Looking into the future...triangles!

On the half sheet of paper, mark three dots in the shape of an equilateral triangle. 

Presentations!

At 2:45 pm, presentations will begin. Please make sure your presentation includes the following:

• Your team name
• A slogan that describes what your team is all about.
• The data that you used in your project.
• A general overview of the data.
• Answers to the "guest" questions. Your answers should include:
• your recommendation.
• How you decided upon your recommendation.
• Why you believe you are providing the best selection.

There will be an assessment on Friday that covers prime factorization, LCM/GCF and the measures of center that we have been using: mode, median and mean + range.

Caffeine Project Update

The information that you have worked up so far has already helped clients choose which drinks they plan on using in upcoming races. Based upon the information that was posted last week, a few questions have come up and it would be great if you could find time today to answer the following:

1. My brother always wants to be up to date with the latest trends. He stood in line for the latest i-phone and he’ll go watch Twilight because everyone else is (he’s not even a vampire). He wants to know what drink to buy if he is to get the typical or most common amount of caffeine. Could you help him out?
2. One of my best friends never pays attention to research, labels or, well anything! I’m trying to get him to slow down and pay attention because it would really help. At the moment he just grabs whatever is the closest drink. What amounts of caffeine could he possibly be putting into his body?
3. Wow! What has happened to drinks these days. I asked my dear Aunt Sally to pick me up a drink before my race the other day. I told her to just get a middle-of-the-road drink. You know, nothing too strong, nothing too weak. She’s really nice and came back with a tall coffee from Starbucks. Talk about the prerace jitters! Was this really a middle-of-the-road caffeine drink? Please let me know.

Those are the latest questions. Based on how well you’ve worked so far, I really hope you can put some presentation together by the end of the day that shows the data you’ve worked up and the answer to these questions.

Is there anything else that your group wants to add? Please do so. Eventually we have to give the job to one group.

Sincerely,

Mr. Big Swig
Project Manager

Working up data

Running Turtles

Cuttlefish

Power Up

Caffeine!

What do you notice?

Poster Source: CoolInfographics

Expert Teams: Endurance Athlete! The fastest, long distant racers are coming to you for advice. 

• What are you going to tell them?
• What supporting evidence will you provide?
• How will you show them your information?

Breaking Numbers Down

Players take turns breaking down a number by multiplication. 

• The first player starts with a whole number. 
• The next player makes a string of two numbers that multiply to give the first. 
• The next player then can break down one of the two numbers, making a three number string. 
• The last player who can break it down is the loser of the game. 
• Numbers chosen must be able to be broken down more than twice. 
• A player may challenge if they disagree with a breakdown, or if they say it's the end but it's not. 
• Players may not reuse starting numbers. 1 may not be used in the breakdown. You can't use a number that's been used this session.
• As you play, what patterns do you notice?

Homework

• PW 34 (1-15)
• PW 35 (1-11)

Division & Measurement

Objectives:

• I will use models to represent division of fractions.
• I will combine measurement skills and fraction division to solve problems.

November Process Words:

• Adapt
• Verify

Opening: Please create a visual model that describes this problem and its solution.
I have 3/4 of a whole cake. I want to divide it equally into 2 containers. How much cake will be in each container?

Group work / explanation (Review of last night’s HW)

Groups of 4 will solve the problem and explain to the class.

1. I have 1/2 of a cake. It fills up exactly 3/4 of my container.
    a. How much cake will fit in 1/4 of the container?
    b. How much cake will fit in 1 whole container?

2. I have 3/4 of a cake. It fills up exactly 2/3 of my container.
    a. How much cake will fit in 1/3 of the container?
    b. How much cake will fit in 1 whole container?


Measurement & Dividing:
Please complete each in your notebook. Make sure to draw a sketch and to show the work of your group’s problem solving.

1. If a lincoln is the width of Lincoln Way, how many lincolns are there between the science building light pole and the MPR bottom floor light pole?

2. How many lincolns are there in one large concrete block?

3. How many lincolns are there in a half of a large concrete block?

4. How many lincolns are there in one-third of a large concrete block?

5. If the distance between science building light-poles is 3/4 of your trip, where will you be at the end of your journey?

Assessment on Friday - Please complete PW51

Fractions: Explaining the operations

I hope you had a great weekend!

Objectives:

• I will use models to represent division of fractions.
• I will summarize the four basic operations with fractions.

Language

• I will create visuals with explanations that describe a mathematical concept.

November Process Words

• Adapt
• Verify

Opening: With a partner (selected by the magic cards!), please create a model using construction paper that shows the following problems (one model / problem):

1. A serving is 3/4 of a Snickers bar, how many servings can be made from 1/2 bar.

2. If a serving is 5/8 of a bar, how many servings can be made from 1/2 of a Snicker's bar.

Please create a model (sketch) in your notebook to show

1. I have 3 whole cakes. They fill up exactly 2/3 of my container.
     a. How much cake will fit in 1/3 of my container?
     b. How much cake will fit in 1 whole container?

2. I have 1/2 of a cake. it fills up exactly 3/4 of my container.
     a. How much cake will fit in 1/4 of the container?
     b. How much cake will fit in 1 whole container?

3. I have 3/4 of a cake. it fills up exactly 2/3 of my container.
     a. How much cake will fit in 1/3 of the container?
     b. How much cake will fit in 1 whole container?


4. 2/5 of a room can be painted in 3/4 of an hour. How much can be painted in 1 hour?

Dividing Fractions

Opening: Last class was spent reviewing the idea behind common denominators. Today, we will begin with a short assessment on this topic.

Objectives:

• I will use models to represent division of fractions.
• Return to estimation - what skills am I using when estimating?

Estimating: How many sheets of toilet paper are on the roll?


Two Scenarios - whiteboard it!
A) Sally has 12 marbles and she wants to give 3 to each friend. To how many friends can she give her marbles?


b) Sally has 12 marbles and she wants to distribute them among three friends. How many marbles will she give to each friend?


To do:

1. Draw a diagram that shows each scenario.
2. What do the two scenarios have in common?
3. What is different about the two scenarios?

Serving Size

Student-initiated Assessment Sign-Up

Please complete this form to schedule an assessment. As you go through the form, it is important to read the "help text" below each question. The "help text" shows up in grey and provides more information about the question.

If you have any suggestions on how to improve the form, please let me know. Thanks!

Student-initiated Assessment Sign-Up

Working with fractions

Some problems for today...


1. How does subtracting 1/3 from 2/5 compare with subtracting 1/10 from 2/5? Which set of fractions will produce a larger difference? Explain your answer.

2. Will adding 4/7 and 3/8 result in a number that is closest to 0, 1, or 2? Explain your answer.

Where are the common denominators in these problems? Are they necessary?

3. Find 2/3 of 7/8. Will the answer be 7/8, less than 7/8, or more than 7/8? Explain your answer. What does it mean to find “2/3 of” some amount? What operation is implied?


Directions: Describe the operation the problem is suggesting, estimate a solution, and explain how you know it is reasonable. Use a model or diagram to find the exact answer.



1. You have a 2 1/3 pound bag of bird seed. Your bird feeder holds 5/6 pound of bird seed. How many
times can you fill your bird feeder from the bag of bird seed?

2. If I I had 2 1/2 pizzas, and I ate a third of that, how much would I have eaten? How much would be left?

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

Four quadrants

By the end of class, I should be able to:

• Identify the four quadrants of a graph.
• Plot points in the four quadrants.

Language Goals:

• Use complete sentences to describe the meaning of the following terms:
• absolute value
• coordinate pair
• opposites (in respect to numbers)

September Process Words

• Investigate
• Produce

Opening: Group task - Prepare a number line from -10 to 10 using scrap paper

Moving to four quadrants on a graph

You sunk my battleship!

Review of Percents

September 19 - Reviewing Percents

In pairs, we will work through a series of problems to review percents. Please draw out your ideas. We will have a final assessment on Thursday that covers ratios and percents.
Skills practice: PW16

Working with Percents

Opening video:

Video clip from Father of the Bride

*What does Steve Martin want?
*How would the cashier do this (if Steve was not put into jail)?
*What could Steve have done instead?

Strips from last class:
20% strip - ratio of 100:20:80 relates to 5:1:4 (What is the relationship described?)

Questions:
1. During a sale, prices were marked down by 20%. The sale price of an item was $84. What was the original price of the item before the discount?


2. A shop increased its workforce by 25%. If 240 workers were working after the increase, how many worked there originally.

Gridding Percents