Minds+On


 * Grade 7 & 8 Mathematics Topics - Minds On Ideas**

** Pythagorean Theorem **
Have a piece of graph paper on every desk before students get into the classroom. Have written on the board: "What do the numbers 4, 9, and 16 have in common?" After this, take it up with the class and then move into the lesson.
 * Squares and Squareroots**

**SRI: Square Root Intelligence (//Nakesha)// ** //Preparation// //The Activity//
 *  Gather/create enough cards for each student (use two different colours; an equal amount of each)
 *  Pair each card with a different coloured card
 *  On one pair, write a perfect square; on the other pair, write the square root of the perfect square (e.g. Card 1 reads "9" and Card 2 reads "3"); do the same for the rest of the cards, using different perfect squares/square roots for each pair
 *  Take a separate sheet of paper and cut it into small strips (the strips should be large enough for you to write a number on them)
 *  Write a different non-perfect square on each slip of paper; make enough for each pair of students
 *  Fold the slips in half and place them in a paper bag
 *  Give each student a coloured card and tell the students with a perfect square to find the person who has the square root of the perfect square they're holding
 *  Once students find their partner, have one person from the pair pull a slip of paper out of the paper bag (without looking into the bag)
 *  Give each pair about five minutes to find the square root of the number on their slip (without using a calculator!); tell them to write their solution in their notebook, explaining how they found their answer (e.g. pictures, numbers and words)
 *  Ask a few students to share their solutions with the class; try to ask for different methods each time

Up to now, we have worked with squaring numbers and square roots of numbers. Today, we are going to begin observing an actual theorem that is based on these ideas. This theory is actually a cornerstone theory and you will build more on it in high school. Not only does it have bases in math, science and engineering, but basic building ideas if you have your mind set on construction, etc… You have all brought in a right angle triangle (have some incase students didn’t). We will be measuring the sides of these objects and filling in the below table, where A, B and C are the defined side lengths (instruct which sides should be A, B, C): After measuring 3-4 Shapes, have students look for a pattern in the side lengths
 * Measuring Triangles**
 * ~ **Shape** ||~ **A Length** ||~ **B Length** ||~ **C Length** ||~ **A+B** ||~ **A2** ||~ **B2** ||~ **C2** ||~ **A2+B2** ||

**Integers**
Please use the following two decoders to decode the poem into math sign rules for multiplication and division : (//Yana Ma//) Decoders: Hate = negative Love =positive Poem: Love or Hate
 * Integer Poem **

If you Love to Love then you Love. ( a positive times a positive equals a positive) If you Love to Hate then you Hate. (a positive times a negative equals a negative) If you Hate to Love then you Hate. (a negative times a positive equals a negative) If you Hate to Hate then you Love (a negative times a negative equals a positive)

** Fractions **
Have the class stand up and congregate in the centre of the classroom. Ask them to split themselves in half; direct where the split will be made if necessary. Pose the question "How many groups are there now in the room?" The students can see that there are two groups in the room. Let them know that they just witnessed a whole number being divided by a fraction, and show it numerically on the board: 1 (class) / 1/2 = 2 (groups). Repeat the exercise by asking the class to split themselves in thirds, and quarters. Do they notice any patterns?
 * Dividing Fractions and Whole Numbers (Alex Willison)**

Challenge question. What if we started with two classes? How would this change the answers?

Here's a short video of a Minds-ON discovery exercise for dividing fractions. I made a video because the topic is best presented as a teacher-guided exercise. It's also my first pathetic attempt at using Smart Notebook, so don't laugh too hard. []
 * Dividing Fractions (Steve Riche)**

** Area and Volume **
**Creating a Triangular Prism (By: Chris Marbbn)** Print off a class set of triangular prism nets and have a large one to display in front of class. The teacher will have the larger one and will construct it along with the students. In addition, I could have examples of other types of prisms (i.e. cubes, rectangular prism, pyramidal prism) and explain the differences. So we have two different sized glasses (see below), and you have to give one to yourself and one to your little brother or sister so you can both have a glass of chocolate milk. Which glass has a larger volume so that way you get more chocolate milk than your little brother or sister?
 * Chocolate Milk Problem**

I want you right now to think in your head if you think the short cup has a larger volume, or if you think the tall cup has a larger volume or the two cups have the same volume. I want you to move to the sign in the classroom which lists the decision you came up with. You and the other people who had the same idea as you have 5 minutes to try and find out if you are right. Next, a sk the students if any groups found out which cup has the larger volume. Show the students using water that actually the two cups have the same volume,

 (See image at: []) How many rectangular prisms would be required to make the general shape of this building? (Don’t worry about windows or doors.) Bonus: How rectangular prism surfaces are visible in this picture?
 * Building Problem: Surface Area of Rectangular Prisms (Vicki)**

** Decimals and Ratios **
A question to go on the board. Mary wants to make a cake. The recipe she has makes enough for 8 people, however, Mary wants to make enough cake for 24 people. The recipe for 8 people says to use 1 egg, 2 cups of flour and 1 cup of sugar. In order to make the cake for 24 people, how many eggs will she need? How many cups of flour will she need? How many cups of sugar? 8 times 3 equals 24 so multiply the amount eggs, flour and sugar by three. You will end up 3 eggs, 6 cups of flour and 3 cups of sugar.
 * Equivalent Ratios**

** Equations **
**Legs Problem** Question: There are 44 legs in the room. People are sitting on stools with 3 legs, around one table with 4 legs. There are no empty stools. How many people are around the table? Answer: 5x + 4 = 44 Therefore there are 8 people in the room. (Students will figure this problem out in many different ways!)  ==**** Challenging Question ** ** == For my topic, I have decided to go with a challenge question. I don't necessarily expect any student to figure it out (although I am sure a few will, they always do) but I want them to want to figure out the answer. The content is a bit cheesy humourous but I can live with making fun of myself if it gets the class involved.

// So I was foolish and waited till the end of July to buy my copy of Eclipse to read on the plane ride. The book already cost 15 dollars before tax. So now instead of charging me only the PST which was 8% tax, I now have to pay 13% tax. How much would I have saved by buying the book before July? //