Lesson+Plan

. __ Starter Activity __  For example:  1. I think of a number, subtract 7 and the answer is 16.  What is my number?   2. A stack of 50 sheets of card is 12 cm high.  How thick is one sheet of card?   3. In this diagram, the number in each  cell is formed by adding the two  numbers above it.  5  ||||    8   ||    7   ||   13   ||||    15   ||   28   ||   31   ||||    ?   ||    45   ||   ?   ||||    ?   ||   182   ||   31   ||||    n   || 45  ||   n + 31   |||| n + 45  || 182  ||  What if the top three numbers are swapped around?  What if you start with four numbers?   4. I think of a number, multiply it by 6 and add 1.  The answer is 37. What is my number? <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> 5. There are 26 biscuits altogether on two plates. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> The second plate has 8 fewer biscuits than the first plate. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> How many biscuits are there on each plate? <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">6. Find the angle // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">in a triangle with angles // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">, // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 10, // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 20. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> 7. Solve these equations: <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">a. // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 5 = 12 c. 7 // h //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 3 = 20 e. 2 // c //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 3 = 19 <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">b. 3 // m //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">= 18 d. 7 = 5 + 2 // z //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">f. 6 = 2 // p //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 8 <span style="font-family: MyriadPro-Regular; font-size: 10pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; font-size: 10pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; font-size: 10pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; font-size: 10pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> 8. There are 376 stones in three piles. The second pile <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> has 24 more stones than the first pile. The third pile <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> has twice as many stones as the second. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> How many stones are there in each pile? 9. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">On Dwain’s next birthday, half of his age will <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">be 16. How old is Dwain now? <span style="font-family: MyriadPro-Regular; font-size: 10pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> 10. Solve these equations: <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> a. 2.4 // z //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 5.9 = 14.3 <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> b. 5z – 7 = 13 – 3z <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">c. 4( // b //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 1) + 5( // b //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 1) = 100 <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> **<span style="font-family: MyriadPro-Regular; font-size: 16pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">A **<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">Solve these equations exactly. <span style="font-family: MyriadPro-Regular; font-size: 16pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">a. 7( // s //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 3) = 45 – 3(12 – // s //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">) <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">b. 3(2 // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 1) = 5(4a – 1) – 4(3 // a //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 2) <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">c. 2( // m //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 0.3) – 3( // m //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">– 1.3) = 4(3 // m //<span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">+ 3.1) <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">d. // 3⁄4(c – 1) = 1⁄2(5c – 3) // <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">e. //__ x – 3 __//// = __x – 2__ // // 2 3  // <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Solve these equations exactly. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Each has two solutions. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">a. <span style="font-family: MyriadPro-It; mso-bidi-font-family: MyriadPro-It; msobidifontfamily: MyriadPro-It; msotextraise: -3.0pt; position: relative; top: 3pt;">               <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> + 24 = 60 <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">b. 3 = <span style="font-family: MyriadPro-It; mso-bidi-font-family: MyriadPro-It; msobidifontfamily: MyriadPro-It; msotextraise: -12.0pt; position: relative; top: 12pt;"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> 11. Begin to use ** graphs ** and set up equations to solve simple problems involving direct proportion. <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Discuss practical examples of direct proportion, <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> such as: <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> • the number of euros you can buy for any amount in  <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> pounds sterling (no commission fee); <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> • the number of kilometres equal to a given number <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> of miles, assuming 8 km to every 5 miles; <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> • the cost of tennis balls, originally at ￡3 each, offered <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> at ￡2 each in a sale. For example, generate sets of <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> proportional pairs by multiplying and test successive <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> ratios to see if they are equal: <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Check by drawing a graph, using pencil and paper or  ** ICT ****<span style="font-family: MyriadPro-Regular; font-size: 16pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">. ** <span style="font-family: MyriadPro-Regular; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';">
 * To be Added **
 * __ Objectives __**
 * Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way) **
 * <span style="font-family: MyriadPro-Regular; font-size: 16pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Extension **
 * __<span style="font-family: MyriadPro-Regular; font-size: 16pt; mso-bidi-font-family: MyriadPro-Regular; mso-hansi-font-family: 'Times New Roman';"> Plenary __**