Last Class: Math Games!

We met all together today for our last 7th grade math classes of the year.

First students shared their homework, and we finished talking about Problem 1.3, Playing the Multiplication Game. Students decided that the game wasn't fair, because 3/4 of the time the products of 2 dice will be even, whereas only 1/4 of the time the products of 2 dice will be odd.

Then we looked at the game of chance Skunk. Students calculated the chances of rolling two ones (snake eyes!) and of rolling one one, and losing their points in the game. Then we played Skunk, and learned the new game Pico, Fermi, Bagels. Class 7B played some other math games with partners to end the session. Class notes may be downloaded here for class 7A and class 7B.

If you still have outstanding homework, I will be checking in with you to turn it in this week.

I hope everyone has a wonderful summer! Thanks for a great year in math.

Percent Error & How Fair are Games of Chance?

Today we met all together, since MaryBeth and Cory are finished for the year. Tomorrow will be the last 7th grade math class.

Students shared their homework. A number of students did not complete the Roller Coaster homework--it can be found here. If you did not finish the homework, please do it tonight and turn it in tomorrow.

Then we discussed Percent Error, and how it can help you determine how good your estimate is. We found that the closer to 0 the percent error is, the better the estimate. Errors can actually be more than 100% if your estimate was more than twice the actual number.

Students also shared their probability homework from yesterday with others who did the same homework. Then we played two games: the Two Dice Sum Game and the Multiplication Game. Both are games played with two people and a pair of dice. In both cases, we compared the experimental probability (the number of times you win out of the number of times you played) to the theoretical probability (the number of favorable outcomes to the number of total possible outcomes). We discussed the likelihood that the sums would be even or odd in the Two Dice Sum Game, and wondered about the likelihood that the products would be even or odd in the Multiplication Game, to figure out whether it was fair or not. Problem 1.3, Playing the Multiplication Game, can be found here, and class notes may be downloaded for class 7A or class 7B. We will continue working on this game tomorrow.

LARGE GROUP HOMEWORK
Ace 1.3 handout which can be downloaded here
Problems 11-12, 25-26, and 30-31

Due tomorrow, Wednesday, June 9.

SMALL GROUP HOMEWORK
Ace 1.1 handout which can be downloaded here
Problems 1-2

Due tomorrow, Wednesday, June 9.

Probability & Test Corrections

LARGE GROUP
Today students received their quizzes back from last week, and we went over corrections to the problems. Then we talked about two games of chance, Match/No Match and Red & Blue Wins! We reviewed experimental probability and theoretical probability, and making tree diagrams and ordered lists for calculating theoretical probability. Students worked on Problem 1.2, Red & Blue Wins, which you can download here, and figured out whether the game was fair, what the chances were for winning, and how much the school would earn. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
1. Please make quiz corrections in colored pencil
2. ACE 1.2 Homework: Problems 3, 21, 22 on handout, which you can download here.
3. Remember to fill out student self-assessment online here if you haven't already.

Due tomorrow, Tuesday, June 8.

SMALL GROUPS
MaryBeth met with the small groups for the last time today. Students went over their quizzes on linear relationships and made corrections. Then they discussed probability, including experimental and theoretical probability, and reviewed tree diagrams and organized lists.

SMALL GROUP HOMEWORK
Please complete Problem 1.1, which you can download here.

An online spinner that you can use to do your work is here. Click on "-1" next to the "Number of sectors" label to reduce the number of sectors to 2. Click on the light blue (cyan) sector in the spinner to change the color to yellow. Click on "spin" below the spinner to spin it.

Due tomorrow, Tuesday, June 8.

Competing Coasters: Estimation & Percent Error

We all met together today, since Cory is no longer working with small groups. And today we had short classes so that we could go to the Upper El Gold Rush performance. Because the performance went long, the 7B class had a shorter class period than 7A.

Both classes talked about roller coasters they had experienced, in preparation for Physics Day at Six Flags tomorrow. We talked about speed, height, length, and duration, and the relationship between these variables in a roller coaster. The learning goal was to talk about Estimation, and how to judge how good your estimates are, by calculating Percent Error.

To do this, we played the game Coaster Competition on the computer. Here are the rules:

Goal: Choose the superlative coaster. Highest points win!

1. Partners take turns
2. Player A chooses a picture of a roller coaster at www.Joyrides.com.
3. Player A estimates & records their estimate on their Roller Coaster Data handout (which you can download here):
· speed
· height
· track length
· duration
4. Player B chooses a picture of a roller coaster they think will be faster, higher, and longer at Joyrides.
5. Player B estimates & records their estimate on their handout:
· speed
· height
· track length
· duration
6. When both players have made their estimates, they check actual data at www.RCDB.com, an extensive roller coaster database. The search box at the top left allows you to find out the actual measurements for your roller coaster. They record the actual measurements on their handouts.
7. One point each is awarded for the fastest, highest, longest track, and longest duration. The player with the most points win.
8. Next time, Player B goes first, and Player A goes second. Players must choose a new roller coaster every time.

In Class 7A, we had a chance to play the game and talk about how to improve our estimates. We discussed how we can figure out how good our estimates are by calculating the Percent Error with this formula:

Estimation Score = Percent Error = (Estimated amt. - Actual amt./Actual Amount) x 100

Class notes may be downloaded here.

HOMEWORK: CLASS 7A
Play the Coaster Competition game 8 times with someone, going to Joyrides to pick a picture and estimate, find out actual measurements on RCDB, and record your data on the Roller Coaster Data handout.

The calculate the Percent Error of your estimates for one of the variables (speed, height, length, or duration) for each of the 8 rounds, and record the percent error on the Estimation Score Chart handout, which you can download here.

Due Monday, June 7.

HOMEWORK: CLASS 7B
Play the Coaster Competition game 8 times with someone, going to Joyrides to pick a picture and estimate, find out actual measurements on RCDB, and record your data on the Roller Coaster Data handout.

Due Monday, June 7.

Student Self-Assessment

Today students shared their homework, then took an assessment of their learning from the past few weeks. Large group students took a quiz on the Filling & Wrapping work they have been doing with cylinders and prisms, and Small group students took a quiz on the Moving Straight Ahead linear equation work they have been doing with MaryBeth and Cory.

As we finish up the school year, we also want students to assess their own learning in math.

HOMEWORK

Please fill out the online student self-assessment form. Answer the multiple choice questions about learning habits, rating yourself as Emerging (starting to show this behavior), Developing (showing this behavior on a regular basis), or Mastering (almost always shows this behavior). Then answer the 3 reflection questions in full sentences, to be included in the progress report that becomes part of your student record that goes to parents and high schools.

Due Tuesday, June 8.

Math Reflections & Fill'R Up

LARGE GROUP
We shared or worked on homework today, then worked on Math Reflections 3, which is included at the bottom of yesterday's Homework handout, which you can download here. Then we worked on a problem looking at the relationship between volume and scale factor in rectangular prisms. In Stretching & Shrinking, we found that the perimeter of two similar figures changed with the scale factor, but that the area of two similar figures changed with the square of the scale factor. In this problem, using the Purple Prisms Applet, we found that the volume of two similar prisms changes with the cube of the scale factor. Class notes may be downloaded here.

No more math this week. Have a great rest of the week and long weekend!

LARGE GROUP HOMEWORK
1. Finish Math Reflections 3, which you can download here.
2. Study for Quiz on Tuesday, June 1.
3. Make up any missing homework.

Due Tuesday, June 1.

SMALL GROUP
Today was Cory's last day with the students; she will be leaving to start an internship in June. Students shared their Math Reflections 1 homework and worked on Problem 2.1 and 2.2 in class. You can download Problem 2.1 and 2.2. here.

No more math this week. Have a great rest of the week and long weekend!

SMALL GROUP HOMEWORK
1. Finish Problem 2.2, which you can download here.
2. Finish Math Reflections 2, which you can download here.
3. Study for the Quiz Tuesday.
4. Make up any missing homework.

Due Tuesday, June 1.

ACE 3.4 Making a New Juice Container

LARGE GROUP
Today students generated formulas for surface areas and volume of cylinders and prism. Then they worked on Problem 3.4, Making a New Juice Container, which you can download here. They designed nets for boxes (prisms) on centimeter graph paper that would have the same volume as the can. A variety of boxes resulted! Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
ACE 3.4 Homework

Option 1
Problems 18 and 20-22 on the handout.

Option 2
Problems 20-22 and 33-34 on the handout.

Due tomorrow, Wednesday, May 26. If you are too busy with the play, that's fine, you can definitely turn this in next week.

SMALL GROUP
Students worked on Problem 1.4 (which you can download here) and ACE homework problem 12 (which you can download here).

SMALL GROUP HOMEWORK

Math Reflections 1 (which you can download here)
Group B: Finish ACE #12 (which you can download here)

Due tomorrow, Wednesday, May 26. If you are too busy with the play, that's fine, you can definitely turn this in next week.

ACE 3.3 Making Cylinders & Prisms from Nets; Linear Equations

LARGE GROUP
Students shared their ACE 3.2 homework, and we talked about the problem involving a room full of cylinders. Then we focused on nets and surface area of cylinders, with Problem 3.3, Making Cylinders & Prisms from Nets, which you can download here. Student groups designed nets to try to duplicate a cylinders they chose (salt shakers, glasses, etc.) and then they worked from nets (you can download the prisms and cylinder nets here) and calculated the surface area of the cylinder and 2 prisms, and their volume. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
ACE 3.3
Option 1
Problems 15-17 on the handout, which you can download here.

Option 2
Problems 17 and 31-32 on the handout, which you can download here.
(Note that you already did problem 26!)

Due tomorrow, Tuesday, May 25, if you are not busy with Play Practice.

SMALL GROUP
Students did more work on Linear Equations with MaryBeth. They worked on Problem 7 on the handout which you can download here.

SMALL GROUP HOMEWORK
ACE 1.3
Finish Problem 7, do 8 and 9 on the handout which you can download here.

Due tomorrow, Tuesday, May 25, if you are not busy with Play Practice.

ACE 3.2: Filling Cylinders and Linear equations

LARGE GROUP
In large group today we did a warm-up identifying prisms and pyramids and solving some measurement problems. We talked about how to find the volume of triangular vs. rectangular prisms, multiplying the area of the Base by the height of the prism. And we also reviewed circles, and found that a little over 3 radius squares fit in the area of a circle.

Then we went over Problem 3.2, in which we compared the volume and surface area of two cylinders, one made of a sheet of paper the long, thin way (Tom), and one made out of the same size paper the short, fat way (Jerry). Students made conjectures about whether the cylinders would have equal volume, then tested to find out. They did the same with surface area. We found that the Jerry cylinder had a larger base circle area, and that the volume ended up being larger than the Tom cylinder, even though the Tom cylinder was taller. We also found that the Jerry cylinder had bigger surface area, because although the curved surfaces were equal, the Base area of Jerry was larger. The problem may be downloaded here, and class notes may be downloaded here.

We don't have another math class until next Monday. Have a great rest of the week!

LARGE GROUP HOMEWORK
ACE 3.2

Problems 2, 8-12, and 26 on the handout, which you can download here.

Due Monday, May 24.

SMALL GROUP
Students worked with Cory today. They shared their answers from the Additional Practice homework, then work on parts A and B of Problem 1.3, Raising Money, which you can download here. Students also looked at Linear Equations like ax+b=c and ax=c, and how they show up on a graph, and how we can write them from story problems.

SMALL GROUP HOMEWORK

ACE 1.3

Problems 6 and 7 on the handout, which you can download here.

Due Monday, May 24.

Volume of Prisms & Linear Function Equations

LARGE GROUP
Students completed a reflection about the ERB, answering these 3 questions:
1. What went well for you?
2. What was difficult?
3. Do you have any questions about any of the math on the test?

Then we discussed Problem 3.1, Filling Fancy Boxes, which you can download here. Student groups made 4 prisms with an increasing number of sides out the same size sheet of paper, with equal height, and compared their volumes and surface areas in different ways. Some groups filled them with unit cubes, others filled them with beans or lentils, and others made measurements and calculations.

We found that the conjecture that the volume increases as the number of sides of the prism increases was correct. Tomorrow we will discuss what happens to the surface area. Class notes may be downloaded here (class 7A, class 7B).

LARGE GROUP HOMEWORK
ACE 3.1 Homework

Problems 1 and 23-25 on the handout, which you can download here.

Due tomorrow, Tuesday, May 18.

SMALL GROUP
Students completed a reflection about the ERB, answering these 3 questions:
1. What went well for you?
2. What was difficult?
3. Do you have any questions about any of the math on the test?

Students worked with MaryBeth today on more about linear functions and equations, working on ACE 1.2, problems #3 h-j, 4, and 5 in Group A, and problems 3h-j and 4 in Group B. The problems can be downloaded here.

Goals for the class were:
1. To understand how rate shows up in a table and on a graph (the higher the rate, the steeper the line).
2. To write equations that can be used to calculate distance traveled in a given number of hours.

3. To use x and y as variables in the equation instead of d and t and understand why (independent and dependent variable).

4. To understand how rate shows up in an equation.

5. To solve equations for either x or y.

SMALL GROUP HOMEWORK:

GROUP A: Additional Practice Investigation 1, problems 1-4 (which you can download here)

GROUP B: ACE #5 which you can download here; Additional Practice Investigation 1, problems 1-4 (which you can download here)

Due tomorrow, Tuesday, May 18.

3D Geometry & Linear Functions

LARGE GROUP
Today the large group finished working on the packaging blocks problem. In the problem, students took 24 cubes and figured out how many different rectangular prisms (boxes) they could make, their dimensions, their surface area, and their volume. They found that long and skinny boxes had big surface areas, whereas short stubby ones that looked more like cubes had smaller surface area, and thus used less paper (more eco-friendly!). We also talked about prisms and pyramids. Class notes may be downloaded here for class 7A and class 7B.

We also talked a bit about exponents and powers, examining patterns in the powers of 10 and powers of 3 with some Montessori materials that illustrate this well. Understanding square and cubic units relies on a good understanding of exponents and powers.

No homework tonight, but students should remember to bring a calculator with them tomorrow for ERB testing.

No math class until Monday; have a great weekend!

SMALL GROUPS
Students met with Cory today to continue work with Linear Functions. They worked on Problem 1.3 from Moving Straight Ahead, and on problems 1-7 on the Skill Sheet on Linear Relationships, which you can download here.

No homework tonight, but students should remember to bring a calculator with them tomorrow for ERB testing.

No math class until Monday; have a great weekend!

Review of Graphs, Unit Test, Fraction Operations, Geometry; Small Group Linear Functions

LARGE GROUPS
The large group covered a lot of ground today. We shared homework analyzing graphs from the work we did Thursday. Then we discussed the Unit Test answers from the Accentuate the Negative unit. We had a quick review of addition, subtraction, multiplication, and division of fractions, sharing strategies, including converting mixed numbers into improper fractions, and decomposing mixed numbers into whole plus fraction numbers using the distributive property. Finally, we talked a little more about 3 dimensional geometry, including pyramids and prisms. You can download class notes here for class 7A and class 7B.

No homework tonight. Get lots of rest for testing tomorrow. No math class till Wednesday.

SMALL GROUPS
The small groups met with MaryBeth today. Students shared homework analyzing graphs from the work we did Thursday. Then students reviewed coordinate graphing, including negative integer coordinates. We made a card about linear functions and linear graphing, and students started work on Problem 1.2, Linear Relationships in Tables, Graphs, and Equations.

No homework tonight. Get lots of rest for testing tomorrow. No math class till Wednesday.

Using Graphs to Interpret Information

Today all the students met together with Sima. Large groups received their Unit Tests back. We all talked about different kinds of graphs, and which kinds of graphs display certain kinds of information best. The graphs we discussed were bar graphs, pictographs, histograms, line graphs, pie graphs (also known as pie charts), and stem and leaf plots. Class notes may be downloaded here.

HOMEWORK
Please complete one of 3 handouts asking for interpretation of different graphs.

What's the Weather may be downloaded here; it asks for interpretation of one pictograph.
Name Your Tune may be downloaded here; it asks for interpretation of 4 different pictorgraphs.
History of Populations may be downloaded here; it asks for interpretation of 4 different pie graphs.

LARGE GROUP: Please make corrections to your Unit Test in colored pencil.

Due Monday, May 10. Have a great weekend, and don't forget to bring a calculator for ERB testing every day next week.

3D Geometry: Nets, Surface Area, and Volume

LARGE GROUP
We talked about 3-dimensional geometry today. First we worked on a problem at a box factory, where Emma had to find all the possible nets (2 dimensional figures that can be folded into a box) that would create a cube; the problem can be downloaded here. Both classes found that there were 11 unique nets that can make cubes. Then we worked on another box problem where a factory wants to find all the possible boxes with volume 24 cubic inches possible. Students were reminded of a couple of formulas:

volume = length x width x height
surface area = 2 (length x width) + 2 (width x height) + 2 (length x height)

Class notes may be downloaded here for class 7A and class 7B.

LARGE GROUP HOMEWORK
Please complete problems 1-5 and 7-14 on the handout, which you can download here.

Due tomorrow, Thursday, May 6.

SMALL GROUPS
The small groups worked with Cory today. Students received their Unit Tests and made corrections, going over their work with Cory, including a review of addition, subtraction, multiplication, and division with fractions. Then they worked on some concepts in 2 dimensional and 3 dimensional geometry including terms often used on standardized tests.

SMALL GROUP HOMEWORK
Please make your corrections to the Unit Test in colored pencil, without erasing or scratching out your original answers.

Due tomorrow, Thursday, May 6.

Standardized Test Taking Skills

BOTH GROUPS
MaryBeth Ventura, our Learning Specialist, taught a lesson on Monday about standardized test taking skills. The ERB tests are not high-stakes criteria based test, but norm-referenced tests, which means results are compared to other students around the country who took the same test, rather than specifically on what the students at this school have been studying. The school uses the results of this test to look at what we cover in the curriculum, for example. Learning how to take standardized tests is a useful skill, since most students will be taking them in the future, for example, college entrance exams.

Students generated the following strategies to feel more prepared and less anxious before and during testing.

Before the test:
Stay calm
Don’t think about it too much
Move a little to get blood moving
Eat for energy (whole grains, protein)
Study—keep up in class
Listen to music on way to school
Self pep-talk/prayer
Get lots of sleep
Practice tests
Have materials ready

During the test:
Stay calm
Take your time/Don’t rush
Read the questions carefully
Read all the choices
Look for key terms
Eliminate obviously wrong answers
Make an educated guess (no penalty for guessing)
Preview whole test to pace yourself
Skip questions you’re stuck on and return if you have time
Look over your answers again at end

We also talked about techniques to reduce anxiety. Positive self-talk is the number one anxiety reducing technique. We also practiced two other techniques: tense & relax, and visualization with cupped eyes.

Finally, we talked about strategies specific to math standardized tests:
1. Read question & instructions carefully
2. Open up right files in your mind
3. Use scratch paper
4. Write down the information and quantities given
5. Write down the question to be answered
6. Draw a picture of the problem
7. Try to put quantities into an equation
(+, -, x, /, proportion)
8. Look for key terms
9. Estimate
10. Rule out & guess

In class on Tuesday we practiced taking a standardized test, and discussed our answers and strategies. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP
In class 7A we started working on a 3 dimensional geometry problem using nets, flat figures that can be folded and made into boxes. We reviewed some terms from geometry, including vertex, edge, area, surface area, volume, square, and cube. The problem we will continue working on tomorrow is to determine how many possible nets can make a cube.

No homework tonight for LARGE or SMALL groups.

Unit Test

Students took the Unit Test for Accentuate the Negative. Those that finished early worked on an optional logic problem.

Have a great travel week! I will see you again on Monday, May 3.

LARGE GROUP ONLY
Please work on your Dealing Down Unit Project, which is due Tuesday, May 4.

Math Reflections 4, Looking Back & Looking Ahead

LARGE GROUP
Students shared their homework and strategies for winning Dealing Down. We used a Think-Pair-Share to discuss Math Reflections 4, to summarize our learning of the Order of Operations and the Distributive Property. Then students worked on the Looking Back, Looking Ahead, and shared their answers. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
Finish Math Reflections 4, questions 1-3 on page 75.
Finish Looking Back, Looking Ahead, questions 1-9 on pages 78-79.
Study for the Unit Test!

Due tomorrow, Thursday, April 22.

SMALL GROUPS
Cory was sick today so students worked for part of the time with MaryBeth, and within the large group for part of the time. Students shared their ACE homework and Math Reflections 4 homework. Then they worked on Looking Forward, Looking Back problems 5-9 as a review for tomorrow's Unit Test.

SMALL GROUP HOMEWORK
Finish Looking Back, Looking Ahead, questions 1-9 on pages 78-79. Skip problem 4 if you did not learn coordinate graphing.

Study for the Unit Test!

Due tomorrow, Thursday, April 22.

ACE 4.3 Distributive Property & Subtraction

LARGE GROUP
Today we talked more about the Distributive Property, and found that it works for multiplication over addition, and multiplication over subtraction. Students practiced drawing rectangle representations for expressions showing the Distributive Property. We also learned that when using the Distributive Property, you can write the expression as a product of factors (one or both of which have two terms), which is called factoring the expression, or you can write the expression as a sum of addends (one or both of which might be products), which is called expanding the expression. Students worked on Problem 4.3, The Distributive Property & Subtraction. Class notes may be downloaded here.

LARGE GROUP HOMEWORK
Dealing Down Homework
Make a list of strategies that worked to win Dealing Down. Label by which math concepts they illustrate.

ACE 4.3 Homework
Please choose one of the options below to complete.

Option 1
Problems 5-7 and 33-35 on pages 70-73

Option 2
Problems 6-7, 33-35 and 45-46 on pages 70-74

Do not use a calculator!
Due tomorrow, Wednesday, April 21.

SMALL GROUPS
Students worked with Cory today to learn more about the Distributive Property by finishing the Skills sheet, Properties of Operations, and shared their ACE 4.3 homework. They started working on Math Reflections 4, on page 75.

SMALL GROUP HOMEWORK

ACE HOMEWORK

Finish Math Reflections 4 on page 75
Problems 17-25 on p.70

Due tomorrow, Wednesday, April 21.

Unit Project: Dealing Down

LARGE GROUP ONLY
Students will be playing the Dealing Down game and writing a report detailing their strategies for winning the game, while providing evidence of their understanding of:

1. Operating with positive and negative numbers
2. Order of operations
3. Commutative Property of addition and multiplication
4. Distributive Property of multiplication over addition and subtraction

The Dealing Down game is described on pages 76-77 of Accentuate the Negative. The handout with the assignment is here, the handout with the game cards is here, and the handout with the score sheet is here.

You will write a report that includes the following Criteria & Procedures:

• Title—“Dealing Down Report”
• Name on paper
• Typed report using size 12 standard font, or handwritten in black ink, skipping every other
line (in order to get the notation correct)
• Introductory paragraph with a topic sentence
• Four detailed supporting paragraphs

1. Operating with positive and negative numbers
2. Order of operations
3. Commutative Property of addition and multiplication
4. Distributive Property of multiplication over addition and subtraction

• Concluding paragraph
• Paragraphs include mathematical examples and explain strategies in detail
• Use correct mathematical vocabulary
• Use correct conventions
• Please use your imagination and creativity in writing your report.

First draft of report due Tuesday, May 4.

Please play 5 rounds of Dealing Down and record your scores on the score sheet tonight.

Due tomorrow, Tuesday, April 20.

ACE 4.2 Distributing Operations

LARGE GROUP
We discussed the Problem of the Week, Area & Volume. We shared our ideas for figuring out perimeter, the sum of the edges of cubes, area, and volume for these problems. We also discussed the Unit Project--click here for details.

Students also worked on Problem 4.2, Distributing operations. We were calculating the area of subdivided rectangles, and writing math sentences to indicate that the are of the entire rectangle was equal to the sums of the areas of the smaller sections. Class notes are available here for class 7A and class 7B.

LARGE GROUP HOMEWORK
ACE 4.2 Homework
Please choose one of the options below to complete.

Option 1
Problems 3-4, 30, 31b, and 44 on pages 69-74
Option 2
Problems 4, 30, 31b, 32, and 44 on pages 69-74

Do not use a calculator!
Due tomorrow, Tuesday, April 20.

There is also Unit Project homework for tonight--click here for details.

SMALL GROUPS
The small groups worked with Cory today to go over their ACE 4.1 homework, review the Order of Operations, and learn about the Distributive Property. Students made a Distributive Property card, and practiced distributing multiplication over addition with a Skills sheet.

SMALL GROUP HOMEWORK
ACE 4.3

Problems 5, 6, and 7 on p. 70 and problem 34 on p. 73

Due tomorrow, Tuesday, April 20.

ACE 4.1 Order of Operations

Students worked all together today with Sima, and we discussed the order of operations, the order in which you do operations when computing the answer in a math sentence. Here is a helpful mnemonic:

Please
Excuse
My
Dear
Aunt
Sally

or PEMDAS.

1. Parentheses
2. Exponent
3. Multiplication
& Division (whichever of these 2 comes first when going left to right)
4. Addition
& Subtraction (whichever of these 2 comes first when going left to right)

We worked on Problem 4.1, Order of operations. Class notes may be downloaded here for class 7A or class 7B.

ACE 4.1 Homework
Please choose one of the options below to complete.

Option 1 (please do this one if you are in a Small Group)
Problems 2, 8-16 on pages 69-70

Option 2
Problems 2, 17-29, 41-43 on pages 69-74

Do not use a calculator!
Due Monday, April 19.

LARGE GROUP ONLY:
POW Area & Volume also due Monday.

Math Reflections 3 & Units of Measure

LARGE GROUP
Students took a mini-assessment using the terms factors, divisors, product, multiples, and divisible by.

Then students did a Think-Pair-Share on Math Reflections 3, to consolidate what we know about multiplying and dividing integers.

Finally, students brainstormed all the measurement terms they could think of, and in small groups categorized and labeled them as to what they measure. Students thought of measurements for length, area, volume, mass, time, temperature, brightness, sound, earth movement/vibration, power, data storage, etc.

We discussed the metric system, and students learned how to convert from one unit to the other within the metric system, for example, from kilometers to meters. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
Finish Math Reflections 3, questions 1-3 on page 59.

Finish Metric Conversions handout, which you can download here.

Due tomorrow, Thursday, April 15.

SMALL GROUPS
Students worked with Cory today to practice word and number problems involving addition, subtraction, multiplication, and division of positive and negative numbers.

SMALL GROUP HOMEWORK
Finish Math Reflections 3, questions 1-3 on page 59.

Due tomorrow, Thursday, April 15.

ACE 3.4 Integer Product Game

LARGE GROUP
Today the large group did a warm-up problem estimating the answers to addition, subtraction, multiplication, and division problem with integers. Then we played the Integer Product Game, a variant of a game we played in sixth grade, but with negative numbers as well as positive numbers. Students were very animated as they determined strategies to get 4 in a row and win the game! You can download class notes here for class 7A or class 7B.

LARGE GROUP HOMEWORK
ACE 3.4 Homework

Please choose one of the options below to complete.

Option 1
Problems 12-17, 18a-i, and 19-21 on pages 52-53

Option 2
Problems 12-17, 18a-i, 19 and 34-35 on pages 52-58

Do not use a calculator!
Due tomorrow, Wednesday, April 14.

SMALL GROUP
Students worked with Cory today to go over the rules for addition, subtraction, multiplication, and division of positive and negative numbers. They practiced all of these on skill sheets including all the operations.

SMALL GROUP HOMEWORK

Please spend 30 minutes with Addition, Subtraction, and Multiplication & Division at the Mathwizz website.

Due tomorrow, Wednesday, April 14.

POW: Area & Volume

LARGE GROUP ONLY
Please choose 2 of the 3 questions on the Problem of the Week, Area and Volume, to complete. You may download the handout here. Class notes discussing the formulas may be downloaded here for class 7A or class 7B.

Due Monday, April 19.

ACE 3.3 Intro to Division of Integers

LARGE GROUP
We worked on Problem 3.3 today, Introduction to Division with Integers, and we used what we know about the relationship between multiplication and division to create fact families and figure out an algorithm for division with negative and positive numbers. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
ACE 3.3 Homework
Please choose one of the options below to complete.

Option 1
Problems 7-8, 10-11, 22c-i, 33 on pages 51-58

Option 2
Problems 7-8, 22f-m, 27, 33 on pages 51-58

Do not use a calculator!
Due tomorrow, Tuesday, April 13.

SMALL GROUPS
MaryBeth went over the Partner quiz again and addition and subtraction of positive and negative numbers. Then she introduced students to division with integers, and students made a card. They went over part B of Problem 3.3, Introduction to Division, and practiced this operation with the Division Skill Sheet.

SMALL GROUP HOMEWORK:
ACE 3.3 Homework

Problems 8-17 on page 52

Do not use a calculator!
Due tomorrow, Tuesday, April 13

Partner Quiz Corrections

Today both groups met together with Sima. We discussed the Partner Quiz answers. Students practiced standardized test math questions, and some students worked at the Mathwizz web site on addition and multiplication of integers.

Homework: Partner Quiz Corrections

Please look at the problems marked with arrows on the Partner Quiz, and try again. You may use your notes, math book, and help from others. Please make your corrections in colored pencil! I will not accept corrections made in regular pencil, or erasing your work, because it is important to make your thinking before and after visible.

Corrections due Monday, April 12.

ACE 3.1 Intro to Multiplication with Integers

LARGE GROUP
The students considered the following puzzler as a warm up problem. Class 7A should consider this problem further, and both classes should share this with their families!

String Burning Puzzle

You have 2 pieces of string of different, unspecified length, and some matches. Each piece of string takes exactly an hour to burn, but the burn rate is not constant. This means that it could take 59 minutes to burn the first 1⁄4, and 1 minute for the rest. The strings have different burn rates, and of course you don't know the rates anyway. Using only the matches and the strings, measure 45 minutes.

Then we worked on Problem 3.1, Introducing Multiplication of Integers, looking at a number line model to see whether products are positive or negative when we multiply integers together. Some students also worked on Problem 3.2, Multiplication Patterns. We found that like addition, multiplication is commutative. If you switch the position of factors in an equation, the product is still the same.

Algorithms for multiplication students came up with called for multiplying the absolute values of numbers together. When multiplying two positive or two negative numbers, the product will be positive. When multiplying a positive and negative number together, the product will be negative. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP ACE 3.1 Homework:
Please choose one of the options below to complete.

Option 1
Problems 1-4 on pages 50-51

Option 2
Problems 2-4, 24, and 30 on pages 51-56

Do not use a calculator!
Due tomorrow, Thursday, April 8.

SMALL GROUPS
Students worked with Cory today on Problem 3.1, Introducing Multiplication, parts A1-5, B1-4, and B6.

SMALL GROUP ACE 3.1 Homework:

Problems 1-4 on pages 50-51

Do not use a calculator!
Due tomorrow, Thursday, April 8.

Measuring Rectangles & Intro to Multiplication of Integers

LARGE GROUP
We discussed the Problem of the Week, the X/O problem, and how experimental probability begins to approach theoretical probability as you do more trials. Then we finished talking about Measuring Rectangles, and how the dimensions are in a constant ratio no matter what they are measured by. Finally, we began thinking about multiplication with negative numbers. Class notes may be downloaded here for class 7A and class 7B.

LARGE GROUP HW
Please finish questions 4-5 on Measuring Rectangles.

Due tomorrow, Wednesday, April 7.

SMALL GROUP
Students worked with Cory on Problem 3.2, Multiplication Patterns, as an introduction to Multiplication with negative numbers. Students made a Multiplication of Integers card.

SMALL GROUP HW:
Problems 4-5, 6a-d on page 51

Do not use a calculator!
Due tomorrow, Wednesday, April 7

Partner Quiz; No New Homework

Today all the students were together and took a Partner Quiz assessment about the addition and subtraction of integers with partners from their group.

No new homework.

LARGE GROUP ONLY
Don't forget that the POW, The X/O problem, is due when we return, Tuesday, April 6. We will discuss the Rectangle Measure work then as well.

Have a wonderful spring break!

Math Reflections 2 & Rectangle Measure

LARGE GROUP
We worked on Math Reflections 2 in class today, to consolidate all we have learned about adding and subtracting positive and negative numbers. Then we started work on a measurement activity, Rectangle Measure. Students measured a rectangle with inches, centimeters, pennies, paperclips, beads, and the width of their index fingers. Homework is to finish these measurements, record them, and graph them. The handout may be downloaded here, and the class notes may be downloaded here.

LARGE GROUP HOMEWORK
Please answer questions 1-3 on Math Reflections 2 on page 41.

Study for Partner Quiz tomorrow!

Rectangle Measure Handout
Answer questions 1-3. You may use other small things to measure if you don't have beads, paperclips, or pennies.

Due tomorrow, Thursday, March 25.

SMALL GROUPS
Students worked with Cory today to firm up what they know about addition and subtraction of positive and negative numbers. They completed Math Reflections 2 in class, and worked on ACE problem 30.

SMALL GROUP HOMEWORK
Study for Partner Quiz tomorrow!

ACE 2.5, Coordinate Graphing

LARGE GROUP
Today we reviewed subtraction with negative numbers, and had a mini-assessment of student understanding of negative variables in expressions. Students discovered that "-n" refers to the opposite of the value of n. So if -n = +8, then - (-8) = +8 and n= -8. We also talked more about the POW Rate problem about speed, because almost all of the students had the wrong answer! When in doubt, remember d = rt (dirt) or d=st (dust).

Then we worked on Problem 2.5, Coordinate graphing. We found that by adding negative numbers to both the x and y axes, you end up with 4 different quadrants. "Opposite" coordinates, whose coordinates are the opposite of the original coordinates, when connected by lines will pass through the zero. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HOMEWORK
ACE 2.5 Homework
Please choose one of the options below to complete.

Option 1
Problems 27-29 and 34-36 on pages 36-39

Option 2
Problems 27-28, 34-36, and 42 on pages 36-40

Due tomorrow, Wednesday, March 24.

SMALL GROUPS

Small groups met with Cory today. They shared homework ACE 2.4, went over Problem 2.4, #C2 and D2, and practiced writing facts from fact families using the opposite operation. They went over rule for subtraction of integers (add the opposite) . Students worked on subtraction practice pages M and A. Students in group B started working on Problem 2.5, Coordinate Graphing.

SMALL GROUP HOMEWORK
Additional practice 2 (which can be downloaded here)
Problems 5,6, 8-14, 23 - 25

Due tomorrow, Wednesday, March 24.

POW: X/O Problem

LARGE GROUP ONLY

Please answer both questions on the Problem of the Week, The X/O Problem. You may download the handout here.

Due Tuesday , April 6.

ACE 2.4, Fact Families

LARGE GROUP
We shared our answers from the What are my Chances homework and the Problem of the Week, Rate Problems. Then we worked on Problem 2.4, Fact Families. By looking at simple fact families like 3 + 2 = 5, 2 + 3 = 5, 5-2 = 3 and 5-3 = 2, we can make similar fact families for problems involving negative numbers, allowing us to convert them into simpler problems to solve. We also used what we knew about the inverse relationship of addition and subtraction to solve for unknown variables in equations. Class notes may be downloaded here for class 7A and class 7B.

LARGE GROUP HW:
ACE 2.4 Homework
Please choose one of the options below to complete.

Option 1
Problems 17-19, 21-26 on pages 35-36

Option 2
Problems 18-19, 21-23, 25-26, and 41 on pages 35-40

Do not use a calculator!
Due tomorrow, Tuesday, March 23.

SMALL GROUPS
Students work with MaryBeth today. The shared homework ACE 2.3 and What are my Chances?

Then they reviewed their Addition and Subtraction of Integers Cards, and Fact Families. They discussed what is true about fact families: the numbers are exactly the same; they are made up of 2 addition and 2 subtraction facts; the addition facts are the same, but addends switched; you subtract each addend from the sum of the addition facts to find the subtraction facts.

Then students worked on Problem 2.4, Fact Families.

SMALL GROUP HW:
ACE 2.4
Problems 17 - 20, 22, 23a, 24-26 on pages 35-36.

Due tomorrow, Tuesday, March 23.

What are My Chances?

Today in math we were all together with Sima. We talked about theoretical and experimental probability, and tested experimental probability with dice, coins, and cards. Students conducted experiments and recorded their results on the handout, which you can download here. Class notes may be downloaded for class 7A and class 7B.

Homework
Finish filling out the handout (above). You will not be able to do the table with the results from the entire class, so don't worry about that table.

Due Monday, March 22.

ACE 2.3 The +/- Connection

LARGE GROUP
Today we reviewed counting numbers, natural numbers, whole numbers, integers, and rational numbers during our warm-up. Then we shared homework, discussed algorithms for subtraction from yesterday's problem, and talked about how there is no Commutative Property for subtraction, unlike addition. We had a mini-assessment to see how students are thinking about adding and subtracting positive and negative numbers. Then we worked on Problem 2.3, The "+/-" Connection, on pages 28-29. Students noticed the relationship between addition and subtraction of integers:

Subtracting a positive number is like adding a negative number.
Subtracting a negative number is like adding a positive number.

These two facts can be quite useful in making problems easier to solve. By turning subtraction problems into addition problems, we don't have to come up with complicated algorithms for subtraction. Class notes may be downloaded here for class 7A or class 7B.

LARGE GROUP HW:
ACE 2.3 Homework
Please choose one of the options below to complete.

Option 1
Problems 10-12 and 15 (a, b, e, f, i) & 16 (a, b, e, f, i) on pages 34-35

Option 2
Problems 10-11, 15 (a, b, e, f, i) & 16 (a, b, e, f, i), and 40 on pages 34-39

Do not use a calculator!
Due tomorrow, Thursday, March 18.

SMALL GROUP
Students worked with Cory today. They shared the ACE 2.1 homework, made Subtraction and Absolute Value cards, then worked on Problem 2.3, The "+/-" Connection, on pages 28-29. Please see notes above for Large Group for more about that problem.

SMALL GROUP HW:
ACE 2.2 Homework

Problems 1a-h, 2, 3, and 10-12 on pages 32-34.

Do not use a calculator!
Due tomorrow, Thursday, March 18.

ACE 2.2 Introduction to subtraction of Integers

LARGE GROUP
After a warm-up to review absolute value and opposites, we went over the last part of problem 2.1. We found that the Commutative Law of Addition says that the order of the addends in an addition problem doesn't matter: the sum is the same. We can use the Commutative Law of Addition with rational numbers (positive and negative integers and fractions) to make addition problems easier for us; for example, in some cases it may be easier to have a negative number first or second, if they are not the same sign.

Then we worked on problem 2.2, Introduction to subtraction of integers. Students found it much more challenging to write down algorithms for all the different cases in subtraction. We will talk more about this tomorrow. Class notes for may be downloaded here for class 7A and class 7B.

LARGE GROUP HW:
ACE 2.2 Homework
Please choose one of the options below to complete.

Option 1
Problems 4-7 on page 33

Option 2
Problems 6-7 and 38-39 on pages 33-39

Do not use a calculator!
Due tomorrow, Wednesday, March 17.

SMALL GROUPS
Today students reviewed Problem 1.4 with Cory, and worked on Problem 2.1, Introducing Addition of Integers. They created cards for the addition algorithm and the Commutative Property.

SMALL GROUP HW:
Finish Problem 2.1 on page 24
ACE 2.1 Homework
Problems 4-7 on page 33

NO CALCULATORS!!
Due tomorrow, Wednesday, March 17.

ACE 2.1 Introduction to Addition of Integers

LARGE GROUP
Today we worked on Problem 2.1, Introducing Addition of Integers, coming up with algorithms (step-by-step plans) to add positive and negative numbers. Class notes can be downloaded for group 7A and group 7B.

LARGE GROUP HW:
ACE 2.1 Homework
Please choose one of the options below to complete.

Option 1
Problems 1-3 and 30a, b, e, g, i on pages 32-37

Option 2
Problems 1-3 and 37 on pages 32-39

Due tomorrow, Tuesday, March 16.

POW: Rate Problems due Monday, March 22.

SMALL GROUPS
Today MaryBeth worked with both small groups to review the integer and opposite numbers cards. Then students learned the chip model for positive and negative numbers, and looked at the idea of opposites using chips (cancelling). Students represented single integers using different combinations of chips, and solve addition and subtraction problems using chips.

Then students worked on Problem 1.4, In the Chips.

SMALL GROUP HW:
Finish Problem 1.4
To do tonight's HW you can use two different colored chips if you happen to have those at home, or even two different coins (nickels and pennies for example.) Just be sure to be clear about which represents positive integers and which represents negative integers. You can also draw the chip representations with red and green (or black) markers.

For problem E, please just use the chip method to solve the problems. You may draw your solutions, but you do not need to write the solution out in words!

Due tomorrow, Tuesday, March 16.

POW: Rate Problems

LARGE GROUP ONLY

Please choose 2 of the 3 questions on the Problem of the Week, Rate Problems, to complete. You may download the handout here.

Due Monday, March 22.

Math Reflections 1, Mathwizz Integer Practice, VoiceThread

LARGE GROUP
We finished talking about problem 1.3, In the Chips, and how the chip board model helps us think about adding and subtracting positive and negative numbers. We completed and discussed Math Reflections 1 on page 21 in class. Students practiced adding and subtracting positive and negative numbers at the Mathwizz web site. Then they commented on the video we watched Cosmic Voyage using a making thinking web site called Voicethread. Class notes may be downloaded here for 7A or 7B.

LARGE GROUP HOMEWORK
Finish Math Reflections 1 questions 1-2 on page 21.
Finish commenting on Cosmic Voyage on Voicethread.

Due Monday, March 15.

SMALL GROUPS
Cory worked on Math Reflections 1. We made cards for adding positive and negative numbers.
We worked on Additional Practice 16-25, and practiced at the Mathwizz web site.

SMALL GROUP HOMEWORK
Finish Math Reflections 1 questions 1-2 on page 21.
ACE 1.3 Homework: Problems 13-31, odd problems only.

Due Monday, March 15.

ACE 1.4 In the Chips

LARGE GROUP
Today we worked on problem 1.4, In the Chips, and used a chip model for integers, in which red chips represent negative numbers and black chips represent positive numbers. Students also finished their conference preparations, reflecting on one strength and one challenge work. Sima met with a few students to go over their reflections. Class notes may be downloaded here.

LARGE GROUP
ACE 1.4 HOMEWORK
Please choose one of the options below to complete.

Option 1
Problems 32-37 on page 18

Option 2
Problems 35-38, and 52-54 on pages 18-20

Conference Prep.
Finish your reflection on Strength & Challenge Works.

Due tomorrow, Wednesday, March 10.

For students who would like more practice adding and subtracting positive and negative numbers, check out this web site:
http://www.mathwizz.com/integers/

SMALL GROUPS
Cory was out but MaryBeth taught today. We did more work visualizing number lines, and practiced positive and negative moves on the visualized number line. Students made cards for: Integers and Change - + change (to the right), - change (to the left). We learned that changes have both a quantity and a direction (positive or negative). We went over problem 1.2, #F and the ACE 1.2 homework yesterday, and started Problem 1.3, What's the Change?

SMALL GROUP
ACE 1.3 Homework
Problems 20, 22, 24, 26, 28, 30-31 on pages 17-18

Due tomorrow, Wednesday, March 10.

ACE 1.3 What's the Change?

LARGE GROUP
Students turned in their Unit Test corrections and finished turning in the Unit Project, Paper Pool. They also discussed the ACE 1.2 homework. Students received more recent work, including tests, quizzes, and math reflections, to put into their portfolios. We started choosing works to discuss at parent-student-teacher conferences.

We also worked on Problem 1.3, What's the Change? Using starting temperatures, ending temperatures, and number lines, we figured out how to calculate the change in temperature. We found out that the change has 2 attributes: a value (like 140 degrees) and a direction (positive or negative. We practiced writing numbers sentences, or equations, for addition problems. Class notes may be downloaded for 7A or 7B.

LARGE GROUP
ACE 1.3 Homework
Please choose one of the options below to complete.

Option 1
Problems 20, 22, 24, 26, 28, 30-31 on pages 17-18
(Evens 20-30 plus 31)

Option 2
Problems 21, 23, 25, 27, 29, 31, 42-43 on pages 17-19
(Odds 21-31 plus 42-43)

Conference Prep.
Choose one strength & one challenge work to reflect on.

Due tomorrow, Tuesday, March 9.

SMALL GROUPS
Students worked with MaryBeth today. She collected Unit Test Corrections, student visualized the number line, located some positive and negative numbers on the visualized number line, and visualized the direction of positive and negative moves on the number line.

Students worked on Problem 1.2, From Sauna to Snowbank, and also did some work choosing Strength and Challenge Works to reflect on, to prepare for conferences.

7A SMALL GROUP HOMEWORK

1. Finish Portfolio Reflections

2. Finish Problem 1.2 on p. 10

3. ACE 1.2, p. 16, 9-19

Due tomorrow, Tuesday, March 9.

7B SMALL GROUP HOMEWORK
1. Finish Portfolio Reflections

2. ACE 1.2, p. 16, 9-19

Due tomorrow, Tuesday, March 9.

Unit Test Corrections & Conference Prep.

Today we all met together and went over the Unit Test answers and did more preparation for conferences. Class notes may be downloaded here (7A and 7B).

Homework

Please look at the problems marked with arrows on the Unit Test, and try again. You may use your notes, math book, and help from others. Please make your corrections in colored pencil! I will not accept corrections made in regular pencil, or erasing your work, because it is important to make your thinking before and after visible.

Corrections to the Unit Test are due Monday, March 8.

LARGE GROUP
If you would like an extension, you may turn it in on Monday, but you will need to do an especially good job to make up points, since projects turned in late will not get full points.

ACE 1.2 From Sauna to Snowbank & Paper Pool

LARGE GROUP
We talked about extremes of temperature, and how thermometers are a type of vertical number line. We worked on Problem 1.2, From Sauna to Snowbank, using number line models to answer each of the questions. For many students, using a representation like a number line was much harder than solving the problems themselves, but this is good practice for more complicated problems, as well as for graphing of all kinds. Class notes may be downloaded here for 7A or 7B.

Students who finished early worked on their Unit Projects, Paper Pool. We went over the requirements again.

· Title
· Name
· Date

12 point black font, double spaced
or
neatly handwritten, skipping lines

· Rules to predict number of hits
· Rules to predict pocket it will drop in
· Clear reasoning and examples to describe each rule
· Easy to follow, clearly organized report
· Handouts completed with drawings (although spreadsheet can substitute for the tables)

Unit Project: Paper Pool is due tomorrow.

LARGE GROUP
ACE 1.2 Homework
Please choose one of the options below to complete.

Option 1
Problems 9, 11-12, 14, 18-19 on pages 16-17

Option 2
Problems 10-11, 17-19, 41, and 50 on pages 16-20

Due tomorrow, Thursday, March 4.

ACE 1.1 Math Fever & Accentuate the Negative

LARGE GROUP
Today we discussed the Conference prep homework and the POW, Logic Puzzle. Students turned in their old books and received books for our new unit, Accentuate the Negative. We had an introduction to integers (whole numbers and their opposites, which sum to zero, including zero) and rational numbers (integers as well as fractions and their opposites, these numbers can be expressed as an integer divided by another integer, except zero).

Students worked on Problem 1.1, Playing Math Fever, which looks at positive and negative scores from a Jeopardy like game. Click the class name to download class notes here (7A or 7B).

LARGE GROUP HOMEWORK: ACE 1.1
Please choose one of the options below to complete.

Option 1
Problems 5-8 and 48 on pages 16-20

Option 2
Problems 6-8, 39, and 48 on pages 16-20

Give your parents the letter describing the new unit! You can download the letter here.

Due tomorrow, Wednesday, March 3.

SMALL GROUPS
Students finished their Unit Tests. Then they worked with Cory on the introduction to Accentuate the Negative (see above), and positive and negative numbers.

7A SMALL GROUP HOMEWORK
No homework tonight.

7B SMALL GROUP HOMEWORK
Please give your parents the letter describing the new unit! You can download it here.

Conference Prep, Unit Test, and more Paper Pool Unit Project

LARGE & SMALL GROUPS
Today we went over the Looking Back, Looking Ahead homework, to make sure we were clear on the answers. Small groups worked with MaryBeth, large groups with Sima. Then we went over the new homework (below), and we took the unit test.

LARGE & SMALL GROUP HOMEWORK
New homework to prepare for the Parent-Student-Teacher conferences on March 11 and 12 was given out. This asks you to look at strengths and challenges in math, since the last conference, focusing on the last 2 units: Stretching & Shrinking and Comparing & Scaling. Please fill out the handout with strengths and challenges with things, ideas/concepts, and skills as specifically as possible. Below are some examples.

Things: homework, quizzes, projects; be specific: which ones?

Ideas/concepts: setting up a proportion, making a comparison statement, that similar figures have equal angles and corresponding sides related by a scale factor

Skills: solving a proportion with scale factors or cross multiplication, solving for a missing side length, graphing a figure using coordinate information, writing equations

You may download a copy of the handout here.

Due tomorrow, Tuesday, March 2.

LARGE GROUP
We also discussed the Unit Project, Paper Pool, which is due this Thursday, March 4. I showed examples of tables and graphs for the project. We discussed that these should be graphed with one dimension (height or width) constant and this indicated in the title of the graph, the other dimension on the x axis, and the number of hits on the y axis. An example graph in PowerPoint may be downloaded here, and class notes may be downloaded here.

Math Reflections 4, Looking Back & Looking Ahead

Today we met as a whole class, and discussed Math Reflections 4 on page 62. Then some students prepared for math night, while others started work on the Looking Back, Looking Ahead work on pages 65-67, to prepare for the Unit Test on Monday. Class notes may be downloaded here.

LARGE & SMALL GROUP HOMEWORK

Finish Math Reflections 4, questions 1-3, on page 62.
Finish the Looking Back, Looking Ahead on pages 65-67.

Study for the Unit Test.

Due Monday, March 1.

LARGE GROUP ONLY
Don't forget that the POW is also due Monday, March 1.

Unit Project: Paper Pool & ACE 4.3

Today we talked about Math Night, which is tomorrow, Thursday, February 25 from 6:00-7:30 p.m. Some students said that they will be able to attend with their families, and everyone voted on their favorite POW's from this year. Students will be sharing the problems with their families, and we will be playing a couple of fun games as a group, including the popular game Skunk!

LARGE GROUP ONLY
The large group worked on the new Comparing and Scaling unit project, Paper Pool. We played the game online here. Students explored how many times the ball would hit and what pockets it would go into depending on the dimensions of the table in small groups. The handout describing the project is here.

LARGE GROUP HOMEWORK
Each person should write a report for homework with these 5 parts:
1. A summary of the rules you found, why you think your rules are correct, and anything else you discovered. You might discuss what you noticed as you examined the paths for the different tables and what helped you to arrive at your rules.
2. A drawing of at least one new Paper Pool table (not that is not on the “Paper Pool Tables” activity sheet) for each rule you identified. The drawing should demonstrate that your rule accurately predicts what will happen.
3. Your drawings of the ball’s path on each Paper Pool Table on the “Paper Pool Table” activity sheet as well as any other Paper Pool tables you constructed to help you derive your rules.
4. Any tables, charts, or other tools you used to organize your information.
5. An explanation of any other patterns you found or ideas you have about Paper Pool tables and the path of the ball. (For example, on which tables does the ball’s path follow similar paths? On which tables does the path of the ball look the same?)

Extension Questions (Extra Challenge Bonus)
Can you predict the length of the ball’s path on any size Paper Pool table? Each time the ball crosses a square, it travels 1 diagonal unit. How many diagonal units will the ball’s path cover?

Due next Thursday, March 4.

Remember that the POW: Logic Puzzle is also due Monday, March 1.

Study for the Unit Test, which will be Monday, March 1.

SMALL GROUPS
Cory worked with students on finishing problem 4.2, and they started problem 4.3.

SMALL GROUP ACE HOMEWORK
Problems 4, 15, and 18 on pages 55-57

Due tomorrow, Thursday, Feb. 26.

ACE 4.3: Developing Strategies for Solving Proportions

LARGE GROUP
We discussed Problem 4.3, Developing Strategies for Solving Proportions. There are 3 main strategies: scale factors, unit rates, and rate tables. We tried each one, and developed an algorithm for solving for an unknown. Multiplication/Division fact families turn out to be a useful way to think about solving for unknowns, using the properties of inverse operations, for example, in problem D. Class notes may be downloaded here.

LARGE GROUP
ACE 4.3 Homework
Please choose one of the options below to complete.

Option 1
Problems 6, 8, 10, 12, 24, 27 on pages 56-61

Option 2
Problems 7, 9, 11, 13, 24, 28 on pages 56-61

Due tomorrow, Wednesday, February 24.

For problem 28, you may need to do some research on how Congress works. There is some good information at http://www.congresslink.org/print_basics_bicameralism.htm.

SMALL GROUPS
Cory went over problem 4.1 homework. She also went over the Partner Quiz corrections. Students started working on Problem 4.2.

SMALL GROUP
ACE homework

ACC2 and problem 5-9 on page 56.
You can download ACC2 here.

Partner Quiz corrections in colored pencil are also due.

Due tomorrow, Wednesday, February 24.

POW: Logic Puzzles

Please choose one of the 2 options on the Problem of the Week, Logic Puzzles, to complete. You may download the handout here.

Due Monday, March 1.

ACE 4.2 Everyday Proportions & Partner Quiz Corrections

LARGE GROUP
Today we got the Partner Quizzes back and discussed the answers. We also discussed our answers for Problem 4.1, which we had done on Thursday, and how to solve these as proportions. Finally, we worked on Problem 4.2, Everyday Use of Proportions, on pages 52-53. We discussed our answers for these rules of thumb. You may download 7A class notes or 7B class notes.

LARGE GROUP HOMEWORK
Partner Quiz Homework
Please make corrections in colored pencil, without writing over or erasing your previous answers.

ACE 4.2 Homework
Problems 3-5, 19-20, and 25-26 on pages 55-60

Due tomorrow, Tuesday, February 23.

SMALL GROUPS
MaryBeth went over the homework skill sheet, Solving Proportions. Then students started working on Problem 4.1.

7A SMALL GROUP HOMEWORK
Finish Problem 4.1 on pages 48-51.

Due tomorrow, Tuesday, February 23.

7B SMALL GROUP HOMEWORK
Finish Problem 4.1 on pages 48-51.
ACE 4.1 problem 1 on page 55.

Due tomorrow, Tuesday, February 23.

ACE 4.1 Proportions

LARGE GROUP
We discussed the last POW, Mean & Median, in class, and people shared various answers. Then we worked on Problem 4.1, Setting Up & Solving Proportions. A proportion is an equation stating that two ratios are equal, and we have worked with lots of different proportions over the past few months. We set up and solved many different kinds of proportions in different contexts. Class notes may be downloaded here.

LARGE GROUP
ACE 4.1 HOMEWORK
Please choose one of the options below to complete.

Option 1
Problems 1-2, 15-17 on pages 55-57

Option 2
Problems 1-2, 21-23 on pages 55-59

Due Monday, February 22.

SMALL GROUPS
Students took their Partner Quiz, about rates and unit rates today. Then they wrote a card defining proportions and how to find them.

SMALL GROUP HOMEWORK
Complete the Skill: Solving Proportions handout. You may download the handout here.

Due Monday, February 22.

Math Reflections 3

LARGE & SMALL GROUPS
We went over Math Reflections 3 in class. If you did not finish, please complete this for homework.

Due Thursday, February 18.

LARGE GROUP: Don't forget that the POW is also due that day.
We also took a Partner Quiz.

SMALL GROUPS
Cory went over the corrections to Check Up Quiz. If you did not finish, please complete this for homework. Be sure to make your corrections in colored pencil.

Study for the Partner Quiz.
Due Thursday, February 18.

Have a great break!

ACE 3.4: What does dividing tell you?

LARGE GROUPS
Today in the large group students received their Check Up Quizzes back, and we went over the correct answers.

We talked about problem 3.4, What does dividing tell you. The bottom line was to keep track of units when calculating unit rates. Class notes for 7A may be downloaded here, and for 7B here.

Large Group ACE 3.4 Homework

Please choose one of the options below to complete.

Option 1
Problems 12, 27-29, and 31 on pages 42-45

Option 2
Problems 12 and 29-32 on pages 42-45

Quiz Corrections
Please correct in colored pencil. Do not erase or write over your original answers.

Due tomorrow, Thursday, February 11.

SMALL GROUPS
In small groups, Cory went over 3.2 homework from Tuesday, and they worked on problems to figure out which is the better value, using unit rates. They worked on problem 3.3 A-B.

Small Group Homework
Problems 11-16 on pages 42-43

Due tomorrow, Thursday, February 11.

Scale & Scientific Notation

Today Cory and MaryBeth were not here, so we had math class together. In 7A, we checked homework, and the large group discussed our answers for problem 3.3. In 7B, we just checked homework.

Then we talked about scale, very large numbers, and powers of 10. We watched a video called Cosmic Voyage, that portrayed the size of the universe moving away from human scale out 26 powers of 10, and then portrayed very tiny things (smaller than an atom) moving in many powers of 10. You can see the video here.

Then we talked about scientific notation, as a way to write very small and very large numbers. We looked at the web site, The Scale of the Universe, that allowed us to zoom out interactively. It is worth playing this at home to see how small theoretical strings that make up matter are, and how large the universe is. Using handouts (you can download page 1 or page 2) we practiced writing very small and large numbers in scientific notation.

Class notes for 7A are here, and class notes for 7B are here.

7A Large Group ACE 3.3 Homework
Problems 9, 11 and 24-26 on pages 41-45.
Due tomorrow, Wednesday, February 9.

7A & 7B Homework (Large & small group)
Either page 1 or page 2 of the scientific notation work.
Due tomorrow, Wednesday, February 9.

Unit Rate Comparisons & POW: Mean & Median

LARGE GROUPS
Today we heard more Stretching & Shrinking Unit Project presentations, and we discussed the POW: Flags. Then we talked about how to calculate mean and median, two measures of center that allow us to analyze data. The POW this week is called Mean and Median, and can be downloaded here.

Finally, we worked on Problem 3.3, Comparing CD prices, where we calculated unit rates (price per CD) and wrote equations for different situations, including tax or shipping fees.

7A Large Group class notes may be downloaded here.
7B Large Group class notes may be downloaded here.

7A LARGE GROUP Homework
Finish Problem 3.3 on pages 36-37.
Due tomorrow, Tuesday, Feb. 9.

Complete one of the two problems for the POW: Mean & Median.
Due Thursday, Feb. 18.

7B LARGE GROUP Homework
Finish problem 3.3, part E on pages 36-37.
ACE 3.3: Problems 9, 11 and 24-26 on pages 41-45.
Due tomorrow, Tuesday, Feb. 9.

Complete one of the two problems for the POW: Mean & Median.
Due Thursday, Feb. 18.

SMALL GROUPS
Today we heard more Stretching & Shrinking Unit Project presentations, and MaryBeth worked with students on Unit Rate Comparisons in class. Then we worked on Problem 3.2, Time, Rate, and Distance.

7A SMALL GROUP Homework
Finish Problem 3.2 on page 35.
ACE 3.2: Problems 4-8 on page 41.
Due tomorrow, Tuesday, Feb. 9.

7B SMALL GROUP Homework
ACE 3.2: Problems 4-8 on page 41.
Due tomorrow, Tuesday, Feb. 9.

ACE 3.2: Time Rate & Distance

In the large group today we worked on Problem 3.2, Time, Rate & Distance, to calculate rates in miles per hour (speed). Class notes may be downloaded here.

LARGE GROUP
ACE 3.2 Homework

Please choose one of the options below to complete.

Option 1
Problems 4-8 and 10 on pages 41-42

Option 2
Problems 5, 10, 19-22 on pages 41-43

Due Monday, February 8.

Remember that the POW: Flags is due Monday as well.

7 A SMALL GROUP
Reviewed Homework, Finding and Using rates, from yesterday.
Started problem 3.1.

7A SMALL GROUP Homework
Finish Problem 3.1.

Due Monday, February 8.

7B SMALL GROUP
Reviewed Homework, Finding and Using rates, from yesterday.
Worked on and finished 3.1

7A SMALL GROUP Homework
Problems 1, 2, and 9 on pages 40-43

Due Monday, February 8.