adding mixed numbers · 2013. 3. 1. · to add mixed numbers with regrouping. students will also...
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Page 1 of 9 MCC@WCCUSD 02/28/13
Introduction: Student’s will be able to use bar models (fraction bars) and decomposition to add mixed numbers with regrouping. Students will also see the use of improper fractions when adding mixed numbers. (5NS 2.3) Materials: Fraction bars Key Concepts: Equivalent forms of one, decomposition, equivalent fractions, least common multiple/denominator, regrouping “We have learned what happens when we add fractions and we have a sum greater than one whole. Today we will examine what to do when we add a mixed number and our fractional part is greater than one whole. Let’s look at an example!”
Example #1 (I do): 82
871 +
Build It:
1 81
81
81
81
81
81
81
81
81
Ask:
• Turn to your partner and tell them what you notice about my fractional parts? (Greater than one, more eights than one whole, etc.) Have students share out their observations.
• Class, how many eighths do I have in all? Let’s count them together. (Have students chorally count out the nine eighths pieces)
• What do we call a number like nine eighths? (Improper Fraction) • Is there a way for me to regroup and rewrite nine eighths? (As a mixed number)
• How would I regroup and rewrite nine eighths as a mixed number? (811 )
Use fraction bars to build and model the two mixed numbers. Collect like pieces and
show that .811
89 +=
ADDING MIXED NUMBERS
Page 2 of 9 MCC@WCCUSD 02/28/13
Bar Model (Fraction Bars)
Decomposition Improper Fractions
82
871 +
8721 ++=
81
881 ++=
8111 ++=
812 +=
812=
82
871 +
82
871 ++=
8271 ++=
891+=
81
881 ++=
8111 ++=
812 +=
812=
82
871 +
82
815 +=
8215+=
817=
8188 ++=
81
88
88 ++=
8111 ++=
812+=
812=
Ask:
• What happened to the sum of the fractional part of our number? (It was an improper fraction, it was greater than one whole)
• What did we need to do to our fractional part? (Decompose, break into one whole and a fractional unit, simplify)
Example #2 (We do): 432
323 +
Build It/ Draw It:
1 1 1 31
31
1 1 41
41
41
Page 3 of 9 MCC@WCCUSD 02/28/13
“With your partner, find the sum of the following mixed numbers using your fraction bars.”
Partner You Try #1 (You Do a Think, Pair, Share): 213
322 +
Build It/ Draw It:
1 1 31
31
1 1 1 21
Bar Model (Fraction Bars)
Decomposition Improper Fractions
432
323 +
43
3223 +++=
=5+ 2
344
⎛⎝⎜
⎞⎠⎟+ 3
433
⎛⎝⎜
⎞⎠⎟
129
1285 ++=
12985 ++=
125
12125 ++=
12515 ++=
1256+=
1256=
432
323 +
432
323 +++=
43
3223 +++=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛+=
33
43
44
325
129
1285 ++=
12985 ++=
125
12125 ++=
12515 ++=
1256=
432
323 +
411
311+=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛=
33
411
44
311
1233
1244 +=
123344+=
1277=
125
1212
1212
1212
1212
1212
1212 ++++++=
125111111 ++++++=
1256+=
1256=
Page 4 of 9 MCC@WCCUSD 02/28/13
Bar Model (Fraction Bars)
Decomposition Improper Fractions
213
322 +
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛++=
33
21
22
3232
63
645 ++=
6345 ++=
61
665 ++=
6115 ++=
616+=
616=
213
322 +
213
322 +++=
21
3232 +++=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛+=
33
21
22
325
63
645 ++=
6345 ++=
61
665 ++=
6115 ++=
616+=
616=
213
322 +
27
38 +=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛=
33
27
22
38
621
616 +=
62116 +=
637=
61
66
66
66
66
66
66 ++++++=
61111111 ++++++=
616+=
616=
Example #3 (We do): 543
214 +
Build It/ Draw It: 1 1 1 1
21
1 1 1
51
51
51
51
Page 5 of 9 MCC@WCCUSD 02/28/13
Bar Model
(Fraction Bars) Decomposition Improper Fractions
543
214 +
54
2134 +++=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛+=
22
54
55
217
108
1057 ++=
10857 ++=
103
10107 ++=
10317 ++=
1038+=
1038=
543
214 +
543
214 +++=
54
2134 +++=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛+=
22
54
55
217
108
1057 ++=
10857 ++=
103
10107 ++=
10317 ++=
1038+=
1038=
543
214 +
519
29 +=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛=
22
519
55
29
1038
1045 +=
103845 +=
1083=
103
1010
1010
1010
1010
1010
1010
1010
1010 ++++++++=
10311111111 ++++++++=
1038+=
1038=
You Try # 2: 872
431 +
Build It/ Draw It:
1 4
1 41
41
1
1 8
1
81
81
81
81
81
81
Page 6 of 9 MCC@WCCUSD 02/28/13
Bar Model (Fraction
Bars) Decomposition Improper Fractions
872
431 +
87
4321 +++=
87
22
433 +⎟
⎠⎞⎜
⎝⎛+=
87
863 ++=
8763 ++=
85
883 ++=
8513 ++=
854+=
854=
872
431 +
872
431 +++=
87
4321 +++=
€
= 3+3422" # $ %
+78
87
863 ++=
8763 ++=
85
883 ++=
8513 ++=
854 +=
854=
872
431 +
823
47 +=
823
22
47 +⎟
⎠⎞⎜
⎝⎛=
823
814 +=
82314+=
837=
85
88
88
88
88 ++++=
851111 ++++=
854+=
854=
“Now that we have found the sum of two mixed numbers let’s take a look and see if we can apply the same strategies with three mixed numbers.”
Example # 4 (I do/We do): In one week during P.E., Mary ran 534 miles, Lauren ran
1031 miles, and Dante ran
523 miles. In one week, how many miles total did the three
students run?
Page 7 of 9 MCC@WCCUSD 02/28/13
523
1031
534 ++
Build It/ Draw It:
1 1 1 1 51
51
51
1 101
101
101
1 1 1 51
51
Bar Model (Fraction Bars)
Decomposition Improper Fractions
523
1031
534 ++
103
55314 ++++=
1031314 ++++=
1039 +=
1039= miles
523
1031
534 ++
52
103
53314 +++++=
103
5238 +++=
103
558 ++=
10318 ++=
1039+=
1039= miles
523
1031
534 ++
517
1013
523 ++=
⎟⎠⎞⎜
⎝⎛++⎟
⎠⎞⎜
⎝⎛=
22
517
1013
22
523
1034
1013
1046 ++=
10
341346 ++=
1093=
103
1010
1010
1010
1010
1010
1010
1010
1010
1010 +++++++++=
103111111111 +++++++++=
1039+=
1039= miles
Page 8 of 9 MCC@WCCUSD 02/28/13
You Try # 3: Carla bought candy at the Candy Shop for the party. She purchased 322
pounds of chocolate almonds, 523 pounds of red vines, and
311 pounds of gummy bears.
How many pounds of candy did Carla buy for the party?
311
523
322 ++
Build It/ Draw It:
1 1 31
31
1 1 1
51
51
1
31
Bar Model
(Fraction Bars) Decomposition Improper Fractions
311
523
322 ++
52
32
316 +++=
52
336 ++=
5216 ++=
527+=
527= pounds of candy
311
523
322 ++
31
52
32132 +++++=
52
3126 +++=
52
336 ++=
5216 ++=
527+=
527= pounds of candy
311
523
322 ++
34
517
38 ++=
⎟⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛+⎟
⎠⎞⎜
⎝⎛=
55
34
33
517
55
38
1520
1551
1540 ++=
15205140 ++=
15111=
156
1515
1515
1515
1515
1515
1515
1515 +++++++=
1561111111 +++++++=
53327
••+=
527+=
527= pounds of candy
Page 9 of 9 MCC@WCCUSD 02/28/13
Do: Have students present out on the overhead/ board their answers. Look for different ways that students approached the problem. Debrief: Ask students to discuss what they discovered today when building the sum of mixed numbers and when using decomposition. Ask what strategies they used today when adding mixed numbers.