For further information about Backward Design refer to
http://www.ubdexchange.org/
Title: _Fractional Parts_ Subject/Course: __Math ________
Topic: _Fraction Operations Grade(s):
___6th___ Designer(s): _Devane/Rogers__ 

Stage
1 – Desired Results 

Established Goal(s) M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems. c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers. d. Add and subtract fractions and mixed numbers with unlike denominators. g. Solve problems involving fractions, decimals, and percents. (enter goals here) 

Understanding(s) Students will understand that... 1. Fractions must have common denominators before they can be added. 2. Common multiples can help students rename fractions with common denominators. 3. Unit fractions always represent one part of the whole. 4. Students will understand that all powers of two have a common multiple of two. 5. Fractions can be represented as a decimal value.

Essential
Question(s) 1. How are fractions with different denominators added? 2. How can we find the least common multiple of a set of numbers? 3. How do we determine successive powers of 2? 4. How do we convert fractions to decimals? 


Students will know... …what is the least common multiple of a set of numbers. …what are powers of two.
K 
Students will be able to... …add fractions with unlike denominators. …convert fractions to decimals. …recognize a pattern. S 


Stage
2 – Assessment Evidence 


Performance Task(s)
Find the sum:
(Student will add the first seven fractions in this series.)
T 

Key Criteria Students should know that 2 to the seventh is the least common multiple of the denominators of the first seven powers of two. The first seven fractions must be written as a fraction with a denominator of two to the seventh power.


Other Evidence Solution: 1/2 = 64/128 1/2^2 = 32/128 1/2^3 = 16/128 1/2^4 = 8/128 1/2^5 = 4/128 1/2^6 = 2/128 1/2^7 = 1/128 The total is 127/128.


Stage
3 – Learning Plan 
Learning Activities 
1) Students will add a series of simple unit fractions to determine a sum. 1/2 + 1/4 = ? 1/2 + 1/4 + 1/8 = ? 1/2 + 1/4 + 1/8 + 1/16 = ? 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = ?
2) Change the solutions of each fractional sum above to a decimal value rounded to the nearest tenthousandth? What do you notice?
3) Suppose the shading in the square below continues forever in
the same pattern. What fractional part of the square is shaded? Can you
change these fractions to decimal values rounded to the nearest ten
thousandth? What do you notice? (Assume that all horizontal
lines are parallel, all vertical lines are parallel, and all angles are
right angles.)
Extensions:
What would happen if the square was cut into thirds, one third
shaded in, and then an additional third was cut into thirds
and so on? Can you draw an accurate example and follow through
with the previous steps? What fractional part of the square is
shaded?
