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The ideas in this multiplication lesson are taken from Multiplication Division 2 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


Estimating products
Free lesson plan from HomeschoolMath.net

Estimate first and use that to check the result.  8 × 67 = ?
 

67 can be rounded up
to 70, or 67 ≈ 70. 
Therefore 8  × 67 ≈
8  × 70 = 560.

5   
67
×  8

356

5   
67
×  8

536

Oops!  356 is 
far from the 
estimation 560.
There must be 
an error. Can 
you find it?
This result 
sounds right,
because it is
fairly close to 
560.

Before we start using estimation as a checking method, let's review the rounding rules.

When rounding to nearest ten, 

  • If the last digit is  __, __, __, or __, round down to the previous ten.
  • If the last digit is __, __, __, __, or __, round up to the next ten.

The symbol  ≈  is used to indicate rounding, and is read as "is approximately" or "is about".

Examples:      

34 ≈ 30

598 ≈ 600

        143 ≈ 140

255 ≈ 260

       

704 ≈ 700

705 ≈ 710


Example problems

1.  First estimate the result by rounding the second factor.  Then multiply to find out the exact result.

a.

91 ≈  90

4 × 91 ≈ 
4 × 90 = 360

    

91
×  4

     364

c.

34 ≈  ____

6 × 34 ≈ 
6 × ___ = ____

    

34
×  6

     

e.

99 ≈  ____

5 × 99 ≈ 
5 × ___ = ____

    

99
×  5

     

g.

48 ≈  ____

3 × 48 ≈ 
3 × ___ = ____

    

48
×  3

     

m.

91 ≈  ____

5 × 91 ≈ 
5 × ___ = ____

    

91
×  5

     

 
2.  These word problems illustrate some situations where you can use estimation.

a)  58 people are invited to the party; you are going to the store to buy supplies.  You figure that for each person you need two cups, two plates, and three napkins.  How many cups, plates, and napkins do you approximately need?

 

e)  A can of beans costs 29 cents.  A bag of lentils costs 42 cents.  Estimate which is cheaper: to buy 8 cans of beans or to buy 5 bags of lentils.

 

h)  Jill needs 21 inches of material to make a skirt.  About how much should she buy for seven skirts?

Now, add to the answer above 10 inches to make sure she has enough.   The material costs 1 dollars per each 9 inches (or 4 dollars a yard).  How much will it cost Jill to buy what she needs?  Draw a picture!  You can for example mark the 9-inch strips in your picture and use that to help.

 

i)  What if you have a situation similar to the one in a) but just with 92 people.   How many cups, plates, and napkins would you need?  

How many packages of each would you buy?

 

 

Next lesson: Division as repeated subtraction (introduction to long division)

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Times Tales

Learn the upper
times tables with
mnemonic stories.

Learn more!




 

 


Download my
Geometry workbook with lots of hands-on drawing problems!

 

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