is < 5, round DOWN
- For mixed fractions, round to the nearest whole number: if the fraction part is $\geq$ $\frac{1}{2}$, round UP. If the fraction part is < $\frac{1}{2}$, round DOWN.
- Three methods to estimate
**products**are:**estimation by rounding, estimation by clustering**, and**estimation with compatible numbers**. **Estimation by Rounding:**
1. - Round each factor to its greatest place value
- For mixed fractions, round to the nearest whole number
- Multiplying mixed fractions requires converting back to
**improper fractions**first **Estimation by Clustering:**
1. **Estimation with Compatible Numbers:**
1. Look at the - A compatible number is something that is close to your original number (i.e. 1-2 more or less), but it’s a multiple of the denominator
- You can
**compare**the**exact product**and the**estimated product**to see how close they are - An
happens when you round DOWN a factor; the estimated product is LESS than the exact product__underestimate__ - An
happens when you round UP a factor; the estimated product is MORE than the exact product__overestimate__

2. Do all the estimates

3.

2. Look at the

3. Change the whole number to a

- IntroductionIntroduction to Estimating Products:a)Example of estimating the product of 49 × 58b)Key terms for estimating productsc)Estimating products by roundingd)Estimating products by clusteringe)Estimating products using compatible numbersf)Underestimating and overestimating products
- 1.
**Estimating Products by Rounding**

Estimate the product using estimation by rounding. Then, find the exact product to check your answer.a)695 × 487 =b)89.32 × 514 =c)0.71 × 2.64 =d)6$\frac{2}{5}$ × 8$\frac{6}{8}$ =e)11$\frac{1}{9}$ × 3$\frac{6}{10}$ = - 2.
**Estimating Products by Clustering**

Estimate the product using estimation by clustering. Then, find the exact answer to check your estimate.a)71 + 68 + 73 + 65 =b)0.318 + 0.299 + 0.256 + 0.341 =c)11$\frac{7}{10}$ + 12$\frac{2}{5}$ + 12$\frac{1}{4}$ + 11$\frac{1}{2}$ + 11$\frac{4}{5}$ = - 3.
**Estimating Products with Compatible Numbers**

Estimate the product using compatible numbers. Is the estimated product less than or greater than the exact product?a)$\frac{3}{4}$ × 7$\frac{5}{6}$ =b)25$\frac{3}{5}$ × $\frac{5}{8}$ = - 4.
**Comparing estimated products**

Compare the products by first estimating each product using compatible numbers. Then, use symbols (for less than <, greater than >, or about equal to $\approx$) to show which product will be greater.8$\frac{1}{2}$ × $\frac{4}{7}$ vs. $\frac{4}{9}$ × 10$\frac{1}{3}$ - 5.
**Estimating Products Word Problem - 1**

If a box of twelve mangoes costs $47.88 and weighs 5.34 pounds:a)About how much will 350 boxes of mangoes cost? Use the estimation by rounding method.b)About how much will 350 boxes of mangoes cost? Use the estimation with compatible numbers method.c)Find the exact cost of 350 boxes of mangoes? Are your estimates from part a) and b) more or less than the exact cost?d)About how many pounds will 350 boxes of mangoes weigh? Use the estimation by rounding method.e)About how many pounds will 350 boxes of mangoes weigh? Use the estimation with compatible numbers method.f)Will the boxes of mangoes weigh more than or less than 1,500 pounds? Are your estimates from part c) and d) more or less than the exact cost? - 6.
**Estimating Products Word Problem - 2**

Elsa used 4$\frac{3}{4}$ flasks full of blue liquid in her science experiment. Charlie wants to use 2$\frac{1}{5}$ times as much as Elsa. About how many flasks of blue liquid would Charlie need for his experiment?a)Use the estimation by rounding method to estimate the number of flasks.b)Use the estimation with compatible numbers method to estimate the number of flasks.c)Calculate the exact product (exact answer) of how many flasks Charlie needs.