Transcript 4 - Morehead4thgrade

Monday, May 5, 2014
POTD
1. Maria has 8 cases of milk to serve in the
cafeteria. In each case, there are 90 cartons of
milk. If Maria only served 2/5 of the milk cartons,
how many are left for the next day?
2. There are 144yellow tulips in the garden. A
wildebeest came through and ate 2/6 of the
tulips out of the garden. How many birds
remain?
4.NF.1
4.NF.5
Equivalent Fractions
Common Denominators
Equivalent Fractions
• Name the same amount but have
different numerators and
denominators.
1
2
1 = 2
2
4
1
4
1
4
Equivalent Fraction Models
1
2
=
4
8
What are the missing numbers?
=
Write the equivalent fraction:
=
Equivalent Fractions
• To find an equivalent fraction, multiply the
fraction by an equivalent of 1.
Example:
Which of the following is equivalent to 2/3 ?
A. 8/12 B. 4/3 C. 6/8 D. 6/4
Solution:
• First, multiply 2/3 by 2/2.
• That is not an answer choice so multiply 2/3 by 3/3 .
• That is not an answer choice so multiply 2/3 by 4/4 .
• This is an answer choice so A is the correct answer
choice.
What do you notice about the area (overall size)
of the shape?
What is happening to the pieces?
What’s the rule for generating
equivalent fractions?
Equivalent Fractions on a number line
Common Denominators with 10 and
100
4.NF.2
Comparing Fractions
Fractions of a set
Strategies for comparing and
ordering fractions:
1. Draw pictures
(squares are easiest to draw!)
2. Remember fraction benchmarks:
Is the fraction closer to 0, ½, or 1?
3. Cross multiply
Cross Multiplication Practice
Which fraction is greater?
Use +, ‹, ›
1.3/4
2.6/8
3.1/3
2/3
5/6
2/8
Terry and Dale each ordered their
own pizza. Terry told Dale that he
ate ¾ of his pizza. How many
pieces will Dale have to eat to have
the same amount of pizza left?
Priyanka ate 2/3 of a pizza. Solomon
ate 3/5 of a pizza. Who ate more?
This is a fraction cookie that was made using pattern
blocks. Which number sentence is true?
a. 1/2 = 2/6
b. 2/3 = 1/2
c. 1/2 = 4/6
d. 2/6= 1/3
Order the fractions from least
to greatest:
¾, ½ , 2/3
Kelwin has 3 whole brownies and two-fourths
of another brownie. Anthony has 3 whole
brownies and three-eighths of another
brownie. Who has more brownies?
Fractions
1. Jai-Lin and Isaijah are playing
fraction war. Jai-Lin turns over a card
with one-sixth written on it.
Isaijah's card has two-thirds written
on it. Who had the larger fraction?
2. 3 friends want to share 4 cookies.
What is each person’s fair share?
• Which fraction shows less than
Fractions of a Set
Example: 2/3 of 12= ?
The denominator tells you to draw 3 groups.
Divide 12 equally until each group has the
same amount. Circle 2 of the groups because
the numerator is 2!
• If a red trapezoid is one whole, which block
shows 1 ? 3
• If the blue rhombus is 1 , which block shows
one whole? 3
• If the red trapezoid is one whole, which block
shows 2 ?
There are 12 birds in a tree. One-third
flew away. How many birds are still in
the tree?
Sky bought 18 mini candy bars. She
ate two-thirds of them. How many
candy bars does she have left?
Mrs. Smith bought 15 tickets to a concert. She
gave 2/3 of them to her friends. How many
tickets did she give away?
Mrs. Talton bought 16 donuts before
school. She passed out 2/4 of them at
lunch. How many donuts were left?
Ms. Mohler placed 16 skittles in a bag.
Jaquez ate 3/4 of them and Trayden ate ½ of
them. Who ate fewer skittles?
• Mary used a 12 x 12 grid to represent 1 and
Janet used a 10 x 10 grid to represent 1. Each
girl shaded grid squares to show 1/4 . How
many grid squares did Mary shade? How
many grid squares did Janet shade? Why did
they need to shade different numbers of grid
squares?
• There are two cakes on the counter that are
the same size. The first cake has 1⁄2 of it left.
The second cake has 5/12 left. Which cake has
more left?
Possible Solutions
Independent/Workshop
Additional Printables
• simplifying fractions
http://www.gscdn.org/l
ibrary/cms/14/13414.p
df
• comparing fractions
http://www.gscdn.org/l
ibrary/cms/92/12392.p
df
• Wiki
• TenMarks
Tuesday, May 6, 2014
POTD
1. There are 912 senior citizens taking a tour of the
National Denture Museum in Oldtown, USA. If 16
people can go on a tour at a time, what is the
minimum amount of tours needed so everyone
can tour the museum?
2. Val had 28 blow pops. She gave 7 of them to her
best friend. What fraction did she give to her
friend? (reduce your answer)
Homework
Review
4.NF.3
Addition/Subtraction of Fractions
Improper to Mixed
Decomposing Fractions
Decomposing Fractions
• 2/3 = 1/3 + 1/3
• 5/6 = 1/6+ 1/6 + 1/6 + 1/6 + 16
• ¾ = 2/4 + ¼
• How could you decompose these fractions?
• 5/7
• 4/10
Decomposition can help with
conversion of Improper to Mixed
Numbers
• Improper Fractions- have numerators that are the
same or larger than the denominator
• Examples: 5/5, 6/5, 13/10, 11/3
• Mixed numbers: whole numbers and fractions
written side by side
• Examples: 1 ½, 3 3/8, 18 7/10
• How could you use decomposition to convert
14/6 to a mixed number?
• How could you use the number line to convert
14/6 to a mixed number?
• Use a number line to find an improper fraction
that is equivalent to 1 7/8.
Use division/multiplication to solve!
• Convert to improper fractions:
– 1¾
– 6 7/8
– 23 1/4
• Convert to mixed numbers:
– 56/8
– 34/3
– 687/3
• Similarly, converting an improper fraction to a
mixed number is a matter of decomposing the
fraction into a sum of a whole number and a
number less than 1. Students can draw on
their knowledge from third grade of whole
numbers as fractions. Example, knowing that 1
= 3/3, they see:
• Susan and Maria need 8 3/8 feet of ribbon to
package gift baskets. Susan has 3 1/8 feet of
ribbon and Maria has 5 3/8 feet of ribbon.
How much ribbon do they have altogether?
Will it be enough to complete the project?
Explain why or why not.
• Trevor has 4 1/8 pizzas left over from his
soccer party. After giving some pizza to his
friend, he has 2 4/8 of a pizza left. How much
pizza did Trevor give to his friend?
• Possible solution: Trevor had 4 1/8 pizzas to
start. This is 33/8 of a pizza. The x’s show the
pizza he has left which is 2 4/8 pizzas or 20/8
pizzas. The shaded rectangles without the x’s
are the pizza he gave to his friend which is
13/8 or 1 5/8 pizzas.
3 3 +2 1
4
4
Possible Explanations
• 3 + 2 = 5 and 3⁄4 + 1⁄4 = 1 so 5+ 1 = 6
• 3 3⁄4+2=5 3⁄4 so 5 3⁄4+1⁄4=6
• 3 3⁄4=15/4and 21⁄4=9/4 so 15/4+9/4=24/4=6
17/6- 5/6
• A cake recipe calls for you to use 3⁄4 cup of
milk, 1⁄4 cup of oil, and 2/4 cup of water. How
much liquid was needed to make the cake?
• 1 1⁄4 - 3⁄4 =
• 4/4 + 1⁄4 =
• 5/4 – 3⁄4 =
• Mary and Lacey decide to share a pizza. Mary
ate 3/6 and Lacey ate 2/6 of the pizza. How
much of the pizza did the girls eat together?
Jimmy is mixing a recipe that calls for ¾ of
a cup of sugar. If Jimmy already put ¼ of a
cup of sugar in the bowl, how much more
sugar does he need for the recipe?
Independent/Workshop
Additional Printables
• adding and subtracting
fractions
http://www.commoncore
sheets.com/Math/Fractio
ns/Word%20Problems%2
0Same%20Denom/1.pdf
• Subtracting fractions
http://www.gscdn.org/lib
rary/cms/12/13612.pdf
• adding fractions
http://www.gscdn.org/lib
rary/cms/09/13609.pdf
• Wiki
• TenMarks
Wednesday, May 7, 2014
POTD
1. Seth was training for a marathon in the spring and trained
for 3 days each week. This week, he ran 8 miles on
Monday, 12 1/5 miles on Tuesday, and 6 ¾ miles on
Wednesday. How many miles did Seth run this week?
2. At the grocery store, Mrs. Talton bought 3 kinds of meat.
She bought ¼ a pound of turkey, 1 ¾ pounds of beef, and
4/5 a pound of ham. What best describes the amount of
meat Mrs. Talton bought?
A. Less than 2 pounds
B. More than 3 pounds
C. Exactly three pounds
D. Between two pounds and three pounds
Homework Review
4.NF.4
Multiplying Fractions
• 3/6 = 1/6 + 1/6 + 1/6 = 3 x (1/6)
• Students should see a fraction as the
numerator times the unit fraction with the
same denominator.
• This standard extended the idea of
multiplication as repeated addition. For
example, 3 x (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 6 x
(1/5).
• Students are expected to use and create visual
fraction models to multiply a whole number by
a fraction.
• The same thinking, based on the analogy
between fractions and whole numbers, allows
students to give meaning to the product of
whole number and a fraction.
Use a visual model to solve!
• In a relay race, each runner runs 1⁄2 of a lap. If
there are 4 team members how long is the
race?
Possible Solutions
Heather bought 12 plums and ate 1/3 of them.
Paul bought 12 plums and ate 1/4 of them. Which
statement is true?
• Draw a model to explain your reasoning.
a. Heather and Paul ate the same number of plums.
b. Heather ate 4 plums and Paul ate 3 plums.
c. Heather ate 3 plums and Paul ate 4 plums.
d. Heather had 9 plums remaining.
3 x (2/5) = 6 x (1/5) = 6/5
• If each person at a party eats 3/8 of a pound
of roast beef, and there are 5 people at the
party, how many pounds of roast beef are
needed? Between what two whole numbers
does your answer lie?
Solution!
• If a bucket holds 2 3/4 gallons and 43 buckets
of water fill a tank, how much does the tank
hold?
• Kevin is making 7 centerpieces for a party. In
each centerpiece, 1/3 of an ounce of flower
food is used. How many ounces of flower food
are used in the 7 center pieces?
• Sarah is filling 6 vases with water. Each vase
will get 5/6 of a liter of water. How many
liters of water will be in the 6 vases?
Independent/Workshop
Additional Printables
• mixed to improper
http://www.gscdn.org/library/cms/1
7/13417.pdf
• Fractions of a number
http://www.gscdn.org/library/cms/6
3/13663.pdf
• Multiplying fractions by a whole
number word problems
http://www.commoncoresheets.com
/Math/Fractions/Multiplying%20Frac
tions%20%28Word%29/1.pdf
• multiplying fractions word problems
http://nolletti.weebly.com/uploads/8
/7/0/3/8703549/multiplying_fraction
s_by_whole_numbers.pdf
•
•
Wiki
TenMarks
Thursday, May 8, 2014
POTD
1. Solve for M
2 x8=M
3
A) 16
24
B)
2
16
C) 5 1
3
D) 5 2
3
2. Amanda and Jenny went jogging. Jenny ran 3/5 of a mile, but Amanda ran
a greater distance. What is one possibility of Amanda’s running distance?
A) 1
B) 5
C) 1
D) 6
3
8
2
10
Homework Review
4.NF.6 and 7
Decimals
• A decimal is used to represent a part of a
whole. Decimal models are used to represent
decimals in picture form.
Converting Fractions to Decimals
Converting Fractions to a Decimal:
• To convert a decimal to a fraction…
– take the place value farthest to the right of the
decimal and make it the denominator
– next remove the decimal point from the number
and make it the numerator
– finally, simplify the fraction to lowest terms.
• 0.6 = 6/10 = 3/5
• 0.25= 25/100 = 1/4
Comparing Decimals
• "less than", "greater than", and "equal to"
• If one value is smaller than another value, it is said to be
less than (<).
• Two is less than three, or 2 < 3.
• If one value is larger than another value, it is said to be
greater than (>).
• Three is greater than two, or 3 > 2.
• If one value is equal to another value, it is said to be equal
to (=).
• Three is equal to three, or 3 = 3.
• To compare two numbers, follow these steps.
1. Line up, by place value, the numbers being
compared.
2. Compare the place value for each digit
starting from the left.
3. Find the first difference. The number with the
largest digit is the largest number.
Example
• Compare the numbers 57.56 and 57.52.
Solution
• Line up the decimal points, and compare the
place value for each digit starting from left to
right to find the first difference.
• 57.56 57.52
• The first difference is in the hundredths
place. Since 2 is less than 6, the number
57.52 is less than the number 57.56.
Compare these two models.
Independent/Workshop
Additional Printables
converting fractions and
decimals
http://www.gscdn.org/l
ibrary/cms/02/11502.p
df
• Wiki
• TenMarks
Friday, May 9, 2014
POTD
1. The Monster Truck Rally at the Civic Center had an
attendance of 39,219 people last year. This year, the
attendance was 3,102 less than last year. What is the
combined total of the Monster Truck Rally’s attendance
rounded to the nearest hundred?
2. Which choice is equal to 2.4?
A) 4
10
B) 1 4
10
C) 40
10
D) 24
10
Homework
Review
Quiz Time 