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Let’s warm up today by practicing adding and subtracting money.
Warm-up Activity
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Look at the following dollar amounts:
$2.45
$5.82
$4.24
$3.00
$0.50
$6.89
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If we add them together, what do we get?$2.45
$5.82
$4.24
$3.00
$0.50
$6.89+$22.90
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If we switch the order of the numbers and then add them, do we still get the same answer?
$5.82
$0.50
$3.00
$6.89
$4.24
$2.45+$22.90 YES!
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The fact that you can arrive at the same answer, even after switching around the numbers, is called the commutative property of addition.
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Write subtraction problems using the dollar amounts from the previous activity. Does the commutative property rule still apply?
NO!
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Today, you will be adding and subtracting decimals, fractions, and negative numbers.
Whole-Class Skills Lesson
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We can represent one-half by using the counters below.
One-half of the counters is white.
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We know this because there are two counters in the set
(denominator).
One of the counters is white (numerator).
12
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How could we represent four-fifths with the counters?
Four-fifths of the counters are red.
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Like with one-half, there are five counters in the set (denominator).
Four of the counters in the set are red (numerator).
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Look at the counters below, what fraction of them are white?
Two-fourths are white.
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Look at the counters below, what fraction of them are white?
Three-sixths are white.
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Look at the counters below, what fraction of them are white?
Four-eighths are white.
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Notice, even though we added counters each time, each of these sets shows
one-half of the counters white.
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Let’s add fractions now. Look at the counters below.
+
First, let’s convert these to fractions.
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+
are white
We have the same denominator, so we can add.
6
8
5
8are white
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6
8
5
8
11
8+ =
Notice, the denominator stayed the same.
We add the numerators.
Same denominator, so we’re ready to add.
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Another example …
this can also be written as …
0.6 + 0.5 = 1.1 (one and one-tenth)
+ =
6
10
5
10
11
10= 1
1
10
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Try these problems.
0.9 + 0.1 =
1.6 + 0.8 =
6.2 + 5.2 =
7.9 – 4.6 =
3.5 – 2.5 =
1.0
2.4
11.4
5.3
1.0
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To subtract from a negative, move further down the negative number line.
– 9 – 5 =
–9–10–11–12–13–14–15
Start at –9.Move five units in the
negative direction (left).
Your answer is –14.
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Try these examples.
3.6 + 6.7 =
9.2 – 4.9 =
–5.1 + 3.2 =
0.5 – 1.6 =
–4.7 – 2.1 =
10.3
4.3
–1.9
–1.1
–6.8
=
=
+ =
6
8
7
8 813
185
+– =
3
9
7
9 9
4
+ =
2
6
1
3 6
4
3
2
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