Using games to estimate and multiply fractions

Opening Estimations! It’s Halloween and Halloween means candy corn!

Objectives:

• I will use games to practice multiplication of fractions.

October Process Words

• Evaluate
• Represent

Estimating Fraction Multiplying

Game - 2 players
1. Each player rolls a pair of dice
2. Using the dice, form fractions (big die represents denominator)
3. Player A estimates the product using benchmarks fractions (0, 1/4, 2/4, 3/4, 4/4, 5/4...)
4. Each player works out the multiplication to see if the estimation was the closest.
5. If estimation is to the closest benchmark, Player A gets a point
6. Player B repeats
7. Play to 10

Fraction Product Game

1. Player 1 puts a marker on a number in the factor list. No space on the product grid fills in with Player 1's color because only one factor has been marked; it takes two factors to make a product.

2. Player 2 puts the other marker on any number in the factor list (including the same number marked by Player 1). The space on the product grid containing the product of the two factors marked is colored in with Player 2's color.

3. Player 1 moves either one of the markers to another number and the new product is filled in with Player 1's color.

4. Each player, in turn, moves a marker and the space with the product is marked with the proper color. If a product is already colored, the player does not get a mark for that turn. The winner is the first player to mark four spaces in a row -- up and down, across, or diagonally.

Game borrowed from Math Hombre

We will have a multiplication assessment on Friday. Review problems - PW47 and 48.

Multiplying Fractions

Objectives:

• I will use models to represent multiplication of fractions.

Language objectives:

• I will create scenarios that can be used to practice fraction multiplication.

October Process Words

• Evaluate
• Represent

Melinda had a birthday yesterday. A quarter (1/4) of the birthday cake remained. This morning, Melinda ate 1/3 of the remaining quarter cake. What fraction of the whole cake did Melinda eat this morning?

Using a whiteboard, please do the following:

• Create a model that shows a result to this question.
• Be prepared to present your model to the class.

Betsy’s mom is sewing a quilt that is 8 feet long and 6 feet wide. Betsy wants to work on the quilt, too. Her mom asked her to sew a rectangular piece of the quilt with length ¼ of the length of the quilt and width ½ of the width of the quilt. What fraction of the area of the whole rectangular quilt will Betsy sew?

Using a whiteboard, please do the following:

• Create a model that shows a result to this question.
• Be prepared to present your model to the class.

Potatoes! Boil’em, Mash’em, Stick em in a stew

Things are _______ (awful, bad, okay, good, great) because you have potatoes!  

Create a model to justify each answer.  Write an equation or number sentence for each story, if you can.

Find how many pounds of potatoes you have if you search the cupboards and find…
1)  1/2 a bag of potatoes, which started with 2 pounds of potatoes.

2)  1/2 a bag of potatoes, which started with 2/3 pound of potatoes.  

3)  3/4 a bag of potatoes, which started with 2/3 pound of potatoes.  

4)  1 ½ bags of potatoes, which each started with 2/3 pound of potatoes.

5)  1 ½ bags of potatoes, which each started with 3/4 pound of potatoes.

6)  4 bags of potatoes, which each started with 1 1/3 pound of potatoes.

7)  2 2/3  bags of potatoes, which each started with 3 ¼ pound of potatoes.

8)  ____ bags of potatoes, which each started with ____ pounds of potatoes.
(You make the problem!)

Review: Adding and Subtracting Fractions

Opening Estimations! How many tissues are in a package? How many tissues are in the box?

Objectives:

• I will review my understanding of adding and subtracting fractions.
• I will use benchmarks to order fractions.

Language objectives:

• I will compare fractions and operations using fractions with sentences.

October Process Words

• Evaluate
• Represent

Using Benchmarks, order fractions on a number line

Our unit will focus on dividing fractions, but I want to make sure that everyone has a good understanding of adding and subtracting fractions. A short pre-assessment will be given today to see where we are as a class on this topic.

Please complete for next class...

1. Compare ⅕ with ⅓. Which fraction is larger? Explain your answer.
2. Compare ⅖ with ⅓. Which fraction is larger? Explain your answer.
3. Will adding 4/7 and ⅜ result in a number that is closest to 0, 1 or 2? Explain your answer.
4. How does adding ⅔  to 1/10 compare with adding ⅜ to ⅘? Which set of fractions will produce a larger sum? Explain.
5. How does subtracting ⅓ from ⅖ compare with subtracting 1/10 from ⅖? Which set of fractions will produce a larger difference? Explain.

Positives and Negatives in the Physical World (cont)

Thanks again for a great class on Monday. I really appreciate the way that each person is respectful of other ideas and ways to do math. Today, we are going to continue where we left off last class. Some of you wrote thoughtful exit note questions that I want us to spend some time thinking about.

Objectives:

• I can use positive and negative numbers to represent quantities in real-world scenarios, and explain the meaning of 0 in each situation.

Language objectives:

• I can explain my mathematical process using words and sentences.  

October Process Words

• Evaluate
• Represent

Opening: Estimation - Day 3

Vocabulary Inventory - Last night you looked over this inventory. What terms are unfamiliar to you?


Exit Note questions to activities
1) How do I "turn" 100 into -100 ?
  Great Question - Come up with a solution, a diagram that illustrates your solution and write the process that you would recommend to someone to do your solution.

2) Is there such a thing as negative zero? and Do negative numbers go on forever like positive numbers?

3) Who found out positive and negative numbers?

4) How is/are negative numbers useful in normal life, not rocket science?


Creating real world contexts for positive and negative quantities

• Groups of 4
• On a whiteboard, create two different real-world scenarios for positive and negative quantities.
• Explain the meaning of 0 in each scenario

Exit Note
Think back to the scenarios that you created to represent positive and negative integers.

• Briefly describe the scenario.
• Pick a pair of opposite numbers.
• What are the numbers?
• What do the numbers mean in this scenario?
• How are the absolute values of these two numbers related?
• What is meant by the absolute value in this scenario?

Assessment on Friday

Estimations

Welcome back to class after a long break. I hope that each of you are refreshed and ready for the second quarter.

Objectives:

• I can estimate values and support my estimation.
• I can define vocabulary that has been discussed in this unit.
• I can use positive and negative numbers to represent quantities in real-world scenarios, and explain the meaning of 0 in each situation.

Language objectives:

• I can discuss my thoughts regarding math activities.  

October Process Words

• Evaluate
• Represent

*	Getting into the Fishbowl & Estimating What does a fishbowl meant to you? What is life like when you are “in” the fishbowl? What is your relationship to the fishbowl when you are outside of it?

Expectations if I am “inside the fishbowl”

1. Focus on the math and what you are thinking.
2. Talk
3. Ignore those hanging outside of the bowl.

Expectations if I am “outside the fishbowl”

1. Focus on the process of doing math
2. Pay attention to the whole activity but pay special attention to one person.
3. Listen and observe

Vocabulary Inventory - Over the last few classes, we have used several words. What do these words mean to you?

Discuss past assessments & input data on Tracking Sheet

Creating real world contexts for positive and negative quantities

• Groups of 4
• On a whiteboard, creating two different real-world contexts for positive and negative quantities
• Explain the meaning of 0 in each scenario

Exit Note

• What is one thing that you enjoyed about the fishbowl activity?
• What is one thing that you learned about the action of doing math that you observed during the fishbowl activity?
• What is one question that you have about positive and negative numbers?

Battleship & Decimal Point Pickle

Everyone is doing a good job working with the coordinate grid, four quadrants and positioning numbers according to values. As we go into a long weekend for you, let's take some time and practice.

Opening - Battleship! You brought in a a grid a few days ago and know the rules. Today, there is a grid limitation. All boats must be in a grid that covers -8 to 8 in both the horizontal and vertical directions.

Please remember the boat lengths:

• Submarine - 2 coordinate pairs
• Destroyer - 3 coordinate pairs
• Battleship - 4 coordinate pairs
• Aircraft Carrier - 5 coordinate pairs

Time limit for set-up: 15 minutes 

• This means that your grid is set up with the appropriate scale (-8 to 8)
• All four boats positioned
• A table containing the coordinate pairs is created.

Checking - find the person that you played battleship with last time. Swap papers. Each person should check to make sure that the other person correctly plotted the location of each boat.

Game on!

Decimal Point Pickle is the great game we played last week.  Today, you will play 2 vs 2. This means that you have a partner. Play with someone other than your battleship partner and checker. If you finish a game with time, find another pair and play. If everyone still has time, join two groups and play 4 vs 4. (You can play on the whiteboards)

In case you forgot the rules:

Set Up:
1.    2 or more teams or players.
2.    Get a deck of cards and remove the Kings, Queens, 10s and Jokers.  Jacks stay in.
3.    Each player or team makes a path with 10 spaces.  It can be straight and rectangles, or it can be curvy and circles, but it needs to have 10 spaces and a clear beginning and end.
4.    Shuffle the cards.

Playing:  Idea is that you’re going to fill in your path from small to big, flipping over cards to get possibilities.
1.    On your turn, flip over a card.  If it’s red, flip over another card.  If it’s red, flip over another card.  But you never flip more than three.  If you run out of cards, shuffle up the used cards.
2.    Arrange those cards to make a decimal number.  Jacks are the zeros. The smallest number you can make is .000, and the largest is .999.  Say your number.
3.    Fill in your decimal number somewhere on the path.  But it can’t go before a smaller number or after a bigger number.  Your path has to start small and end big.  If there’s no place to fill in your number, you don’t.  
4.    Winner is the first person to completely fill in their path, with all the numbers in order.

Examples: 
1.    J ♥, 3 ♣.  You can make .03 or .30.  
2.    5 ♥ hearts, so you flip 2 ♦, so you flip 7 ♥ hearts.  (You stop because you can’t have more than three.)  You can make one of .275, .275, .527, .572, .725 or .752.  Which you want depends on your path. 

Game Source: Math Hombre