Birthday Cake.

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Presentation transcript:

Birthday Cake

Starter Find the area of these shapes:

Starter Find the area of these shapes: 157.08 cm² (2 d.p.)

The problem… Can I use this block of icing… …to cover the top of this cake? I bought the icing as part of a 5 colour set to make an In the Night Garden themed cake. I mainly wanted the blue and red icing to make Iggle Piggle, and was wondering if the green from the set would be enough to cover the top of the cake to look like grass.

Try to use mathematical words What do we need to know? THINK PAIR SHARE Try to use mathematical words

Today’s objectives To apply prior knowledge to solve a practical problem and make informed decisions. To think about how practical our solutions would be in a real-life situation. Prior knowledge: Volume of cuboid Area of a circle Volume of a cylinder Circumference of a circle Metric units of measurement You may wish to conceal the prior knowledge topics at this stage so that pupils identify the methods independently.

Need to know: Can it be done? The block of icing measures 11cm x 4cm x 2cm. The diameter of the cake is 18cm. The icing needs to be 5mm thick. Only the top of the cake needs to be covered. Can it be done? These can be shown, or withheld until pupils ask for the information.

Peer assessment Swap your work with someone else and peer assess the working. Think: Is it easy to follow what they’ve done? Do you agree with their method and their solution? Can you suggest how they can improve their work?

Solution Volume of the icing block = length x width x height = 11 x 4 x 2 = 88 cm3 Volume needed = Area of the top of the cake x 5mm (0.5cm) thick = πr²h = π x 9² x 0.5 = 127.23 cm³ (2 d.p.) So…not quite!

Talking points Ext: How thin would we need to roll the icing to make it fit the top of the cake? Think: How significant is this answer? Can you visualise the difference? In real life, what might you do in this situation?

I decided to try and do it anyway! I rolled it out as thin as I could… (it was quite tricky!!)

…and used Smarties around the edge to cover the gaps… How many Smarties will I need? Think: What mathematical questions could we ask? What do we need to know?

Need to know… The diameter of a Smartie is 1.5cm. We can work out the circumference of the cake. Useful to know… I’ve got 4 tubes of Smarties. Each tube contains approximately 30 Smarties.

Solution How would you interpret this answer? Circumference of the cake = πd = π x 18 = 56.55 (2 d.p.) ÷ 1.5 = 37.7 Smarties How would you interpret this answer?

Finished!

Today’s objectives To apply prior knowledge to solve a practical problem and make an informed decisions. To think about how practical our solutions would be in a real-life situation. Prior knowledge: Volume of cuboid Area of a circle Volume of a cylinder Circumference of a circle You may wish to conceal the prior knowledge topics at this stage so that pupils identify the methods independently.

Plenary What other mathematical problems /questions could arise from baking cakes? Pictures can be shown as stimulus or left out

Exam question 4 × 4 × 4 =64 (cm³) 64 / (8×4) or 32h=64 =2 (cm) GCSE MATHEMATICS UNIT 2: CALCULATOR-ALLOWED INTERMEDIATE TIER SPECIMEN PAPER SUMMER 2017 4 × 4 × 4 =64 (cm³) 64 / (8×4) or 32h=64 =2 (cm)