Intermediate Math: Targeted Implemented Planning Supports for Revised Math (TIPS4RM).
TIPS4RM are the Guide to Effective Instruction for Middle School. They offer interesting lessons and activities for students.

To download TIPS4RM for Grade 7 please click here
To download TIPS4RM for Grade 8 please click here

Homework Help Line Information Sheet for Grade 7-10

Want to know more about how the differentiate your instruction for Grade 7/8 students?
Then check out this brochure put out by the Ministry of Ontario: Brochure
Great Video by Dan Meyer discussing why we need to change the Math Classroom click here

Geometer's Sketch Pad on Math Gains, for Tutorials and Activities for Grade 7 and 8 click here

Developing Mathematical Literacy: TIPS4RM put out this document to help teachers develop and implement the Three Part Lesson into their math classroom which promotes math talk and the sharing of mathematical ideas.

GIZMOS: Please check out Gizmos for your students. Gizmos are online simulations for students in Grade 3 -12 for math and science. Please contact Evelyn Heath at Evelyn.Heath@tdsb.on.ca to get set up on Gizmos.

Grade 8:
Students design a rollercoaster or skateboard park using circles. They use circumference and area formulas to find the length of the coaster and the area underneath it. At first it seems complicated but once they get started they get. I have to keep reminding them to keep it simple! I've attached the outline, the rubric and my examples. I will have the students examples up shortly. Submitted by Sudeep Sanyal, Karen Kain School of the Arts.

Diagnostic, Assessment For & Of Learning: The Diagnostic was taken from the Grade 7 Ministry Exemplars, the Mid-Point and Final Assessment were taken from Susan O'Connell's, The Math Process Series, Reasoning and Proving. Example Pieces of Work Title: A Dicey Situation Grade(s): 7 & 8 Strand(s): Data Management & Probability Problem:
Jamie made up a new dice game. Two players each roll an ordinary six-sided die. Of the two numbers shown, the smaller number is subtracted from the larger. Scoring:- If the difference is 0, 1, or 2, player A gets 1 point.- If the difference is 3, 4, or 5, player B gets 1 point.
The game ends after 12 rounds. The player with the most points wins the game.
A) If you are given the choice of being Player A or Player B, which would you pick, assuming you want to win? (Remember to explain all the steps you use in making your decision.)
B) Describe another way of scoring that is fair for this game of differences. Explain how you know it is fair.

What to look for: Students should be given the opportunity to play the game with a partner. Level four students might make the connection immediately as to who is more likely to win, but they can still be expected to calculate the individual probabilities.

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Posted by: Mark Ross, Norseman JMS Title: The Monty Hall Problem Grade(s): 8, 7 and 6 Strand(s): Data Management & Probability, Number Sense (fractions) Problem:
You are on a game show and you are presented with a choice of 3 doors. Behind one is a luxury car, and behind the two others are nothing. The game show host asks you to pick one of the doors.
After you select one, and as part of the game, the host opens an unpicked door which he knows to be empty. You are asked if you would like to keep the door that you chose, or switch your choice to the remaining unopened door.
Should you switch? Why or why not?

What to look for: This problem can be examined by using a tree diagram. If computers are available, students may try the link below. It is a Monty Hall Problem simulator that works quite well and keeps track of their choices so that they can work out the probabilities on the go. Links:http://www.grand-illusions.com/simulator/montysim.htm Links:http://www.youtube.com/watch?v=mhlc7peGlGg (an excellent 5 minute video providing a full explanation of the answer).

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Posted by: Mark Ross, Norseman JMS Title: Squares & Circles Grade(s): 8 Strand(s): Measurement Problem:This is simply an extra worksheet that can be used for students to practice and apply the formulas for area and circumference of circles. What to look for: Questions 12-15 can be quite tricky. Their solutions require students to divide the square into triangles and apply the formula for the area of a triangle. If they are not prompted beforehand they will often miss this point.

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Posted by: Mark Ross, Norseman JMS Title: Burning Candle Grade(s): 8,7 Strand(s): Data Management & Probability Problem:
Candle manufacturer companies advertise that their products are better quality and have the longest mean burning times. John decides to select same size candles form three different companies, Bright Candle, Fire Candle and Shiny Candle – and do an experiment with 15 candles in order to test which company has a better product. He recorded the number of minutes that each candle burned. (see .pdf for list of values and remainder of question). What to look for: This question can be used to prompt a discussion about the most appropriate measure of central tendency (mean, median and mode).

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Posted by: Mark Ross, Norseman JMS Title: Painted Cubes Grade(s): 8,7,6 Strand(s): Patterning & Algebra, Number Sense Problem:
A toy company wants to create and sell a game that uses solid colored cubes of varying sizes. They use smaller cube-a-links to create (solid) cubes that are 2x2x2, 3x3x3, 4x4x4 and so on.
Once the larger cubes are created, they are dipped (fully) into red paint, so that the outsides are painted entirely red.
The company wants to keep track of the paint they use, but they must first know how many cube-a-link faces are painted.

Size of large cube

# of small cubes with 3 red faces

# of small cubes with 2 red faces

# of small cubes with 1 red face

# of small cubes with 0 red faces

Total # of small cubes

2x2x2

3x3x3

4x4x4

5x5x5

6x6x6

10x10x10

nxnxn

Can you see the patterns in the table?
Can you generalize these patterns (create equations predicting how many cubes with 3, 2,1,0 and total) for a large cube nxnxn?
How are those equations (or columns) related to what you see?

What to look for: Generalized patterns can be observed by completing the missing values in each column. (Each column generates a separate equation). The nice part about this problem is that it affords an opportunity to relate the equations to visual patterns.

(TIPS4RM).TIPS4RM are the Guide to Effective Instruction for Middle School. They offer interesting lessons and activities for students.

To download TIPS4RM for Grade 7 please click here

To download TIPS4RM for Grade 8 please click here

Homework Help Line Information Sheet for Grade 7-10

Want to know more about how the differentiate your instruction for Grade 7/8 students?

Then check out this brochure put out by the Ministry of Ontario: Brochure

Great Video by Dan Meyer discussing why we need to change the Math Classroom click here

Geometer's Sketch Pad on Math Gains, for Tutorials and Activities for Grade 7 and 8 click here

Developing Mathematical Literacy: TIPS4RM put out this document to help teachers develop and implement the Three Part Lesson into their math classroom which promotes math talk and the sharing of mathematical ideas.

GIZMOS: Please check out Gizmos for your students. Gizmos are online simulations for students in Grade 3 -12 for math and science. Please contact Evelyn Heath at Evelyn.Heath@tdsb.on.ca to get set up on Gizmos.

Grade 8:

Students design a rollercoaster or skateboard park using circles. They use circumference and area formulas to find the length of the coaster and the area underneath it. At first it seems complicated but once they get started they get. I have to keep reminding them to keep it simple! I've attached the outline, the rubric and my examples. I will have the students examples up shortly. Submitted by Sudeep Sanyal, Karen Kain School of the Arts.

Lanor Exemplars for Grade 7 Patterning:Diagnostic, Assessment For & Of Learning: The Diagnostic was taken from the Grade 7 Ministry Exemplars, the Mid-Point and Final Assessment were taken from Susan O'Connell's, The Math Process Series, Reasoning and Proving.

Example Pieces of Work

Title:A Dicey SituationGrade(s):7 & 8Strand(s):Data Management & ProbabilityProblem:Jamie made up a new dice game. Two players each roll an ordinary six-sided die. Of the two numbers shown, the smaller number is subtracted from the larger.

Scoring:-If the difference is 0, 1, or 2, player A gets 1 point.- If the difference is 3, 4, or 5, player B gets 1 point.The game ends after 12 rounds. The player with the most points wins the game.

A) If you are given the choice of being Player A or Player B, which would you pick, assuming you want to win? (Remember to explain all the steps you use in making your decision.)

B) Describe another way of scoring that is fair for this game of differences. Explain how you know it is fair.

What to look for:Students should be given the opportunity to play the game with a partner. Level four students might make the connection immediately as to who is more likely to win, but they can still be expected to calculate the individual probabilities.Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMSTitle:The Monty Hall ProblemGrade(s):8, 7 and 6Strand(s):Data Management & Probability, Number Sense (fractions)Problem:You are on a game show and you are presented with a choice of 3 doors. Behind one is a luxury car, and behind the two others are nothing. The game show host asks you to pick one of the doors.

After you select one, and as part of the game, the host opens an unpicked door which he knows to be empty. You are asked if you would like to keep the door that you chose, or switch your choice to the remaining unopened door.

Should you switch? Why or why not?

What to look for: This problem can be examined by using a tree diagram. If computers are available, students may try the link below. It is a Monty Hall Problem simulator that works quite well and keeps track of their choices so that they can work out the probabilities on the go.Links:http://www.grand-illusions.com/simulator/montysim.htmLinks:http://www.youtube.com/watch?v=mhlc7peGlGg (an excellent 5 minute video providing a full explanation of the answer).Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMSTitle:Squares & CirclesGrade(s):8Strand(s):MeasurementProblem:This is simply an extra worksheet that can be used for students to practice and apply the formulas for area and circumference of circles.What to look for:Questions 12-15 can be quite tricky. Their solutions require students to divide the square into triangles and apply the formula for the area of a triangle. If they are not prompted beforehand they will often miss this point.Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMSTitle:Burning CandleGrade(s):8,7Strand(s):Data Management & ProbabilityProblem:Candle manufacturer companies advertise that their products are better quality and have the longest mean burning times. John decides to select same size candles form three different companies, Bright Candle, Fire Candle and Shiny Candle – and do an experiment with 15 candles in order to test which company has a better product. He recorded the number of minutes that each candle burned.

(see .pdf for list of values and remainder of question).What to look for:This question can be used to prompt a discussion about the most appropriate measure of central tendency (mean, median and mode).Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMSTitle:Painted CubesGrade(s):8,7,6Strand(s):Patterning & Algebra, Number SenseProblem:A toy company wants to create and sell a game that uses solid colored cubes of varying sizes. They use smaller cube-a-links to create (solid) cubes that are 2x2x2, 3x3x3, 4x4x4 and so on.

Once the larger cubes are created, they are dipped (fully) into red paint, so that the outsides are painted entirely red.

The company wants to keep track of the paint they use, but they must first know how many cube-a-link faces are painted.

Size of large cube# of small cubes with 3 red faces# of small cubes with 2 red faces# of small cubes with 1 red face# of small cubes with 0 red facesTotal # of small cubes2x2x23x3x34x4x45x5x56x6x610x10x10nxnxnCan you generalize these patterns (create equations predicting how many cubes with 3, 2,1,0 and total) for a large cube nxnxn?

How are those equations (or columns) related to what you see?

What to look for:Generalized patterns can be observed by completing the missing values in each column. (Each column generates a separate equation). The nice part about this problem is that it affords an opportunity to relate the equations to visual patterns.Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Posted by:Mark Ross, Norseman JMS