Page—100-101 of notebook Title Circles Objective: I can find area and circumference of circles. Essential Question: How can I find the area and circumference of circles? How can I find the radius or diameter given area or circumference?

Shape and Space Circles The aim of this unit is to teach pupils to: Identify and use the geometric properties of triangles, quadrilaterals and other polygons to solve problems; explain and justify inferences and deductions using mathematical reasoning Understand congruence and similarity Identify and use the properties of circles Material in this unit is linked to the Key Stage 3 Framework supplement of examples pp 184-197. Circles

The diameter is the segment that goes thru the center and Vocabulary The diameter is the segment that goes thru the center and connects both sides of the circle. Diameter Radius The segment from the center to the outside edge, 1/2 the diameter Pupils should be asked to learn these formulae. The perimeter of the circle Circumference Area The amount of space inside the circle

Circumference Formula C = 2πr C = πd Area A = πr2 Pupils should be asked to learn these formulae.

The circumference of a circle Use π = 3.14 to find the circumference of this circle. Step 1: Start by writing the formula, we have the diameter, so we are using this C = πd 8 cm Step 2: Substitute 3.14 for π and in this problem 8 for diameter = 3.14 × 8 Tell pupils that when solving a problem like this they should always start by writing down the formula that they are using. This will minimize the risk of using the radius instead of the diameter, for example. Step 3: Multiply all together = 25.12 cm

The circumference of a circle Use π = 3.14 to find the circumference of the following circles: 4 cm 9 m C = πd C = 2πr = 3.14 × 4 = 2 × 3.14 × 9 = 12.56 cm = 56.52 m 23 mm 58 cm C = πd C = 2πr For each one, start by asking pupils what formula we have to use. Estimate each answer first using  = 3, or use this to check the answer. = 3.14 × 23 = 2 × 3.14 × 58 = 72.22 mm = 364.24 cm

Finding the radius given the circumference Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? C 2π r = ? Link: A3 Formulae – changing the subject of a formula 12 2 × 3.14 = = 1.91 cm (to 2 d.p.)

Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π × r × r radius or Area of a circle = πr2

Use π = 3.14 to find the area of this circle. The area of a circle Use π = 3.14 to find the area of this circle. Step 1: Write down the formula A = πr2 Step 2: Substitute 3.14 for π and 4 for r. r * r = r2 4 cm = 3.14 × 4 × 4 Step 3: Multiply together = 50.24 cm2

Today’s Task In your groups match each circle to the correct area.

Pupil hand out. Print slides 17 and 18 two to a page.

78.55cm2 201.088cm2 ????????? 380.182cm2 132.749cm2 908.038cm2 50. 272cm2 283.566cm2 7.070cm2 25.12 cm 50.24 cm 40.82 cm 106.76 cm ????????? 9.42 cm 69.08 cm 31.4 cm 59.66 cm Pupil hand out. Print slides 17 and 18 two to a page.

The area of a circle Use π = 3.14 to find the area of the following circles: 2 cm 10 m A = πr2 A = πr2 = 3.14 × 22 = 3.14 × 52 = 12.56 cm2 = 78.5 m2 23 mm 78 cm A = πr2 A = πr2 Explain that rather than use the formula on the previous slide, it is usually easier to halve the diameter mentally to give the radius, before substituting it into the formula. The most common error is to neglect to half the diameter to find the radius and to substitute this value into the formula. Ensure that pupils do not make this mistake. = 3.14 × 232 = 3.14 × 392 = 1661.06 mm2 = 4775.94 cm2