Download Common Core Learning Standards

Common Core Learning Standards
GRADE 5 Mathematics
NUMBER & OPERATIONS – FRACTIONS
Common Core Learning
Standards
Use equivalent fractions as a
strategy to add and subtract
fractions.
Concepts
Adding and
subtracting
fractions
5.NF.1.
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.)
Embedded Skills
4
foot piece of wood to make shelves for
5
shelves measuring 2

Rewrite two fractions with unlike denominators to
have common denominators in order to add or
subtract fractions.
The painter painted 3/10 of a wall blue and 2/5 of the wall
orange. How much of the wall is painted? Use the rectangle
below to show your work.
his living room. Does he have enough wood to make four


Add fractions with unlike denominators (including
mixed numbers).
Subtract fractions with unlike denominators
(including mixed numbers).
Simplify fraction solutions.
RIGOROUS SAMPLE TASKS
Dule′ is cutting a 12
Vocabulary






Simplify
common
denominators
unlike
denominators
fraction
equivalent
reduce
mixed number
improper
fraction
numerator
SCAFFOLDED SAMPLE TASKS
These rectangles have been divided into fifths. Use the rectangles
above to create equivalent parts
Example:
Fifths
Tenths
Twentieths
Jesse has three pieces of rope that are each 2
3
inches long. How
7
much rope does he have all together?
7
feet each?
8
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
fractions and
real world
situations
Use equivalent fractions as a
strategy to add and subtract
fractions.
5.NF.2.
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.
Embedded Skills
Solve word problems involving addition and
subtraction of fractions of unlike denominators
referring to the same whole.
Justify the reasonableness of a solution using
estimation and benchmark fractions.
to share it with his friends. He wants to keep
share
4
of it for himself,
6
1
of the fruit roll up with Jimmy, and give the rest to Tom.
9









RIGOROUS SAMPLE TASKS
Rob has one fruit roll up. The fruit roll up is one foot long. He wants
Vocabulary
unlike
denominators
benchmark
fractions
estimation
fraction
equivalent
reduce
mixed number
improper
fraction
numerator
SCAFFOLDED SAMPLE TASKS
-You are making trim for a quilt. You need 5
and 3
1
feet of purple lace
2
3
feet of pink lace. How much lace do you need in all to
4
complete this project?
How much will Tom get? Reduce to lowest terms.
- Sally ate
1
of her candy bar. How much of the original candy bar is
3
left?
Joanne feeds her cat
2
5
of a can of cat food in the morning and
of
3
6
a can in the afternoon. How many cans of cat food will she need to
feed her cat for five days?
Rey feeds his dog
2
4
of a can of dog food in the morning and
of a
5
5
can in the afternoon. How many cans of dog food will he need to
feed his dog for two days?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
Embedded Skills
fractions
Define a fraction as division of the numerator by its
denominator.
Solve word problems involving the division of two
whole numbers where the solution is a fraction or
mixed number.
Explain between what two whole numbers the
fraction solution lies.
5.NF.3.
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?
Vocabulary




Numerator
Denominator
Division
Quotient
RIGOROUS SAMPLE TASKS
SCAFFOLDED SAMPLE TASKS
Four friends combine their money to buy three large pizzas. If they
share the pizzas equally, what fraction of a whole pizza does each
friend eat?
Jack bakes 10 trays of cookies using 8 cups of milk. How many cups of
milk does he use for each tray of cookies?
Four friends share three candy bars. What part of one candy bar does
each friend get? Draw a model to illustrate.
Renee is making pasta. She makes 3 cups of noodles using 6 cups of
water. How many cups of water were needed for each cup of
noodles?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication and
division to multiply and divide fractions.
Concepts
Embedded Skills
multiplication
of fractions
and whole
numbers
Draw a fraction model to illustrate a product of a
fraction by a whole number and a fraction by a
fraction.
Relate multiplying by a fraction as taking "part of" a
whole number.
5.NF.4a.
Vocabulary




part of
area
tiling
unit fraction
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.)
RIGOROUS SAMPLE TASKS
The fifth grade teachers bought three party pizzas to celebrate good
behavior. Each party pizza has twenty-four slices. They order three
kinds of party pizzas; one cheese, one pepperoni, and one sausage.
20
7
3
They eat
of the pepperoni pizza,
of the cheese pizza and
of
24
8
4
SCAFFOLDED SAMPLE TASKS
Molly’s mother baked a cake. There were 12 pieces, and only
2
of
3
the cake is left!
A.
How many pieces are left?
the sausage pizza.
A. What fraction of each pizza is left?
______of the cheese pizza
______ of the pepperoni pizza
______ of the sausage pizza
B. How many slices of each pizza are left?
_______ slices of cheese pizza are left
_______ slices of pepperoni pizza are left
_______ slices of sausage pizza are left
Lena has some eggs. She uses
scrambled eggs. She uses
3
of the eggs to make waffles and
5
B. What fraction of the cake was eaten? How many pieces is
this?
- Using visual fraction models, multiply
1
3
x
.
2
4
2
of the eggs she took to make the
3
waffles. What fraction of the total number of eggs does Lena use to
make waffles?
- Develop a real world problem to illustrate
7 4
x
8 5
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
5.NF.4b.
Find the area of a rectangle with fractional side
lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and
show that the area is the same as would be
found by multiplying the side lengths. Multiply
fractional side lengths to find areas of
rectangles, and represent fraction products as
rectangular areas.
Concepts
Embedded Skills
Area of
rectangles
with
fractional
side lengths
Compute the area of a rectangle with fractional side
lengths.
Tile a unit square into unit fraction side lengths.
1
1
inches by 2 inches. Allison’s cell
2
4
phone is pictured below. Which cell phone has a greater area?
2
1
8
Tiling
unit square
equivalence
SCAFFOLDED SAMPLE TASKS
Find the area of a farmer’s field with a width of
length of


4



Prove through tiling the equivalence of
multiplication and area.
RIGOROUS SAMPLE TASKS
Katie’s cell phone measures 3
Vocabulary
5
of a mile and
6
3
of a mile.
4
Calculate the area of the farmer’s field.
Draw a picture using tiling to show your solution.
3
mi
4
3
8
5
mi
6
How much larger is the bigger cell phone?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
Embedded Skills
size of
products
Describe the size of a product in terms of how many
times larger one factor is to another without
multiplying.
5.NF.5a.
Comparing the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
Vocabulary




Explain and show why multiplying by a fraction
equal to 1 result in an equivalent fraction.
RIGOROUS SAMPLE TASKS
Carl ate of of a pizza.
- Explain without finding the exact product. Did Carl eat more or less
Product
Factor
improper
fraction
mixed number
SCAFFOLDED SAMPLE TASKS
Determine whether the product is larger (or smaller) than the
underlined factor. Use models to illustrate if necessary.
1. 1 x 18
2. 3 x 16
than of the pizza? Did he eat more or less than of the pizza?
3. 14 x
1
2
4. 1
1
x 28
2
B. Create a story problem for one of the multiplication problems
above.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
Embedded Skills
size of
products
Explain and show why multiplying by a fraction less
than one will result in a product less than the
greater number.
Explain and show why multiplying by an
improper/mixed number will result in a product
greater than the given number.
5.NF.5b.
Explaining why multiplying a given number by a
fraction greater than 1 results in a product
greater than the given number (recognizing
multiplication by whole numbers greater than
1 as a familiar case); explaining why multiplying
a given number by a fraction less than 1 results
in a product smaller than the given number;
and relating the principle of fraction
equivalence a/b = (n × a)/(n × b) to the effect of
multiplying a/b by 1.



Product
Factor
equivalent
fraction
Rewrite the number 1 as an equivalent fraction i.e.
2/2, 3/3, 4/4, etc.
RIGOROUS SAMPLE TASKS
A baker orders five sacks of flour to use in a week. Each day from
1
Monday through Friday he uses 1 sacks of flour when baking. Will
4
he have enough flour to last the week? Explain your answer without
solving the problem.
Vocabulary
SCAFFOLDED SAMPLE TASKS
Without multiplying, identify which of the expressions has the
greater product.
x 30 or
x 30
Explain how you know.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
Embedded Skills
multiplication Solve word problems involving multiplication of
of fractions fractions and mixed numbers.
Represent the product of fractions in simplest form.
and mixed
numbers
5.NF.6.
Solve real world problems involving
multiplication of fractions and mixed numbers,
e.g., by using visual fraction models or
equations to represent the problem.
1
3
pints of blueberries. He used
of the
4
4
blueberries to make tarts. How many pints of blueberries did the
baker use?



Fractions
mixed number
visual models
Write equations to represent word problems
involving multiplication of fractions.
Draw/show multiplication of fractions through
visual models.
RIGOROUS SAMPLE TASKS
A baker bought 2
Vocabulary
SCAFFOLDED SAMPLE TASKS
Predict whether the product will be bigger or smaller than each
factor. Then multiply the following:
1.
1
1 3
x
2 8
Prediction:
2.
3 2
x
7 5
Prediction:
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
division of
unit fractions
and whole
numbers
5.NF.7a.
Interpret division of a unit fraction by a nonzero whole number, and compute such
quotients. For example, create a story context
for (1/3) ÷ 4, and use a visual fraction model to
show the quotient. Use the relationship
between multiplication and division to explain
that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
RIGOROUS SAMPLE TASKS
Mrs. Smith had
1
of a pumpkin pie left over. She split the leftover
2
pie between her three children. What fraction of the pie did each
child get?
Embedded Skills
Vocabulary






Define a unit fraction as fraction with a numerator
of 1.
Divide a unit fraction by a whole number.
Draw/show division of a unit fraction by a whole
number as dividing the unit fraction into smaller
parts.
Create a story in which division of a unit fraction by
a whole number is used.
unit fraction
whole number
divide
estimation
quotients
lowest terms
Explain the effects of dividing a unit fraction by a
whole number.
Justify the reasonableness of answer in the context
of a problem.
Simplify/reduce quotients to lowest terms.
SCAFFOLDED SAMPLE TASKS
Draw a model and explain the difference between:
A) 9 ÷
1
3
AND
B)
1
÷9
3
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
Embedded Skills
division of
unit fractions
and whole
numbers
Define a unit fraction as a fraction with a numerator
of 1.
Divide a whole number by a unit fraction.
5.NF.7b. Interpret division of a whole number
by a unit fraction, and compute such quotients.
For example, create a story context for 4 ÷
(1/5), and use a visual fraction model to show
the quotient. Use the relationship between
multiplication and division to explain that 4 ÷
(1/5) = 20 because 20 × (1/5) = 4.
Create a story in which division of a whole number
by a unit fraction is used.
Explain the effects of dividing a whole number by a
unit fraction.
Vocabulary








unit fraction
whole number
divide
estimation
quotients
lowest terms
numerator
denominator
Define the reciprocal of a unit fraction for the
purpose of division.
Simplify/reduce quotients to lowest terms.
Justify the reasonableness of answer in the context
of a problem.
RIGOROUS SAMPLE TASKS
SCAFFOLDED SAMPLE TASKS
A rope is 9 meters long, and John needs six pieces. If each piece is cut
Mario ordered 5 pizzas. How many slices did Mario order if each slice
to be
1
m will he have enough?
4
is ⅛ of a pizza?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Apply and extend previous
understandings of multiplication
and division to multiply and divide
fractions.
Concepts
division of
unit fractions
and whole
numbers
5.NF.7c.
Solve real world problems involving division of
unit fractions by non-zero whole numbers and
division of whole numbers by unit fractions,
e.g., by using visual fraction models and
equations to represent the problem. For
example, how much chocolate will each person
get if 3 people share 1/2 lb of chocolate
equally? How many 1/3-cup servings are in 2
cups of raisins?
Embedded Skills
Divide a whole number by a unit fraction (vice
versa) in the context of word problems.
Solve a story/word problem in which division of a
whole number by a unit fraction (vice versa) is used.
Explain the effects of dividing a whole number by a
unit fraction (vice versa) in the context of a word
problem.
Justify the reasonableness of answer in terms of the
context of the problem.
2
gallon carton of ice
3
cream. How much ice cream did each girl eat?








unit fraction
whole number
divide
estimation
quotients
lowest terms
numerator
denominator
Simplify/reduce quotients to lowest terms.
RIGOROUS SAMPLE TASKS
Tina and her two friends equally shared a
Vocabulary
SCAFFOLDED SAMPLE TASKS
For a party, Selma invites 24 people. If she makes pasta salad and
gives everyone
1
cup, how many cups of pasta salad will she need
2
to make?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.