Starter – Algebraic Pyramid Challenge 6d + 7e -x - 6y 2d + 4e 4d + 3e -2x - 3y -3y + x d d +4e 3d - e -2x -3y x -7d - 2e -5d - e -e – 2d -5d -e -2d

Top 3 HW HW Quiz

Homework Quiz Write expressions for all 4 questions below. Patrick decided to go jogging each morning. As a results, he lost 6 kg. If he initially weighed w kg, how much does he weigh now? Find the change from $100 when buying h hammers at $15 each. Frank buys b balls at $m each and r racquets at $n each. Find the total cost. Rick is now 14 years old. How old was he x years ago?

Homework Quiz Write expressions for all 4 questions below. Patrick decided to go jogging each morning. As a results, he lost 6 kg. If he initially weighed w kg, how much does he weigh now? Find the change from $100 when buying h hammers at $p each. Frank buys b balls at $m each and r racquets at $n each. Find the total cost. Laura buys a apricots and p peaches. Find the cost (in dollars) if each apricot is 60 cents and each peach is 90 cents.

4E – Algebraic Substitution I can: Evaluate an algebraic expression by substituting values for the variables.

Example 1: Substitution We can evaluate the expression 4 + 3n by substituting different values for n. 4 + 3n When n = 5 = 4 + 3 × 5 = 4 + 15 = 19 Example 1: When n = 11 4 + 3n Ask pupils to think about the activity they were doing at the start of the lesson. What we were actually doing was a kind of substitution. We were replacing a symbol (the box) with a number each time. Ask pupils how we could write 4 + 3 ×  as an algebraic expression. It doesn’t matter what letter they use but do remind pupils that we don’t write the multiplication sign in algebra. Define the keyword, evaluate – to find the value of. Discuss the substitution and order of operations: When n is 5, what is 3n? (15) So what is 4 + 3n? (4 + 15 = 19) Suggest to pupils that they may wish to work out the value of 3n before writing anything down. This would avoid errors involving order of operations. In other words, they can write 4 + 3n = 4 + 15 and leave out the intermediate step of 4 + 3 × 5. This might be incorrectly evaluated to 35. (We have written 4 + 3 × 5 on the board to reinforce the meaning of 3n). = 4 + 3 × 11 = 4 + 33 = 37

Example 2: Example 3: Substitution 7n 2 = 7 × 10 2 When n = 10 = 70 2 = 35 Example 3: n2 + 6 Stress that when we are multiplying and dividing, it doesn’t matter what order we do it in. For example 7 × 4 ÷ 2 will always give the same answer as 4 ÷ 2 × 7. (The order is important when we combine multiplying and dividing with adding and subtracting. If there aren’t any brackets we always multiply or divide before we add or subtract.) When n = 0.6 = 0.62 + 6 = 0.36 + 6 = 6.36

Example 4: Substitution 2(n + 8) When n = 13 = 2 (13 + 8) = 2 × 21 = 42 Remind pupils again that when there are brackets we need to work out the value inside the brackets before we multiply.

Substitution exercise Evaluate these expressions when a = 5, b = 2 and c = –1 5) 3a + 2c 7) a b2 – c = 3 × 5 + 2 × –1 = 15 – 2 5 22 – (–1) = = 13 6) a(b + c) = 5 5 Tell pupils that expressions can contain many different variables. Remember when we use a letter to represent a number in an expression it can have any value. The value can vary and so we call it a variable. If pupils are ready you may wish to use the above examples as a pupil exercise before revealing the solutions. Alternatively, talk through each example stressing the correct order of operations each time. Then set pupils an exercise made up of similar problems. Edit the slide to make the numbers being substituted more or less challenging. = 5 (2 + –1) = 1 = 5 × 1 = 5

Independent Practice Finish Murder Mystery activity Investigation - Equal Expressions, p85 p83 - 84  #1 – 7 REMINDERS Chapter 4 test reminder (4A – 4G) View Ch.1 Tests during extra help times

Starter WWK Algebraic products – products that contain at least one variable

Math Investigation Answers

Top 3 HW HW Quiz

4. 1. 2. 3. 5. Homework Quiz a(b2 – 4) 6. Evaluate Complete 5 of the 6 questions. Evaluate #1 - 3 when j = 5, k = -3, l = 2, m = 4 Evaluate #4 - 5 when x = -1, y = 4, z = -2 4. 5. 1. 2. 3. a(b2 – 4) 6. Evaluate when a = -1 and b = 5

4. 2x + y 1. 2. 3. 5. Homework Quiz a(b2 – 4) 6. Evaluate Complete 5 of the 6 questions. Evaluate #1 - 3 when j = 5, k = -3, l = 2, m = 4 Evaluate #4 - 5 when x = -1, y = 4, z = -2 4. 2x + y 5. 1. 2. 3. a(b2 – 4) 6. Evaluate when a = 4 and b = 2

4F – Algebraic Products I can: Simplify algebraic products.

4F – Algebraic Products We can use index notation to simplify expressions. 3p × 2p Example 1: Example 3: 9xy3 × 3x2y = 3 × p × 2 × p = 6p2 Example 2: 3r × r2 Example 4: (4g)2 × g = 3 × r × r × r Discuss each example briefly. In the last example 2t × 2t the use of brackets may need further clarification. We must put a bracket around the 2t since both the 2 and the t are squared. If we wrote 2t2, then only the t would be squared. Give a numerical example, if necessary. If t was 3 then 2t would be equal to 6. We would then have 62, 36. If we wrote 2t2, that would mean 2 × 32 or 2 × 9 which is 18. Remember the order of operations - BIDMAS. Brackets are worked out before indices, but indices are worked out before multiplication. = 3r3

4F – Algebraic Products Example 5: (-3x2) × (-2x) Example 6: 2g2 × 5g2 Discuss each example briefly. In the last example 2t × 2t the use of brackets may need further clarification. We must put a bracket around the 2t since both the 2 and the t are squared. If we wrote 2t2, then only the t would be squared. Give a numerical example, if necessary. If t was 3 then 2t would be equal to 6. We would then have 62, 36. If we wrote 2t2, that would mean 2 × 32 or 2 × 9 which is 18. Remember the order of operations - BIDMAS. Brackets are worked out before indices, but indices are worked out before multiplication.

Graphic Organizer Addition Subtraction Collect like terms Collect like terms Ex. Ex. Products Fractions Multiply numbers and simplify using index notation Ex. Simplifying Expressions Summary

There are 8 QR codes around the room. QR Scavenger Hunt There are 8 QR codes around the room. You can work in pairs and start anywhere. Scan the QR code (question)  3a^2 x a^4 is 3a2 x a4 Once you answer the question, you must find your answer on another card around the room (this leads you to your next question!) You should finish at the first card you started with.

Independent Practice p86  #1 – 2 REMINDERS Chapter 4 test reminder (4A – 4G) View Ch.1 Tests during extra help times