- The document is from a presentation on fractions given on April 27, 2013 by Joan Cotter.
- It discusses why fractions are important to learn, such as for sharing pizza, cooking, reading rulers, and preparing for algebra.
- It includes examples of using fractions in comics and charts showing fraction relationships. Games are presented to help students understand unit fractions and that combinations of fractions can make a whole.
27. Sometimes called quarter.
• A quarter of a hour (15 min.)
• A quarter of a dollar (25¢)
• A quarter of a gallon (quart)
Fourths
28. Sometimes called quarter.
• A quarter of a hour (15 min.)
• A quarter of a dollar (25¢)
• A quarter of a gallon (quart)
• A Quarter Pounder (4 oz.)
Fourths
35. Unit Fraction War
Object of the game:
To collect all, or most, of the cards
with the greater unit fraction.
Objective:
To help the children realize a unit
fraction decreases as the denominator
increases.
54. Concentrating on One Game
Objective:
To help the children realize that 5 fifths, 8
eighths, and so forth, make a whole.
55. Concentrating on One Game
Object of the game:
To find the pairs that make a whole.
Objective:
To help the children realize that 5 fifths, 8
eighths, and so forth, make a whole.
85. Fraction War
Object of the game:
To capture all the cards.
Objective:
To practice comparing ones, halves,
fourths, and eighths in preparation for
reading a ruler.
118. Faulty Fractions
= part
whole
“Goal: To develop the spatial organization, visually
and kinesthetically, to read and write fractions
correctly.
CRA model
119. Faulty Fractions
= part
whole
“Goal: To develop the spatial organization, visually
and kinesthetically, to read and write fractions
correctly.
“Materials: Red squares and larger black squares are
displayed to help with sequencing and number
placement.”
CRA model
129. Faulty Fractions
Experts in visual literacy say that
comparing quantities in pie charts is
difficult because most people think
linearly. It is easier to compare along a
straight line than compare pie slices.
askoxford.com
Circles
130. Faulty Fractions
Experts in visual literacy say that
comparing quantities in pie charts is
difficult because most people think
linearly. It is easier to compare along a
straight line than compare pie slices.
askoxford.com
Specialists also suggest refraining from
using more than one pie chart for
comparison.
www.statcan.ca
Circles
131. Definition of a Fraction
What is the definition of a fraction?
132. Definition of a Fraction
What is the definition of a fraction?
A part of a set or part of a whole, a small part.
133. Definition of a Fraction
What is the definition of a fraction?
A part of a set or part of a whole, a small part.
This is the everyday meaning of fraction.
134. Definition of a Fraction
3
2What about ?
What is the definition of a fraction?
A part of a set or part of a whole, a small part.
This is the everyday meaning of fraction.
135. Definition of a Fraction
An expression that indicates
the
quotient of two quantities.
American Heritage Dictionary:
136. Definition of a Fraction
An expression that indicates
the
quotient of two quantities.
This is the mathematical meaning of fraction.
American Heritage Dictionary:
137. Definition of a Fraction
This is the mathematical meaning of fraction.
3
2
An expression that indicates
the
quotient of two quantities.
American Heritage Dictionary:
140. Mixed to Improper Fractions
Each row of connected rectangles represents 1.
Write each quantity as a mixed number
and as an improper fraction.
141. Mixed to Improper Fractions
Each row of connected rectangles represents 1.
Write each quantity as a mixed number
and as an improper fraction.
142. Mixed to Improper Fractions
Each row of connected rectangles represents 1.
2 =3
4
11
4
Write each quantity as a mixed number
and as an improper fraction.
143. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
Each row of connected rectangles represents 1.
two 4s
144. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
24
two 4s
Each row of connected rectangles represents 1.
145. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
24
Each row of connected rectangles represents 1.
two 4s + 3
146. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
44
3
Each row of connected rectangles represents 1.
two 4s + 3
2
147. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
44
3
Each row of connected rectangles represents 1.
two 4s + 3 = 11
2
148. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
44
3 11
Each row of connected rectangles represents 1.
two 4s + 3 = 11
2
149. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
4 =2
3
14
34
113
Each row of connected rectangles represents 1.
two 4s + 3 = 11
2
150. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
4 =2
3
14
34
113
Each row of connected rectangles represents 1.
two 4s + 3 = 11
four 3s + 2 = 14
2
151. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
4 =2
3
14
3
4 =3
5
23
5
Each row of connected rectangles represents 1.
4
113
two 4s + 3 = 11
four 3s + 2 = 14
2
152. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
4 =2
3
14
3
4 =3
5
23
5
Each row of connected rectangles represents 1.
4
113
four 3s + 2 = 14
two 4s + 3 = 11
2
153. Write each quantity as a mixed number
and as an improper fraction.
Mixed to Improper Fractions
2 =3
4
11
4
4 =2
3
14
3
4 =3
5
23
5
Each row of connected rectangles represents 1.
24
113
four 3s + 2 = 14
two 4s + 3 = 11
four 5s + 3 = 23
154. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
155. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
= 211
5
1
5
156. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
= 211
5
1
5
157. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
= 211
5
1
5
158. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
= 211
5
1
5
= 15
3
2
3
159. Improper to Mixed Fractions
Circle the wholes and write each quantity as
an improper fraction and as a mixed number.
= 211
5
1
5
= 15
3
2
3
259. Multiplying Fractions
4 x 4 = 4 + 4 + 4 + 4
• Repeated addition doesn’t work well with
fractions.
• Multiplication is more than repeated
addition.
260. Multiplying Fractions
• Repeated addition doesn’t work well with
fractions.
1
2
x = + ?
1
2
1
2
4 x 4 = 4 + 4 + 4 + 4
• Multiplication is more than repeated
addition.
306. Dividing Fractions
Sometimes textbooks put a 1 under a
whole number to make it look like a
fraction, but it is not necessary.
÷ =
1
2
1 2
÷ =
1
3
1 3
1
3
1
4
÷ =1 3
1
÷ =1 4
1
3
4
÷ =1 4
3
÷ =
2
3
1 3
2
316. Dividing Fractions
= x = =
3
2
1
25 7
÷ = __
2
3
5
÷ =
2
3
1 3
2
First find
To find
Then ÷ =
2
3
5 5 (1 )x ÷
2
3
15
2
Does the answer make sense?
About how many 2/3s are in 5?
326. Dividing Fractions
÷ =
3
4
1 4
3
First find
To find ÷ = __
3
4
2
3
Then
3
4
2
3
3
4
2
3
÷ = x (1 ÷ )
= x =
4
3
2
3
327. = x =
Dividing Fractions
÷ =
3
4
1 4
3
First find
To find ÷ = __
3
4
2
3
Then
3
4
2
3
3
4
2
3
÷ = x (1 ÷ )
8
9
4
3
2
3
328. = x =
Dividing Fractions
÷ =
3
4
1 4
3
First find
To find ÷ = __
3
4
2
3
Then
3
4
2
3
3
4
2
3
÷ = x (1 ÷ )
8
9
4
3
2
3
The answer should be < 1 and it is.
329. = x =
Dividing Fractions
÷ =
3
4
1 4
3
First find
To find ÷ = __
3
4
2
3
Then
3
4
2
3
3
4
2
3
÷ = x (1 ÷ )
8
9
4
3
2
3
The extra step of dividing by 1 can be omitted.
330. ÷ = x (1 ÷ )
= x =
Dividing Fractions
÷ =
3
4
1 4
3
First find
To find ÷ = __
3
4
2
3
Then
3
4
2
3
3
4
2
3
8
9
4
3
2
3
The extra step of dividing by 1 can be omitted.
334. Fraction Meanings
• One or more equal parts of a whole.
• One or more equal parts of a collection.
335. Fraction Meanings
• One or more equal parts of a whole.
• One or more equal parts of a collection.
• Division of two whole numbers.
336. Fraction Meanings
• One or more equal parts of a whole.
• One or more equal parts of a collection.
• Location on a number line.
• Division of two whole numbers.
337. Fraction Meanings
• One or more equal parts of a whole.
• Ratio of two numbers.
• One or more equal parts of a collection.
• Location on a number line.
• Division of two whole numbers.