Math 7: Algebra Test Exemplars

Here are a few responses that were very thorough. Great work!

Math 7: Algebra Success Criteria for Unit Test

Math 7 Unit Test: Wednesday, December 19, 2012!

Okay Grade 7s we've been working on Algebra for the last month and it's time to put it all together to show what you've learned. You have all done a great job on Algebra this term. On The test you will be asked to:

•  model expressions
•  write expressions from word descriptions
• Solve equations by substituting variables
• Solve equations by creating a balance
• Use a table of values to solve equations

Learning Goal
By the end of the term I will be able to model algebraic expressions and solve algebraic equations using variables and constant rates

Success Criteria
To reach my learning goal I can...

• Use tiles and pictures to model algebraic expressions
• Understand that any letter (x,y,z) is a variable that can change
• Understand that a constant number does not change
• Use guess and check to solve an algebraic equation
• Use a table of values to solve an algebraic equation that involves rate of change

Please see the math wall examples and review Pencasts as a review. See Mr. C if you need extra help!

Math 7: Modelling Equations

Here is another way we can model equations. This time we can use pictures to help our minds make sense of algebra.

Mr.C Pencast
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Algebra and Cell Phones

After our discussion yesterday about Verizon. I thought we should actually look at how a data plan works mathematically. This is only a surface level look at the variable cost of using a cell phone, but it will get the discussion going.

A phone plan costs 55 dollars a month for 2GB of data. For every GB you use it is an extra $27.00 a month. Roaming charges and downloading will eat up your data plan quickly. If you plan to leave the country for a vacation your data will go through the roof. How could you figure out how much your monthly bill would be if you used 7GB in one month? What about 4GB in one month? What Algebraic expression would you use to find out how much the monthly bills would be? Let's try to get some thorough responses so we can pencast it!

Pencast: Math 6 Perimeter and Area

Mr. C Pencast
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Math Will Follow You Wherever You Go!

One day you will have a job of your very own. Rest assurred, math will come up, tap you on the shoulder and say, "Remember, me?" This is a phone conversation between Verizon mobile employees and a customer. Pay attention to the numbers that they are talking about. The customer claims that his bill is wrong. Who is right? How do you know?

Pencast: Math 7 Algebra Tiles

We've just completed our first assessment of what we know about now about algebra tiles and expressions. It is important to look at the feedback provided to you by your friends and then try using algebra tiles on a different expression. If you have forgotten some of the ideas we have been talking about in class please review the pencasts below. The pencast is supported by flash it will not work on your Apple device, I'm working on a solution!

MR. C Academy Pencast (will not play on apple devices)
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MR. C Academy Pencast
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Pencast: Math 6 Area and Perimeter Pencast

Today we looked at a problem in class:

Matteo bought a rectangular rug for his bedroom. The room has an area of 24 square meters. The label on the rug says 20 square meters, but the rug did not fit. How could this be?

This was an interesting problem that Nick, Marcus and I were working on together at the guided math table.

test
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Patterning: Winter's Coming, Yeah Snow Days!

Whether you like it or not Winter is coming. Every year It comes, without fail, which is of course a predictable pattern itself. One of the most exciting events that sometimes occurs with winter snowfalls is the Snow Day. Sometimes Snow Days are called the night before. How does our Director, Mr. Milloy know when to call a Snow Day? You guessed it...patterning! If he knows how much snow will accumulate hour to hour, then he will be able to predict when it will reach an unsafe level.

Try predicting the amount of snow that will fall yourself. What strategies could you use to figure out the pattern? How could you graph the amount of snow that will fall?

If the snow is 11 cm deep at 3 p.m. and 6 cm of snow falls each hour. How deep is the snow at 7 p.m.?

It's Algebra Time

Welcome to the world of Algebra! Algebra is one of the coolest ways to solve problems both in math and in real life. For instance, if Mars is 225,000,000 KM away from earth and the Space Shuttle travels at a speed of 38,500 KM/H how long will it take to get to the Red Planet? Or if One Direction had a concert in Hamilton at 7pm on a Saturday and they were in Japan on Thursday, when would they land in Toronto? If you can figure this out right now that is awesome, if you can't I guarantee you will be able to by the end of the unit.

Parachute Fun

Felix Baumgartner recently completed the highest free fall from space. Jumping was the easy part, the hard part was creating a parchute that would slow him down enough to get him to the ground safely.

Today you are a parachute designer. You will use plastic, scissors, twine, tape and a paperclip person!
Rules:
1. String can only by 30 cm in length
2. You must make two parachutes one a square with 10cm sides the other a square with 30cm sides
3. Attach your paperclip man to the parachute
4. Stand on a chair with a spotter
5. Let the parachute drop to the floor and time it with a stopwatch

What do you notice about the flight of each parachute? Which parachute stays airbourne longest?

Problem of the Week: Fibonacci Numbers

Leonardo Fibonacci

Leonardo Fibonacci was born in Italy way back in 1170. When Fibonacci began using numbers he used numbers just like everyone else in Italy at the time: III + IV = ???. Infact he was one of the first people in Europe to say, "hey there must be an easier way!"

As a young man he helped his father, a merchant, with the family business. As a merchant, Fibonacci travelled to Africa where he learned 3+4=7. It was the first time he encountered Arabic numbers. He loved them so much that he wrote a book to tell all of the Italy about the new numerical system.

Here's one of the first patterns he came up with:

0,1,1,2,3,5,8,13,21,34

Continue the pattern. What do you notice? How does it increase? Does it relate to Pascal's Triangle? Does it have a real world application?

Let the Trading Begin!

Every year on Halloween we go out looking for our favorite candy. What is your favorite candy? More importantly what is it worth to you. What would you trade in order to get your favorite? Consider this problem: If 3 lollipops count the same as 2 peanut butter cups, and you have 12 lollipops, how many peanut butter cups can you trade them for? Bonus: If someone offers you 10 peanut butter cups for 18 of your lollipops, are you getting enough candy in return for your loot? If this doesn't work for you devise your own trade using your own favorite candies. Source:http://bedtimemathproblem.org/

Will Frankensteinstorm Effect Halloween?

The news is telling us that a huge storm is on Its way. The Storm is thought to be one of the biggest on record. Some people are calling for Halloween to be moved until the storm passes. Should Halloween be postponed? How could our knowledge of science and math be applied to this problem?

Check Out Your Hometown!

Just thought you'd like to see a great video about the great City of Hamilton. Enjoy.

Problem of the Week: Pascal's Triangle

At the age of 13 a young Frenchman named Blaise Pascal was sitting around his house one day. He didn't have an iphone, he didn't have a computer, he didn't have an xbox, he only had his mind and a pencil. Can you continue Pascal's Triangle? What patterns do you notice?

A Tiny Zoo Problem

My favorite game App for my iphone is Tiny Zoo friends. My daughters and I have spent countless hours buying, feeding and taking care of the animals. I love seeing my zoo get bigger and bigger. Yes this is a silly obsession, but hey I like it!

In the game the animals are born and grow at different rates and they only start making you money once they start growing. Here's a Tiny Zoo problem to think about...

In the Tiny Zoo, a newborn Siberian Tiger weighs 1300g when it is born. It gains 100g a day. A newborn spider monkey weights 3300g when born and it gains 200g every week. Who weighs more after two weeks, who weighs more after 6 weeks? The big question is, which animal needs the most food after 6 weeks? Food costs money! Take it beyond math now. If you were a real zoo keeper how much food would you have to feed these animals, what would you feed them, how much would it cost to feed them? Where would you find the information?

***As always review our learning goal and success criteria.

Math 6: Patterning

Learning Goal

I will be able to identify patterns and their rules to decide if they are increasing or decreasing. I will also be able to make my own patterns and rules using different strategies.

Success Criteria

To achieve my learning goal I can…

·         Use my fingers to add and subtract to find the gap in numbers

·         Use a t-table to find how a pattern is increasing or decreasing

·         Use an input and output machine to create patterns and see what operations are being used

·         Draw and build patterns with concrete materials

·         Make rules to decide if a pattern is increasing or decreasing

·         Use all of my strategies to solve real world problems

Math 7: Perfect Squares

Check out what we noticed about square numbers. What do you notice about our figures?

Math 7: Could You Manage McDonald's?

We have been discussing factors and multiples. We have been seeing how numbers have a lot in common, but does this have anything to do with the real world? Let's take a look.

Learning Goal: I will be able to understand the difference between multiples and factors. I will produce multiples and factors for whole numbers, using a variety of tools and strategies.

Success Criteria:

• I can start at a number and skip count to find multiples
• I can use a 100s chart to count up by a number to find multiples
• I can compare the multiples of two or more numbers, by creating lists and using a 100s chart to identify the Least Common Multiple
• I can use mental math to find factors of a number
• I can use a 12x12 chart to find the factors of a number
• I can use a calculator to divide numbers to find factors
• I can compare the factors of two or more numbers to identify the Greatest Common Factor
• I can use my personal device and google, calendars and any other apps that will help me solve real world problems

The Problem
You are the manager of McDonald's. Kevin, Alison and Fred work part-time at McDonald's. Kevin works every second day. Alison works every third day. Fred works every fourth day. Today they all worked together, when will they work together again? They need to know so they can drive in together. You need to make a schedule for these three workers. Use any tools or strategies that may work.

Factors and Venn Diagrams

Remember to organize factors by listing numbers in order. Circle all common factors and identify GCF. Remember factors are two numbers that make a product.

Math 6: Patterning

This week we are looking at inputs and outputs to identify patterns. Also, Jeffrey helped me with my splitting fence post problem. You are going to be a great carpenter some day Jeffrey.

Math 7: Factoring

Today we began looking at how numbers can be broken down into manageable chunks. We explored both prime numbers and composite numbers.

Homework: on your chart from class fill in each square until you arrive at 100. When you are done shade in all the prime numbers. Use the math wall for help.

One Direction at Cardinal Heights?

One Direction's manager, Sid Smeal called me last night. He's looking for a middle school for the band to do a show in. He needs to know the specifications of the gym and seating arrangements pronto.

Today's Learning goal: Operation One Direction
Today I will...

• I will organize a concert
• Use an open array to solve a real-life concert emergency
• Use a different strategy to check if my solution makes sense
• make use of friendly numbers so I can communicate my ideas to Sid Smeal and the class

This is a ficticious problem. There is no way that One Direction is coming here. Or are they?

Problem of the week

Each week we will have a problem of the week to solve. It will be handed out Monday and explored on Friday. Students should work on it in class or on their own time in preparation for Friday.

Hard At Work

Our learning goal over the past few days has been to create a variety of multiplication strategies to make numbers more friendly. Some of our favorite strategies are: strings, closed arrays and open arrays.

Never Underestimate What You Can Accomplish

Life isn't always easy. Sometimes things are going to get tough for you. Maybe something is hard for you in math class, maybe things are tough on the playground, maybe things aren't going well with friends. Just like Arthur, you will fall many times, but you can always get back up and try again. Remember what Arthur says..."Just because I can't do it today, it doesn't mean I'm not going to be able to do it someday!" You can do anything in this life, you just have to have the desire and the courage to try. I believe in you. You just have to believe in YOU!

Pumpkin Problem Solving

You all know about my fascination with pumpkins. Every weekend from September until October 31st I will be found with my two children At Howell's Pumpking Farm running in corn mazes, sitting on a hay ride and trying to trick Grace and Charlotte into going into the spook barn.

But although Howell's Pumpkin Patch is intended to be a fun family experience, it's also intended to be a money maker.

Today we started off with a problem. Owner, Jerry Howell is trying to organize his pumpkins. He has harvested 120 pumpkins total and would like them organized in rows and columns. What are the ways he can arrange these pumpkins? You can use interlocking cubes, your personal electronic devices, markers and chart paper, but you must show your thinking.

This is only the beginning, by the end of the week we will add more layers to this question. Our goal this week is to begin to create a model for the way we will solve problems in Mr. C's Math Academy!

Happy Harvesting.

Arrange these pumpkins so they will be easy to sell!

You're Out Of Order!

This week the Grade 7s are learning about Order of Operations. We have spent time asking questions such as: how come my calculator is wrong, why is BEDMAS unreliable and why does Mr. Child keep referring to brackets as the UFC fighter of the math world?

In class we begin each new topic by "Getting Started", we look at a problem and work as a team to search for solutions. Sometimes we know the answer right away, sometimes we activate our prior knowledge by thinking about past lessons, sometimes we just take a chance and try our best to come up with something to contribute.

Our next step is to discuss our findings as a class and to build our "Math Wall". It is messy and imperfect but it helps us to develop ideas as a group and build upon the thoughts of everyone in the class.

Math Wall: Building Rules for Order of Operations

Raft Rally

During the week of September 10th we had our first problem solving task in Mr. C's Math Academy. We were challenged with a learning goal: in teams, create a raft out of a 20cm x 20cm square of tin foil and four plastic straws. The only tool permitted was a pair of scissors. Students had 20 minutes to build their raft before it was launched in "Lake Child"

Each team did a great job and had fun in the process. The winning raft was able to hold 112 pennies. The prize...112 pennies! Hey Mimi I hoped you split your winnings with your teammates. Who says school doesn't pay?

The Famous "Lake Child" Brought Mysteriously By Fairies

Welcome To Mr. C's Math Academy!

Hi Everyone,

Thanks for checking out our blog. On this blog I will post information about the daily happenings at Mr. C's Math Academy located in Room 3 at Cardinal Heights Middle School. This blog is for both students and parents to get a look at what is going on.

I will be posting specifically about classes 63, 71, 72 and 73. So if you are away or need to check out what we recently covered it will all be on this blog.