Download Add, Subtract, and Multiply Whole Numbers and Decimals

Add, Subtract, and Multiply Whole Numbers and Decimals.notebook
Adding, Subtracting, and Multiplying Decimals
October 07, 2015
Lesson 1: Adding Decimals
Aug 3­3:45 PM
Aug 3­3:46 PM
Adding Whole Numbers and Decimals
Remember that when adding whole numbers, you MUST line up the place values.
You cannot add the hundreds place to the ones place.
Adding Decimals
The first strategy we will learn is using decimal models to add decimals. Recall
how to show decimal numbers with grid models. An entire grid shaded in shows
one whole, groups of ten blocks shaded show tenths, and single blocks shaded
show hundredths.
Complete the following problem in your notes to review.
45,657 + 7,802 =
Did you line up the numbers one on top of the other and then add each place
value? That is what is called the traditional algorithm. That is a fancy way of
saying the regular way. We will learn the traditional algorithm for adding
decimals as well as other strategies.
0.44
3.47
Aug 3­3:46 PM
Adding Decimals
Let's add 0.44 and 0.47.
First, we need to make a
decimal model to show our
first addend, 0.44.
Next, We need to shade
in 0.47 in another color to
represent our second
addend.
0.97
0.58
1.54
Aug 3­3:46 PM
Checking Your Work:
Adding decimals with the traditional algorithm is just like adding whole numbers. To do this problem the regular way, you just line up the place values and bring the decimal straight down when you add.
Adding Decimals
Let's show the previous problem on a number line. The steps are basically the
same. You will show the first addend on the number line and add the second
addend to the first.
0.44 + 0.47
+ 0.47
1
0.44
+0.47
0.91
0
0.44
0.91
1
Try this one in your notes. Use a number line, a decimal grid model, and the
traditional algorithm. Correct if necessary.
Last, we need to count the total number shaded. There are ninety-one hundredths
shaded in, making the answer 0.91.
Aug 3­3:46 PM
1.53 + 0.27
Aug 3­4:19 PM
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Add, Subtract, and Multiply Whole Numbers and Decimals.notebook
October 07, 2015
Is it Reasonable?
Teachers show different strategies because different strategies
work better in different situations. For example, if you want to show
1.56 + 0.97 or other smaller decimal numbers, it is reasonable to use
decimal grid models, number lines, and the traditional algorithm.
Lesson 2: If you want to show 15.56 + 11.67, it would not be reasonable to use
grid models because they would take forever to draw. Use the
strategy or strategies that are best for the problem given.
Subtracting Decimals
The traditional algorithm can be used for any decimal problem, but
you will be expected to know every strategy.
Aug 3­4:19 PM
Aug 3­4:19 PM
Subtracting Decimals
Subtracting Whole Numbers and Decimals
Let's
Remember that when subtracting whole numbers, you MUST line up the place
values. You cannot subtract the hundreds place from the ones place.
complete the following
subtraction problem using
decimal grid models.
1.85 - 0.65
Complete the following problem in your notes to review. Make sure you are
regrouping (borrowing) correctly.
Step 1: Shade in the grid
model to represent 1.85
45,657 - 7,802 =
Step 2: Since you are taking
away 0.65, we are going to
cross out 0.65 on our existing
grid model.
Did you line up the numbers one on top of the other and then subtract each
place value? That is what is called the traditional algorithm. That is a fancy way
of saying the regular way. We will learn the traditional algorithm for adding
decimals as well as other strategies.
Aug 3­4:56 PM
Step 3: Determine what is
left shaded. That is your
answer.
1.2 (or 1.20) is left shaded. This is your
answer. Go ahead and try this problem with
the traditional subtraction algorithm. Be
sure to line up the decimal places!
Aug 3­4:56 PM
Subtracting Decimals
Let's show the previous problem on a number line. The steps are basically the
same. You will show the first number (the larger one) on the number line and
take the other number away.
­ 0.65
1.85 - 0.65
0
0.5
1
1.2
1.5
1.85
2
Try this one in your notes. Use a number line, a decimal grid model,
and the traditional algorithm. Correct if necessary.
1.53 - 1.27
Aug 3­4:56 PM
Lesson 3: Estimating Sums and Differences
Aug 3­4:56 PM
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Add, Subtract, and Multiply Whole Numbers and Decimals.notebook
Estimating Sums and Differences
You can use rounding to estimate what a sum or a difference might be. The
main purpose of estimating is to make sure your actual answer is reasonable or
makes sense.
For instance, if you wanted to know the sum of 11 + 17, you would round them
both to the nearest ten (10 + 20) and then you can easily add them mentally
(30). The actual answer is 28, which is very close to 30, so the answer is
reasonable.
You can round to different place values. You need to round to the place value that will make it easy for you to mentally solve the problem. Here is an example.
1
1.86
1.86 is close to 2. + 0.92
0.92 is close to 1
2.78
October 07, 2015
Estimating Sums and Differences
You can also estimate sums and differences by using benchmark numbers.
Remember from fourth grade that benchmark fractions are fractions like
1/2 and 1/4. Benchmark numbers are those that are easy to manipulate in
your head.
The best way to do this is to think about money and quarters. You can round
your numbers to the nearest quarter.
Here is an example:
6.79
­ 0.20
6.59 is very 6.59
close to our Think, 6.79 is close to 6.75 (6 and 3 quarters)
0.20 is close to 0.25 (one quarter)
6.75 ­ 0.25 is 6.50, so our answer should be close to that
estimate of 6.50, so our answer is reasonable.
1 + 2 = 3 so the answer should be close to 3.
2.78 is close to 3, so our answer is reasonable.
Aug 3­4:56 PM
Aug 4­4:08 PM
Estimating Sums and Differences
Lesson 4: Click the link to see a quick video on estimating sums and differences.
Multiplying Whole Numbers
https://learnzillion.com/lesson_plans/8902­
estimate­the­addition­and­subtraction­of­
decimals­using­smart­rounding#fndtn­lesson
Aug 4­4:08 PM
Aug 4­4:33 PM
Multiplying Whole Numbers
We will start with a review of multiplying whole numbers. Remember that the
expression 7 x 3 means 7 groups of 3 and can be shown with an array like
this:
Multiplying Whole Numbers
Now we will review the traditional algorithm for multiplying whole numbers. In
fourth grade you should have learned how to multiply by one digit numbers and 2
digit numbers. We will complete an example of both.
7 x 3 = 21
Let's try another review problem using an area model with partial products.
71 x 6
Break each factor into expanded form then label your area model with the parts. One number goes across the top and the other will go on the side. 70
6 420
1
6
https://
learnzillion.com/
lessons/4389­use­
area­models­for­
multiplication
50
5
10 500 50
3 150 15
Aug 4­4:33 PM
420 + 6 = 426
1
Let's try one more with two double digit factors.
55 x 13
23
x 45
126
x 5
Remember the place holder when you start the second row of multiplying.
500
150
50
+ 15
715
https://learnzillion.com/lesson_plans/8041­use­the­
standard­algorithm­for­multiplication#fndtn­lesson
Aug 4­4:33 PM
3
Add, Subtract, and Multiply Whole Numbers and Decimals.notebook
Lesson 5: Multiplying by 3 Digit Numbers
October 07, 2015
Multiplying by 3 Digit Numbers
We will start with using an area model with partial products to multiply by 3 digit
numbers. Let's start with the expression 132 x 114.
10
100
100
Break each factor into expanded form then label your area model with the parts. One number goes across the top and the other will go on the side. 4
10,000 1,000 400
30
3,000
2
200
300 120
20
Aug 4­4:33 PM
8
=11,400
=3,420
11,400
3,420
+ 228
15,048
=228
Aug 4­4:33 PM
Multiplying by 3 Digit Numbers
Multiplying by 3 Digit Numbers
2
123
x 227
Try these problems in your notebook using area models.
307 x 432
1. Begin by
multiplying the
digits on the top
by seven as you
normally would.
861
2. Next, put a
place holder zero
then begin
multiplying the top
digits by the 2.
123
x 227
861
2460
298 x 123
place holder zero
123
x 227
861
2460
+ 24600
27,921
3. Put 2 place
holder zeros, then
begin multiplying
the top digits by
the last 2.
4. Add the 3
numbers (partial
products) together
then you will have
your product.
Use an area model to complete this problem in your
notebook. Did your answers match?
Aug 4­7:04 PM
Aug 4­7:04 PM
Multiply Decimals and Whole Numbers
Lesson 6: Remember that multiplication is repeated addition. For example, 7 x 3 is the same
as 7 + 7 + 7, or 3 groups of seven. Multiplying decimals by whole numbers is the
same. Let's start with a sample problem. We will model this problem with quick
pictures of base ten blocks and with decimal grids.
3 x 0.27
Multiplying Decimals by Whole Numbers
Aug 4­7:04 PM
Now we will count what we have in total.
We have 6 tenths and 21 hundredths. We
will group 10 hundredths together to
make tenths, then recount.
This means 3 groups of twentyseven hundredths. We will do a
quick base ten model of 0.27
and then make 2 more to make
3 groups. In this case, the lines
will represent tenths and the
dots will represent the
hundredths.
There are 8 tenths and 1 hundredth,
making our answer 0.81.
Aug 5­12:12 PM
4
Add, Subtract, and Multiply Whole Numbers and Decimals.notebook
Multiply Decimals and Whole Numbers
Let's try the same problem,
but with decimal grids.
3 x 0.27
We need to
shade in 0.27
three times since
we want 3 groups
of it. Using
different colors
makes it easier to
see.
0.81 is now
shaded. That is
the product.
Aug 5­12:12 PM
October 07, 2015
Multiply Decimals and Whole Numbers
Now we will multiply using the traditional algorithm for multiplication.
You will multiply these just as
you would whole numbers. One
important thing to know is that
you should put the longer (not
necessarily larger) number on
top.
3 x 0.27
2
.27
x 3
81
2 decimal places
Ignore the decimal till you complete
the multiplication.
+ 0 decimal places
2 decimal places
Now that you have multiplied, you need to place the decimal in your answer.
DECIMALS ARE NOT BROUGHT STRAIGHT DOWN LIKE IN ADDITION AND
SUBTRACTION. To place the decimal in your product, you count haw many places
are behind the decimal in both of your factors. Then you add them up and that's
how many places should be in your answer.
Aug 5­12:12 PM
Multiply Decimals by Decimals
Lesson 7: Strategies for multiplying decimals by other decimals are different from multiplying decimals by whole numbers. The traditional algorithm is exactly the same and can be your go­to strategy if needed. 0.4 x 0.2
Multiplying Decimals by Decimals
Aug 5­12:12 PM
Step 1: Shade in the first factor
vertically (up and down)
Step 2: Shade in the second factor
horizontally (side to side)
https://learnzillion.com/lesson_plans/
6683­use­multiplication­to­multiply­
decimals­by­decimals#fndtn­lesson
The boxed area is where the decimals
overlap. The overlapping portion is the
product.
Aug 5­12:45 PM
Multiply Decimals by Decimals
Let's practice the traditional algorithm for multiplying decimals once more.
Try the following problem. Remember to ignore the decimal until you are
finished multiplying, then you can see how many decimal places are in your
factors.
6.32
x 3.4
2528
+ 18960
21488
2 decimal places
+ 1 decimal place
3 decimal places in the product
The product is twenty one and
four hundred eighty-eight
thousandths.
Aug 5­12:45 PM
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