1. 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
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2. Lesson 1 Rounding and approximation Level 4-5
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Starter
Work out the following:
26/6, 13/4, 17/9, 29/6, 43/7, 17/ x2.75, 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…
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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
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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
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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
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This is also an opportunity to identify the more able students. These students will do the equivalent work on volumes
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8. 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)
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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
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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
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11. 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
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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
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13. Find the surface area of the following shape
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14. Estimate the surface area of the following shape
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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:
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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”
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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
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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
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Plenary
Estimate the volume of the shape, then estimate the volume of water displaced if this was a ship
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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
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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
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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.
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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
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Resources
Squared paper/squared tracing paper, scissors, ruler
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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
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