Cooking Up Fractions

In
this WebQuest, students are asked to adjust recipes.  This involves adding, subtracting, multiplying and dividing fractions.  Students will review adding and subtracting fractions and learn
how to multiply and divide fractions by a whole number.  Students will use a variety of methods to
gain an understanding of how to manipulate fractions.  Students will also gain an insight as to how
fractions are used in their daily lives. 
In addition, students will also use proper mathematical terminology to
explain processes and concepts.

The New Illinois Learning Standards for Mathematics
Incorporating the Common Core

CC.5.NF.1 Use equivalent fractions as a strategy to add and
subtract fractions. Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with equivalent
fractions in such a way as to produce an equivalent sum or difference of
fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 =
23/12. (In general, a/b + c/d = (ad + bc)/bd.

CC.5.NF.2 Use equivalent fractions as a strategy to add and
subtract fractions. Solve word problems involving addition and subtraction of
fractions referring to the same whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations to represent the problem.
Use benchmark fractions and number sense of fractions to estimate mentally and
assess the reasonableness of answers. For example, recognize an incorrect
result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2. 

CC.5.NF.3 Apply and extend previous understandings of
multiplication and division to multiply and divide fractions. Interpret a
fraction as division of the numerator by the denominator (a/b = a � b). Solve
word problems involving division of whole numbers leading to answers in the
form of fractions or mixed numbers, e.g., by using visual fraction models or
equations to represent the problem. For example, interpret 3/4 as the result of
dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3
wholes are shared equally among 4 people each person has a share of size 3/4.
If 9 people want to share a 50-pound sack of rice equally by weight, how many
pounds of rice should each person get? Between what two whole numbers does your
answer lie?

CC.5.NF.4 Apply and extend previous understandings of multiplication
and division to multiply and divide fractions. Apply and extend previous
understandings of multiplication to multiply a fraction or whole number by a
fraction.

CC.5.NF.4a Interpret the product (a/b) � q as a parts of a partition
of q into b equal parts; equivalently, as the result of a sequence of
operations a � q � b. For example, use a visual fraction model to show (2/3) �
4 = 8/3, and create a story context for this equation. Do the same with (2/3) �
(4/5) = 8/15. (In general, (a/b) � (c/d) = ac/bd.)

CC.6.NS.1 Apply and extend previous understandings of
multiplication and division to divide fractions by fractions. Interpret and
compute quotients of fractions, and solve word problems involving division of
fractions by fractions, e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context for (2/3) � (3/4)
and use a visual fraction model to show the quotient; use the relationship
between multiplication and division to explain that (2/3) � (3/4) = 8/9 because
3/4 of 8/9 is 2/3. (In general, (a/b) � (c/d) = ad/bc.) How much chocolate will
each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup
servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?

CC.6.NS.2 Compute fluently with multi-digit numbers and find common
factors and multiples. Fluently divide multi-digit numbers using the standard
algorithm.

CC.6.RP.3 Understand ratio concepts and use ratio reasoning to
solve problems. Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of equivalent ratios,
tape diagrams, double number line diagrams, or equations.