TEXT DEPENDENT QUESTIONS TO CONSIDER FOR UNIT 4
Compare, inequality : Can you solve these inequalities without using models and by using equivalent fractions? What exactly is an inequality? What do I do with it? How does that relate to comparing fractions? Fractions are parts of a whole, so how do I determine if the fraction is bigger or smaller? What kind of models should I make? How will I make sure they are equal size? What if one of my models is not the same exact size as my other, will that affect my answer? I wonder how equivalent fractions are useful in determining the inequality. Why is it called an inequality?
MATH VOCABULARY:
Benchmark Fraction Data Denominator Difference Dividend Divisor Frequency Table Equivalent Improper Fraction Line Plot
Mixed Number Numerator Outlier Product Quotient Reciprocal Sample Scale Simplest Form Survey Sum Whole
STANDARDS OF MATHEMATICAL PRACTICE: (SMP)
Habits of Mind of a Productive Mathematical Thinker (Math Sense Making)
(1) Make sense of problems and persevere in solving them (6) Attend to precision
Reasoning and Explaining (Math Talk)
(2) Reason abstractly and quantitatively (3) Construct viable arguments and critique the reasoning of others
Modeling and Using Tools (Math Drawings)
(4) Model with mathematics (5) Use appropriate tools strategically
Seeing Structure and Generalizing (Math Structure)
(7) Look for and make use of structure (8) Look for and express regularity in repeated reasoning
HELPFUL PROCEDURES:
The LCM is used for unlike denominators. When adding fractions, it is only a portion of a whole. The bigger the denominator, the smaller the piece.
1.Find the LCM and change improper fractions to mixed numbers and vice versa. Simplify the answer.
2.Decide which order of operation to use: add or subtract, multiply or divide
3.Use models to visualize the answer
4. Reread the text multiple times to ensure you know WHAT THE QUESTION IS ASKING
5. Remember when dividing, you must use the RECIPROCAL of the SECOND fraction
December 9-10, 2015 5.NF. 3Division of Fractions
ENGAGEMENT
Are fractions always part of division?
GROUP QUESTION
Write whether the statement below is true or false. Explain your answer using words and numbers. The product of 3/5 and 6 is greater than 6.
EXIT SLIP
What is the product of ½ and ¼ ? Draw a model to represent this.
December 11-14, 20155.NF.4Extend Understandings of Multiplication and Division
ENGAGEMENT
In real life, when would it be advantageous (beneficial) for you to use fractions and then MULTIPLY them?
GROUP QUESTION:
Chicken Little was tired of being called scrawny. He was only half as tall as Chicken Middle and only a quarter as tall as Chicken Grande! Chicken Little went to Marshalls and bought lifts to place in his shoes. He could only find 2 inch lifts. What is a possible measurement of Chicken Grande? What about Chicken Medium? If Chicken Little only buys one set of lifts, what is a possible measurement for how tall he is once he places the lifts inside his shoes?
How many times taller is Chicken Grande than Chicken Little?
EXIT SLIP:
Blue:
What fraction does this number represent? Represent as a mixed number and an improper fraction. 2.13
Red:
Find the product of 5 and 5/6. Represent as a mixed number and an improper fraction.
Green:
Find the product of 2 and ¼. Simplify that using your journal notes.
December 15-16, 2015 NF. 4aMultiplication and Division of Fractions
Engagement
How would your life be impacted (affected) without fractions? (Not for school!)
GROUP QUESTION:
Three-fourths of the class are boys. Two-thirds of the boys are wearing Jordans. What fraction of the class are boys wearing Jordans?
EXIT SLIP:
Every day Tim ran 3/5 of mile. How far did he run after 6 days?
DECEMBER 17, 2015 NF 4bArea using fractions
ENGAGEMENT
What would happen if shoes didn’t come in half sizes? How would that affect your life?
GROUP QUESTION:
Thor and Carter are running for President and Vice President of the United States.They decided to make campaign posters. Carter created a square-shaped poster. The length and width of his poster is 3½ feet each.
Use the grid below to draw and shade Carter’s poster.
1 square foot
EXIT SLIP:
What is the area of her poster in square feet?
December 18, 20155.NF.5Interpret Multiplication Resizing
ENGAGEMENT NF. 5
In what profession would someone use a scale (model) in their line of work? For what and why?
GROUP QUESTION:
Explain why this statement is true:
Scaling is a multiplicative comparison. It compares the size of a product to the size of one factor on the basis of the size of the other factor. Example: 12 = 3 x 4 so 12 is 3 times as many as 4 and 4 times as many as 3.
EXIT SLIP:
If four is multiplied by a fraction greater than one, which of the following is true or false about the product?
TF
The product is greater than four. ______
The product is less than four. ______
The product is equal to four. ______
The product is always equal to one.______
December 21-22, 2015 5.NF.5aCompare Fractions by Estimation
ENGAGEMENT
When have you multiplied fractions (not in school!) in real life?
GROUP QUESTION:
Ms. Evans teaches in a room that is 60 feet wide and 40 feet long. Mr. Hentz teaches in a room that is half as wide, but has the same length. How do the dimensions and area of Mr. Hentz’s classroom compare to Ms. Evans? Draw a picture to prove your answer.
EXIT SLIP:
Is the product of ¾ and 7 greater or smaller than 7? Show your work to prove your answer.
Jan. 4-5, 20165.NF. 5bMultiply Fractions
ENGAGEMENT
Why would someone use improper fractions to multiply instead of mixed numbers?
GROUP QUESTION:
Thor and Carter are planting two tomato beds. The first tomato bed is 5 meters long and 6/5 meters wide. The second tomato bed is 5 meters long and 5/6 meters wide. How do the areas of these two tomato beds compare? Is the value of the area larger or smaller than 5 square meters? Draw pictures to prove your answer.
EXIT SLIP:
The shaded part of the square below has a length of ¾ foot and a width of ½ foot.
I------1 foot------I (The height is also 1 foot)
What is the area, in square feet, of the shaded part of the square?
January 6-7, 20165.NF. 6Multiply Mixed Numbers
ENGAGEMENT
When would we use mixed numbers to multiply in real life and WHY?
GROUP QUESTION:
There are 2 ½ bus loads of students standing in the parking lot. The students are getting ready to go on a field trip to the Owens Science Center. 2/5 of the students on each bus are girls. How many busses would it take to carry only the girls? (Draw a model)
EXIT SLIP:
Which of the following equations is modeled by the figure below?
SHOW YOUR WORK BELOW:
Yes No
4 x 5/1 = 5/4 ______
1/5 x 4= 4/20 ______
4 x 1/5= 4/5 ______
4 x 5/1= 20/4 ______
SHOW YOUR WORK HERE:
ENGAGEMENT (January 8, 2016) 5.NF. 7Division of Fractions
When would you divide a fraction in real life, and when would you multiply a fraction in real life? (NOT MATH CLASS!!) How do the numbers increase and decrease?
GROUP QUESTION (SMP: MP 4)
Carter loves hamsters. His hamsters ate 4/5 of food from a bag. The remaining food is split equally between the three hamsters. (SHOW YOUR WORK!!!!)
Which model below represents the part EACH hamster received?
A.
I I I I / I I I I / I I I IB
I I / I I / I I / I I / I IC
I I I I / I I I I / I I I ID
I IEXIT SLIP (SMP: MP 1, MP 6)
Which expression represents the part each hamster received?
- 1 divided by 3 True______False______
- 1/5 divided by 3 True______False______
- 4/5 divided by 5 True______False______
- 1/3 divided by 1/5 True______False______
January 11, 20165.NF. 7a
ENGAGEMENT
Think about a time when you multiplied and divided fractions at home. When did the answer get larger and when did it get smaller? Why?
GROUP QUESTION (SMP: MP 4, MP 5)
Multiplication ‘undoes’ division. Which relationship below shows the INVERSE (opposite) operation in explaining how to get the quotient?
4÷ (1/5)= 20 because 20 x (1/5)= 4
6÷ (1/3)= 18 because 18 x (1/3) = 1/18
3÷ (1/2)= 3/2 because 3/2 x (1/2)= 3
2÷ (1/4)= 1/8 because 1/8 x (1/4)= 2
EXIT SLIP (SMP: MP 4)
Give the inverse equation for:
7÷ (1/4) =______because ______x (___/______)=______
January 12, 20165.NF.7bDivision of whole numbers by fractions
ENGAGEMENT
Can you turn any object into a fraction? How and why?
GROUP QUESTION (SMP: MP 4, MP 7)
Thor wants to make a bowl of rice to have with his dinner. A bowl holds 4 cups of rice. If he uses a measuring cup that holds 1/8 of a cup, how many times will he need to fill the measuring cup in order to fill the entire bowl? Use a visual fraction model to explain your answer.
EXIT SLIP (SMP: MP 2)
Use multiplication to explain why your answer in the above question is reasonable.
January 13, 2016 5.NF. 7cReal World Fraction Problems
ENGAGEMENT
How have you multiplied and divided something in real life at home? When and why?
GROUP QUESTION (SMP: MP 4, MP 7)
Thor and Carter are going on a shopping outing at PetCo. They plan to be there all day. They bring a container that holds 1½ of a gallon of water. If they share the water equally, what fraction will Thor get and what fraction will Carter get?
EXIT SLIP (SMP: MP 4, MP 7)
Carter gets excited and trips. Thor drops the jug of water and 1/4 spills out. How much water will they both get now? (Thor is super mad at Carter and decides to spank him. Carter starts to cry, so Thor apologizes by buying him a taco.)
January 14-15, 20165.NBT. 7Decimals
ENGAGEMENT
When do you use decimals in real life (BESIDES money)?
GROUP QUESTION
Thor, Carter, Simon, and Soldier (the American Bulldog from next door) went to PetsMart to buy Ms. Evans a gift. They each spent $19.85. How much did they spend altogether?
EXIT SLIP
Thor and Carter decide to go play golf. Simon isn’t going because he needs to take a bath. Thor and Carter meet up with 26 other friends. If there are 172 golf balls, how many will each friend (including Thor and Carter) get? Between what two whole numbers will they lie?
TASK PERFORMANCE 5.NF. 3 DIVISION WITH MODELS AND FRACTIONS
Thor purchased a cake for Christmas dessert. Thor and Carter shared equally one-third of the cake. The remainder was left for Simon, Mom, Dad, and brother Hunter to share equally.
Draw a model to represent the amount of cake that Carter and Thor shared. Write an equation to represent the amount shared.
What fraction represents the portion of cake that Simon ate? Explain your thinking using numbers, words, and or models.
Carter said that he received less cake than Simon. Do you agree with Carter? Why or why not. Explain using words, numbers, and or models.
HOMEWORKDECEMBER 9, 20155.NF.3
GREEN, RED, BLUE:
Little Hugo and Little Teacora decide to go have some fun at the Country Club. They see that 25 Seniors (like Grandma and Grandpa) will be sharing 200 golf balls equally. Little Hugo and Little Teacora decide to grab handfuls of golf balls and throw them into the pond. They manage to toss 33 golf balls before security chases them off the grounds. How many golf balls will the Grandmas and Grandpas each get now? Between what two whole numbers will the number lie?
RED, BLUE
Little Delany and Little LG feel bad for the Grandmas and Grandpas so they dive head first into the pond to retrieve the golf balls. They can only find 17 of the golf balls and that dirty boot that keeps showing up everywhere the fifth graders go. How many will each Grandma and Grandpa get now? Between what two whole numbers will they lie?
BLUE:
Little Rico and Little Jenny did not like these antics one bit. They hailed a cab and went to target to buy more golf balls for the Grandmas and Grandpas. They scraped together enough money to buy 1/5 of the original amount of golf balls. They called Little Pierce to come pick them up and drive them to the country club. Little Pierce showed up riding a donkey with a sled attached to it and took them to where they needed to go. Little Rico and Little Jenny threw the new golfs into the pile with the remaining golf balls, wet golf balls, and dirty boot. Now how many do each Grandma and Grandpa get? Between what two numbers will the answer lie?
HOMEWORKDECEMBER 10, 2015 5.NF.3
GREEN, RED, BLUE
Little Rosie and Little Amman went to Giant to buy a sheet cake to celebrate Flag day. (After all, who doesn’t love flags?) The girls left the remaining for Mrs. Murphy her three kids. Draw a model to represent the amount of sheet cake the two girls shared. Write an equation to represent the amount they shared.
RED, BLUE
Little Bryan and Little Dejanae snuck into the kitchen to eat some cake. They grabbed two pieces before an attack pug came out of the laundry and chased them away. Now divide the remaining cake into enough pieces for Mrs. Murphy and her three kids. How much of the original cake was left?
BLUE
Little Pinkie and Little Sunshine felt bad that the cake was ruined. They purchased a cake the same size and shape as the first one and divided it into enough pieces to feed Mrs. Murphy and her 3 kids, as well as themselves (after all they did but another cake!) What is the mixed number that represents the cakes in a fraction and a decimal?
Homework December 11, 20155.NF. 3
GREEN, RED, BLUE (You’ll need yesterday’s homework to answer this question)
Little Jalen and Little CC want in on this cake action. But first they must answer some fraction problems regarding the cake. What fraction represents the portion of cake that Mrs. Murphy ate? Explain using words, numbers, and models. Little Bryan said she received less cake than Mrs. Murphy. Do you agree with Little Bryan, why or why not? Explain.
RED, BLUE
Little Daniel Hernandez snuck in and grabbed the cake. He measured the size of the pieces and then put 8 more pieces of fruit cake with the regular cake remaining. What is the mixed number and the whole number with a decimal?
BLUE
Little Malik and Little Douglas HATE fruit cake. They wanted to grab the fruit cake and throw it away. They managed to get 1/3 of the fruit cake and toss it. What is the fraction now (in a mixed number and a decimal)?
HOMEWORK NF. 4 DECEMBER 14, 2016
GREEN, RED, BLUE:
What is the product of ½ AND ¼ ? Draw a model to represent it. Now multiply by 2 and ¼ . What is the product? Draw another model.
RED, BLUE
Little Markel got mad and scribbled on the model above. But he only got half way through scribbling on the ½ when Little Zakiya snatched the crayon from his hand. What is the product now?
BLUE:
Little Daniel G thought he’d be super funny and he cut the model of 2 wholes into 24 pieces. Then he threw away ¾ of those pieces. When Little Churacame back she FLIPPED out. Little Daniel dug through the trash (yuck) but could only find ½ of those ¾ pieces he tossed. How many did he actually find? What if he found the product of what he found and ¼? What is that answer?
HOMEWORK NF. 4 DECEMBER 15, 2015
GREEN, RED, BLUE
Little Pedro wants to make flan, his favorite dessert. He uses 1 ¼ cups of milk to make 1 flan. What is the total amount of milk Little Pedro needs to make 6 flans? (He loves them!)
RED, BLUE
Little Jaiden got distracted by the shiny lights and dumped twice as much milk into the first flan. OOPs! How much did she pour in? What about dumping in twice as much sugar if it is 2/3 cup for one flan?
BLUE:
Little Nicolas was irritated by the mistake, he takes cooking seriously. He decided to multiply every ingredient by 2. But now, how does that affect his ability to make 6 flans? He has twice as much milk now for the first one, what should he multiply that by now to make 6 flans? Why? What about sugar? How much total sugar for 6 flans? What if he wants to make 9 flans? How much sugar and milk?
HOMEWORK NF. 4a DECEMBER 16, 2015
GREEN, RED, BLUE
If Little Payton multiplies three by a fraction greater than one, which of the following is true or false about the product?
TF
The product is greater than three. ______
The product is less than three.______
The product is equal to three.______
The product is always equal to one.______
RED, BLUE:
Little Faith decides to use cupcakes to model the above problem. Draw a model for each statement.
BLUE:
Little Markie is in a feisty mood, so he eats half of each cupcake that Little Faith put out to model the statements. Now what is the answer to each statement?
HOMEWORK NF. 4b DECEMBER 17, 2015
GREEN, RED, BLUE
Little Nevaeh decided to draw during The Voice because she didn’t like the contestant. This is what she drew.
The shaded part of the square below has a length of ¾ foot and a width of ½ foot.