Monday, May 5, 2014

POTD1. 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.14.NF.5

Equivalent FractionsCommon Denominators

Equivalent Fractions

• Name the same amount but have different numerators and denominators.

12= 24

12

1414

Equivalent Fraction Models

12

48

=

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. 8/12B. 4/3C. 6/8D. 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 FractionsFractions 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 2/3 2.6/8 5/6 3.1/3 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 = 2/6b. 2/3 = 1/2c. 1/2 = 4/6d. 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?

Fractions1. 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/library/cms/14/13414.pdf

• comparing fractions http://www.gscdn.org/library/cms/92/12392.pdf

• Wiki• TenMarks

Tuesday, May 6, 2014POTD

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 FractionsImproper 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:– 1 ¾– 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.commoncoresheets.com/Math/Fractions/Word%20Problems%20Same%20Denom/1.pdf

• Subtracting fractions http://www.gscdn.org/library/cms/12/13612.pdf

• adding fractions http://www.gscdn.org/library/cms/09/13609.pdf

• Wiki• TenMarks

Wednesday, May 7, 2014POTD

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 poundsB. More than 3 poundsC. Exactly three poundsD. 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/WorkshopAdditional Printables• mixed to improper

http://www.gscdn.org/library/cms/17/13417.pdf

• Fractions of a number http://www.gscdn.org/library/cms/63/13663.pdf

• Multiplying fractions by a whole number word problems http://www.commoncoresheets.com/Math/Fractions/Multiplying%20Fractions%20%28Word%29/1.pdf

• multiplying fractions word problems http://nolletti.weebly.com/uploads/8/7/0/3/8703549/multiplying_fractions_by_whole_numbers.pdf

• Wiki• TenMarks

Thursday, May 8, 2014POTD1. Solve for M 2 x 8 = M 3

A) 16 B) 2 C) 5 1 D) 5 2 24 16 3 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.

• 57.5657.52• 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 Printablesconverting fractions and

decimals http://www.gscdn.org/library/cms/02/11502.pdf

• Wiki• TenMarks

Friday, May 9, 2014

POTD1. 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 B) 1 4 C) 40 D) 24 10 10 10 10

Homework Review

Quiz Time