Give a brief outlook about Archimedes and his work Lessons objectives Give a brief outlook about Archimedes and his work Possible topics covered: number-dividing using a calculator, rounding to a given number of decimal places and round to whole number- Area and perimeter: finding the area by counting squares, estimating the area of a shape using the square method- measurement: understand volumes and learn how to measure and read volumes, learn how to describe volumes Visualise how much is 1 cm squared and understand that any surface area can be partitioned into 1 cm square pieces Students will learn how to round figures to whole numbers Students will learn how to find the surface area of a shape using the squares methods 21/09/2018 Collaborative_planning

Lesson 1 Rounding and approximation Level 4-5 21/09/2018 Collaborative_planning

Collaborative_planning Starter Work out the following: 26/6, 13/4, 17/9, 29/6, 43/7, 17/36 1.25x2.75, 4.65x3.25, 12.23x11.64, 9.6x8.3 (all students should be able to do this)After using calculators to work out the answer, encourage students to look into the questions and see if they can work them out, example 6 goes into 24 4 times and reminder 2 etc… 21/09/2018 Collaborative_planning

Collaborative_planning Ask students to give their answers to 1 then 2 decimal places Now ask students to attempt to give their answers as whole numbers (stop and move on, don’t give the answers) as a measure of their understanding of the lesson (plenary), students will be asked to round the above answers to 1and 2 significant figures. -Some students will be able to answer the first question 21/09/2018 Collaborative_planning

Collaborative_planning Main activity 10 ticks Level 4, Pack 3, Start Page 7, Rounding to the nearest 1, 10, 100, 1000 Level 6, Pack 3, Start Page 19, Rounding off 21/09/2018 Collaborative_planning

Collaborative_planning plenary As a measure of their progress, students will be asked to go back to the starter and work out the answers Whole class discussion 21/09/2018 Collaborative_planning

Collaborative_planning This is also an opportunity to identify the more able students. These students will do the equivalent work on volumes 21/09/2018 Collaborative_planning

Lesson 2 Surface area Starter Students will be given a list of shapes and names Students are required to mach the names to the shapes (resource: Edexcel Hodder text book page 323) 21/09/2018 Collaborative_planning

Collaborative_planning Lesson 2 students will cut 10, 20,30 cm squares pieces of paper Students will cut the same pieces diagonally in half, to make triangles, and estimate the area of each piece of paper. Students will produce a table (see next slide) Using a calculator, students will be asked to calculate the ratios (Area of square/Area of triangle) according to the table, round their answers to 1 significant figure/ give their answers as a whole number/integer 21/09/2018 Collaborative_planning

Collaborative_planning height width Activity: students will cut 1, 2,3, 4, 6, 8 and 10 cm squares pieces of paper. Students will produce again the same pieces, but this time they will attempt to make triangles out of them and estimate the area of each piece of paper (triangle). Students will produce a table. base Length 21/09/2018 Collaborative_planning

10 20 30 40 60 80 100 Area of square piece (cm2) Area of triangular piece (cm2) Ratio (square/triangular) 10 20 30 40 60 80 100 21/09/2018 Collaborative_planning

Collaborative_planning Students will write a conclusion, giving a general relationship between the surface area of a square and a triangle Most students should come to the conclusion that a triangle has half the surface area of a square and be able to write a general expression using length and width Students will use their findings to estimate surface areas of different objects. Examples can be: their class books, pencil cases etc… Tracing paper, which has squares on it, can also be used to determine the surface area of the objects 21/09/2018 Collaborative_planning

Find the surface area of the following shape 21/09/2018 Collaborative_planning

Estimate the surface area of the following shape 21/09/2018 Collaborative_planning

Collaborative_planning Lesson 3 Volume Starter Whole class discussion of the meaning of volume. Some students will say it’s the button to adjust the sound on stereos. This can be build on to say what is happening when you turn the volume, referring to the room. Match 3-D shapes to their names: http://www.primaryresources.co.uk/maths/powerpoint/3D_Shapes.ppt#256,1,Shapes 21/09/2018 Collaborative_planning

Collaborative_planning Students will visualise what actually a 1 cm cube is, and describe it in their own words! Learn how to estimate volumes using the “counting the cubes method” 21/09/2018 Collaborative_planning

Collaborative_planning Main Activity depth Height length Use the 3-d on and off option to enable students to visualise the transition from a square to a cube Use the 3-d on and off option to enable students to visualise the transition from a cube to a square 21/09/2018 Collaborative_planning

Collaborative_planning Teacher will model how to find the volume of an object by counting the number of cubes Give an example on how to calculate the volume of an object using the formula V= Lx HxW Exercise sheet : 10 ticks, Level 5, Pack 4, Start Page 36 21/09/2018 Collaborative_planning

Collaborative_planning Plenary Estimate the volume of the shape, then estimate the volume of water displaced if this was a ship 21/09/2018 Collaborative_planning

Collaborative_planning Using tracing paper, students will estimate the volume of the ship, therefore should be able to work out the volume of the water that will be displaced, after they carried out the experiment. Use a full scale ship (example from the internet) to work out the volume displaced. Estimate the number of ships in the ocean and estimate the volume of water displaced… question: do you think that, this has something to do with the flooding of certain areas around the world? Estimate the volume of water displaced by the above ship 21/09/2018 Collaborative_planning

Collaborative_planning Rich task Students will carry out the following experiment using Archimedes Purpose of the experiment: To determine why a heavy ship floats. Materials used: two 12-inch (30-cm) square pieces of aluminium foil 20 paper clips Small bucket Tap water 21/09/2018 Collaborative_planning

Collaborative_planning 21/09/2018 Collaborative_planning

Collaborative_planning Procedure: 1. Wrap one of the foil squares around 10 paper clips and squeeze the foil into a tight ball. 2. Fold the four edges of the second foil square to make a small boat. Place the remaining 10 paper clips in the boat. Spread the clips as evenly as possible. 3. Fill the bucket about three-fourths full with water. 4. Set the foil boat and ball on the surface of the water in the bucket. 21/09/2018 Collaborative_planning

Collaborative_planning Discussion and Results The boat floats and the ball sinks. Why? The ball and boat both have the same weight, but the ball has a smaller volume than does the boat. The weight of water pushed aside by an object equals the buoyant force of water pushing upward on the object. The hollow boat has a larger volume than the compressed ball, thus it displaces more water. This results in a greater  buoyant force on the boat than on the ball. Since the boat floats, you can conclude that the upward buoyant force of the water is greater than the downward force due to the weight of the boat 21/09/2018 Collaborative_planning

Collaborative_planning Resources Squared paper/squared tracing paper, scissors, ruler 21/09/2018 Collaborative_planning

Collaborative_planning Areas Touched up on Rounding and approximation Measurement Finding the area by counting the squares Find the volume by counting the cubes Area of triangles Area of squares and other shapes Volume of shapes Use of ICT 21/09/2018 Collaborative_planning