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# Fractions

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by

## Amelie Huang

on 19 July 2015

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#### Transcript of Fractions

numerators
denominators

What is a fraction?
How to illustrate it?
What are numerators and denominators?
Do denominators identify amounts of equal parts or unequal parts?
Prior Knowledge
Activate students' prior understanding of factors, multiples, integers, improper fractions, equivalent fractions. Students should be able to represent fractions with words, concrete materials and notation.

Sample Question:
Place fractions: 7/10, 1/2, -9/10, 1 1/10, and - 3/5 on a number line.
Number Sense and Numeration

Comparing fractions, ratios, decimals, and percents.

Sample Question
: Arrange these numbers "13/20, 0.78, 31:50, and 62%" from smallest to largest. (G.7)

G. 7 students solve problems involving rate, unit rate. G.8 and up solve problems involving percent and proportion.

Facts & Skills
Adding and subtracting fractions with different denominators.
7/8+ 5/6 = 12/ 36 + 1/3 =
4 2/3 + 5 4/9 = 7/3 + 5/8=
7/8 - 5/6 = 9/4 - 6/5 =
5 1/2 - 8 1/4= 4 4/7 - 2 7/8 =

More worksheet for students:

Students may require clarification of LCD, LCM, or GCF. Videos such as the ones on the next slide can help.
Game and Quiz for Students

Quiz - Finding equivalent fractions:
http://www.bbc.co.uk/bitesize/quiz/q56128425

Facts & Skills
Students can multiply and divide fractions and mixed numbers.
1 1/7 x 12/ 13 = 4/9 X 18 =
2.5 ÷ 1/2 = 4/7 ÷ 13/3 =
6/13 ÷ 5/9 = 6 1/3 X 1 1/2 =
Big Ideas & Fractions
Fractions
Sample question
: Apart from a number line, what other ways do you know to illustrate fractions?
Sample word problems:
1) Edward won 80 dollars, which is 2/5 of the total cash prize for winning a race. In the same race, Stewart won 50 dollars. What was the percentage of Stewart's prize of the total cash prize of the race?

2) You have three quarters of a pizza, and you want to split it between yourself and 3 friends. How much pizza will each of you get?

Students may confuse the uses of part-whole relations and miss-use multiplication, division, addition and subtraction.
Game - Converting Decimals & Fractions: http://www.helpingwithmath.com/resources/games/bbc/decimals01.html
Skills and Applications
Teacher Resources

Fractions and decimals
http://www.helpingwithmath.com/printables/worksheets/fractions/4nf6fractions01.htm

http://www.helpingwithmath.com/printables/worksheets/fractions/4nf5fractions01.htm

Fractions worksheets
http://www.math-aids.com/Fractions/

Fractions and word problems
http://www.mathocean.com/2009/08/fraction-word-problems.html

http://www.analyzemath.com/middle_school_math.html

geometry formulas
http://www.iq.poquoson.org/2005vasol/eocgeom/eocgeomformulas05.htm

LCM and GCF of 3 numbers
Students may have difficulty with the conceptual understanding of multiplication and division of fractions.
Sample question
: Could you use pictures or diagrams to illustrate:
1/3 x 1/2 = 1/6 4/5 ÷ 1/5 = 4
Skills
Solve:
2n/5 + n/5 = 20
t/7 - 3/5 = 8 + t/4
a/6 + 1/5 = a/3 - 4
m/9 x 6 = 5/12
4 2/7 ÷ t/5 = 4/3

Measurement & Geometry
Students solve problems involving the
area of a trapezoid (G. 7), a circle (G. 8), composite figures (G. 9); and problems involving the volume of pyramids or cones (G. 9)

Sample Question
: A circle has a perimeter of 15 1/3 m, what is the area of this circle? (G. 8)
Thank you for your following along.
Sample problem
: In language class, the girl to boy ratio is 5 to 8. If there are a total of 65 students, how many girls are there?

Note: If you need support for this question, play the video below.
Note
: If students have any problems solving an equation with fractions, they can watch the video below:
Note
: See the video for
help clarifying GCF and LCD/LCM
GCF
LCD/LCM
More word problems
: http://www.mathocean.com/2009/08/fraction-word-problems.html
and suggestions at :
Measurement and Trigonometry
Solving problems involving surface
area and volume of pyramids and
cylinders. (G. 10 Applied) Determining, through investigation,
the trigonometric ratios of sine,
cosine, and tangent as ratios.
Patterning and Algebra
Model everyday relationships involving
rates G.7 Translate statements into
algebraic expressions and equations G. 7&8.
Sample question
: A triangle has a perimeter of 50 2/5. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side? (G.7&8)
Sample question
: A cylinder has a volume for 90 4/5 square meters, the height is 8 1/2 m, what should be the surface area? (G. 10)
More geometry problems for grade 10
:
http://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Multiplying+Dividing%20Fractions%20and%20Mixed%20Numbers.pdf
More worksheet for students

Describing a linear relation and a graphical point of intersection G.9; Solving equations involving fractional coefficients, slope and quadratic relations. (G.10)
http://roensmath.edublogs.org/files/2013/05/lessson-2-solving-linear-systems-by-graphing-1lecw8x.pdf
http://www.mathworksheets4kids.com/equations/linear/point-of-intersection-1.pdf
http://www.mathworksheets4kids.com/equations/multi-step-fractions-1.pdf
http://www.mathworksheets4kids.com/equations/multi-step-fractions-2.pdf
sample question
: Two lines 2/3 x + y = 2/9
3x - y = 3
Solve by graphing each line and finding the point of intersection

More resources:
Data Management and Probability
Students can use fractions to express the
experimental and theoretical probability of an
event. (G.7&8)
Sample questions:
Taye has the following data: 1/10,
d
, 1/10, 1/17, 1/3, 1/17. If the mode is 10, which number could
d
be?

Blaine has the following data: 1/12, 1/11, 1/11,
a
, 1/13. If the median is 1/12, which number could
a
be?
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