Forming and Solving Equations Main lesson forming equations
- Slides: 30
Forming and Solving Equations
Main lesson – forming equations Lesson Objectives: • All students must be able to solve simple equations • Most students should be able to form and solve simple equations • Some students could be able to form and solve equations involving unknowns on each side © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 b) 7 x + 2 = 16 c) 13 = 5 x -12 d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → 3 x = 27 (add 5 both sides) b) 7 x + 2 = 16 c) 13 = 5 x -12 d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 (÷ 3 both sides) b) 7 x + 2 = 16 c) 13 = 5 x -12 d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → 7 x = 14 (-2 both sides) c) 13 = 5 x -12 d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 (÷ 7 both sides) c) 13 = 5 x -12 d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 15 = 5 x (+ 2 both sides) d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x (÷ 5 both sides) d) 2 x + 17 = 90 e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → 2 x = 73 (-17 both sides) e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → x = 36. 5 (÷ 2 both sides) e) 4 x + 22 = 2 f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → x = 36. 5 e) 4 x + 22 = 2 → 4 x = -20 (-22 both sides) f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → x = 36. 5 e) 4 x + 22 = 2 → x = -5 (÷ 4 both sides) f) 3 x – 2 = -13 © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → x = 36. 5 e) 4 x + 22 = 2 → x = -5 f) 3 x – 2 = -13→ 3 x = -11 (+2 both sides) © Educate & Celebrate 2005 -2018 All rights reserved
Starter Solve the following: a) 3 x – 5 = 22 → x = 9 b) 7 x + 2 = 16 → x = 2 c) 13 = 5 x -12 → 3 = x d) 2 x + 17 = 90 → x = 36. 5 e) 4 x + 22 = 2 → x = -5 f) 3 x – 2 = -13→ x = -3 (÷ 3 both sides) © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations Sometimes our equations don’t come neatly written using algebra. Sometimes they come like this: “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” So how do we solve this? © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” Firstly, identify what it is we are trying to find out © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” Firstly, identify what it is we are trying to find out So the number of invitations in a pack will be our ‘unknown’ quantity. We’ll call that ‘x’. We’re now ready to form the equation. © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” 6 packs of invitations is 6 lots of the unknown quantity. © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” 6 x 6 packs of invitations is 6 lots of the unknown quantity. © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” 6 x - 3 Three mistakes means that they had to throw away three invitations © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations “Daisy and Meryl are planning their wedding. They buy 6 packs of invitations and make mistakes on three of them but still have exactly enough invitations to send to all of their 75 friends and relatives. How many invitations are in a pack? ” And this was equal to the number of relatives and friends that they had 6 x - 3 = 75 © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations Now solve this as normal 6 x - 3 = 75 ++ 3 3 © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations Now solve this as normal 6 x = 78 ÷ ÷ 6 6 © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations Now solve this as normal X = 13 So there were 13 invitations in each pack © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations: your turn! Kamarr is organising this year’s London Pride Charity Ball and has booked a room with 27 identical tables. He invites enough people to fill the seats at all the tables, but then remembers that he has to invite an extra 25 VIPs. 349 people attend the event. How many seats are there around each table? Form the equation and solve it! © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations: your turn! Kamarr is organising this year’s London Pride Charity Ball and has booked a room with 27 identical tables. He invites enough people to fill the seats at all the tables, but then remembers that he has to invite an extra 25 VIPs. 349 people attend the event. How many seats are there around each table? Equation: © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations: your turn! Kamarr is organising this year’s London Pride Charity Ball and has booked a room with 27 identical tables. He invites enough people to fill the seats at all the tables, but then remembers that he has to invite an extra 25 VIPs. 349 people attend the event. How many seats are there around each table? Equation: 27 x + 25 = 349 © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations: your turn! Kamarr is organising this year’s London Pride Charity Ball and has booked a room with 27 identical tables. He invites enough people to fill the seats at all the tables, but then remembers that he has to invite an extra 25 VIPs. 349 people attend the event. How many seats are there around each table? Equation: 27 x + 25 = 349 Solution: x = 12 seats per table © Educate & Celebrate 2005 -2018 All rights reserved
Main lesson – Forming Equations Now turn to the worksheet and try your hand at the question. Green questions are the easiest Orange questions are a bit trickier Red questions are the hardest © Educate & Celebrate 2005 -2018 All rights reserved
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