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30 No rotational symmetry Rotational symmetry No lines of symmetry One or two lines of symmetry More than two lines of symmetry

31 No rotational symmetry Rotational symmetry No lines of symmetry One or two lines of symmetry N&!.)!1(&&.7+%!)(!O"'!#! &/#1%!)/#)!/#&!"(! -()#*("#+!&6$$%)-6! =/.2/!/#&!$(-%!)/#"! )=(!+."%&!(4! &6$$%)-6L More than two lines of symmetry

32 Factorizes with integers Does not factorize with integers Two x intercepts One x intercept No x intercepts

33 Factorizes with integers Does not factorize with integers N&!.)!1(&&.7+%!)(!O"'!#! J3#'-#*2!43"2*("! =[4DIH!)/#)!4#2)(-.\%&! 73)!/#&!"(!I!.")%-2%1)&L Two x intercepts One x intercept No x intercepts

34 M#"&&+=>+,1(=$,-68,& N)'%$,%,)' N11 A3') O'*$"'( 4#)9%$,%,)' f(x) = x + 3 f(x) = ln x f(x) = x 4-4x f(x) = sin x f(x) = cos 2x f(x) = x 2 - x + 6

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78 <,3%*.*%3(",/(C"#+/"3% Try a special case. Make a prediction and check it. Suppose that: w = 4 metres and r = 5 metres. x w x = 5± 25!16 x = 8 or 2 r - x r What does the x = 8 solution mean? Is this reasonable? NP

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85 K'$#*&'1%&'00,)%<&#)0 SUGGESTED LESSON OUTLINE Introduction: Cats and Kittens (10 minutes) Begin the lesson by briefly reintroducing the problem: Do you remember the problem I asked you to do last time? I have had a look at your work and I have some questions on it. Today you are going to work together to improve your initial attempts. First, though, I would like you to work individually again. Read through the questions I have written about your work. Use your mini-whiteboard to note answers to these questions. It is helpful to ask pupils to write their ideas a mini-whiteboard using a felt-tipped pen, as you will be able to monitor their work more easily. This will also help pupils to share their ideas easily later in the lesson. Collaborative activity: Producing a joint solution (20 minutes) The time given for this activity is an approximate guide. You may find your class would benefit from spending more (or less) time on this activity. Organize the class into small groups of two or three students and give each group a large sheet of paper and a felt-tipped pen. Ask students to try the task again, this time combining their ideas. I want you to work in groups now. Your task is to produce a solution that is better than your individual solutions. ^3,,%&)%'! &)-32)3-%!4(-! +%&&(" ^3,,%&)%'!."&)-32*("&!#"'! J3%&*("& ^3,,%&)%'! 1%'#,(,.2#+! $(?%& Take turns to explain how you did the task and how you now think it could be improved, then put your individual work aside. Try to produce a joint solution to the problem. While students work in small groups you have two tasks: to note different student approaches to the task, and to support student problem solving. You can then use this information to focus a wholeclass discussion towards the end of the lesson. OM

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92 M8558,(+&&$%&(3":#%& Has difficulty starting Can you describe what happens during first five months? Does not develop suitable representation Can you make a diagram or table to show what is happening? Work is unsystematic Could you start by just looking at the litters from the first cat? What would you do after that? Develops a partial model Does not make clear or reasonable assumptions Makes a successful attempt Do you think the first litter of kittens will have time to grow and have litters of their own? What about their kittens? What assumptions have you made? Are all your kittens are born at the beginning of the year? How could you check this using a different method? PB

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