Bexleyheath School - Inner College
Maths Unit Plan for “The Sea” Module
Phases
1. Classification of shapes. This build on the classification of sea creatures in Science to
emphasise the cross curricular dimension of classification. The use of Venn and Carroll
diagrams should be a common link across the subjects
2. Measurement of solids and liquids. This work on reading scales and finding areas and
volumes will provide the skills students need for the work on floating and sinking in Science.
3. Temperature and Depth of the Oceans. This is an opportunity to work with negative
numbers in context.
4. Handling data. This is an opportunity to build skills associated with the handling data cycle.
5. Scuba diving project. Either This is an opportunity to collect and interpret data for the
purpose of hiring scuba diving equipment or they can work on a complete project from
“where are going?” to “what did we find?”.
PHASE 1: CLASSIFICATION OF SHAPES
LO:
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Identify, visualise and describe properties of rectangles, triangles, regular polygons and 3D
solids
Use knowledge of properties to draw 2D shapes and to identify and draw nets of 3D shapes
Describe, identify and visualise parallel and perpendicular edges or faces; use these
properties to classify 2D shapes and 3D solids
Estimate, draw and measure acute and obtuse angles in shapes
Identify all the symmetries of 2D shapes
Identify and use angle, side and symmetry properties of triangles and quadrilaterals
Possible Outcomes for Assessment:
Level 2
 Use mathematical names for common 3D and 2D shapes
 Describe their properties, including numbers of sides and corners
 Sort objects and classify them using more than one criterion
Level 3
 Classify 3D and 2D shapes in various ways using mathematical properties such as reflective
symmetry for 2D shapes
 Begin to recognise nets of familiar 3D shapes e.g cube, cuboid, triangular prism, square
based pyramid
 Use Venn and Carroll diagrams to record sorting and classification of information
 Understand
Level 4
 Use the properties of 2D and 3D shapes
 Make 3D models by linking given faces or edges
 Continue to use Venn and Carroll diagrams to record sorting and classification of information
Level 5
 Use a wider range of properties of 2D and 3D shapes and identify all the symmetries of 2D
shapes
 Use language associated with angle and know and use the angle sum of a triangle
 Measure and draw angles to the nearest degree when constructing models and drawing or
using shapes
Level 6
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Classify quadrilaterals by their geometric properties
Solve geometrical problems using properties of angles, of parallel and intersecting lines, and
of triangles and other polygons
Activity 1
Resources: Set of shape cards, flipchart version of shape cards
Working in pairs or threes, students are asked to identify names for all the shapes. Any they do not
know or are not sure about, they need to keep to one side. Students are then invited to come to the
board to draw the shapes they cannot name. When all the shapes have been collected, students are
invited to see if they can name any of the shapes others have drawn. Draw out vocabulary of
regular, irregular, polygon, quadrilateral, pentagon, hexagon, octagon, ellipse, parallelogram,
trapezium, rhombus, kite, isosceles, equilateral, scalene. Ask students to find in their packs e.g all
the hexagons, all the regular shapes to assess their understanding. Ask students to draw in their
books and name any shapes they think they need to remember the names of.
Activity 2
Resources: Set of shape cards, plain paper, large paper, flipchart version of shape cards.
Working in pairs or threes, students are asked to sort their shapes into two piles according to a
criterion of their choice. Ask them to decide on a second criterion to sort each of their piles into two
piles. Ask each group to share with the class the criteria they used for sorting. Collect all the criteria
on the board together with an explanation of what this means and correct vocabulary. E.g the
criterion was “shapes with or without right angles”, explanation is “a right angle is 90 degrees, a
quarter turn, the angles in a square”. Suggest criteria like two equal angles, types of symmetry, and
properties of diagonals if they are not mentioned. Look at some examples to ensure they
understand.
Ask students how they could record the results of their sorting on a piece of paper, and to
demonstrate on the paper provided. Each group feeds back. We would expect to get lists, tables,
Carroll diagrams and Venn Diagrams. Introduce Carroll diagrams and Venn diagrams if necessary
using an example, and ask the students to choose two different criteria from the list (ones they think
they need to know more about) and choose the type of diagram they think will represent the data
best and produce a poster with some of the shapes stuck in the correct place. Try and make sure
there are shapes in each of the regions. (If there are some regions that none of the shapes fit in, ask
them if they can draw a shape that would fit).
Put Posters on the wall.
Activity 3
Give each pair or group of three the name of a shape. Each group to come up with the smallest
number of statements needed to describe the shape. Using miniwhiteboards students listen to each
description in turn, using the miniwhiteboard to help them work out what each shape is. They put
the shape name on their board and then put their hand up. First student to get each one right gets a
stamp. They must explain how they worked it out.
Activity 4
Resources: One copy of each net per group,A3 paper
In pairs or threes, ask students to try and identify the 3D shape that each net will make. Write the
shape on one of the faces of the nets. Number each net on another of the faces and draw a table on
a large sheet of paper like:
Net number
Shapes of
faces
Number of
faces
Numbers of
edges
Number of
vertices
Name of 3D
solid
Ask them to complete as much of the table as they can from the net and then make the net up into
the 3D solid and check their answers. Teachers can check their work as they circulate.
Ask students for definitions of the following names and collect on the board:
Prism, cuboid, cube, pyramid
Ask students what criteria they could use to sort the solids and collect ideas on the board. (eg shapes
with rectangular faces, shapes with six faces etc). Record their classification in their books.
Activity 5
Resources: Sheet of nets split into two pieces
In pairs or threes cut out the pieces of net and match them up into pairs to form nets of 3D solids.
In their books they should name each solid and record as much information as they can about two of
them in the way they think is best.
Homework
Diagonal Trace from NRICH (http://nrich.maths.org/925)
The Sea
Phase 2: Measurement of solids and liquids.
LO:
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Read, choose, use and record standard metric units to estimate and measure length weight
and capacity to a suitable degree of accuracy.
Select and use standard metric units of measure and convert between units using decimals
to two decimal places.
Read and interpret scales on measuring instruments.
Calculate the perimeter of regular and irregular polygons.
Find the area of shapes a by counting the squares or by using the formula for the area of a
rectangle.
Find the capacity of cuboids by using the formula or by counting cubes.
Find a method to use to calculate the capacity of unusual shaped objects.
Possible outcome for assessment.
Level 2
 Estimate compare and measure lengths weights and capacities.
 Read the numbered divisions on a scale and interpret the divisions between them.
 Choose the correct units standard or otherwise to measure.
Level 3
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Choose and use standard metric units and their abbreviations when estimating, measuring
and recording length, weight and capacity.
Read to the nearest division and half division scales that are numbered or partially
numbered.
Draw rectangles and measure and calculate their perimeters.
Use decimal notation to recrd measurement.
Level 4
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Select and use standard metric units of measure and convert between units using decimals
to two decimal places.
Calculate the perimeter and area of rectilinear shapes.
Estimate the area of an irregular by counting squares.
Level 5
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Solve problems by measuring, estimating and calculating.
Calculate the area of right-angled triangles given the lengths of the two perpendicular sides.
Calculate the volume of a cuboid.
Level 6
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Know and use the formula for the volume of a cuboid and shapes made from cuboids.
Find the surface areas of cuboids and shapes made from cuboids.
Lessons 1 and 2
Resources
Card sets A and B, mini white boards, fish sheets (these must be kept for Data handling
topic). PowerPoint on reading dials. Metre rule. Rulers. Paper for fish pictures.
Measuring
 In the middle of the board write: Measuring quantities
Ask learners to think of anything they know about measuring things. If necessary ask
questions to draw out different ideas.
What units do you measure length in?
What different units do you know?
Do you know any relationships between units?
Can you think of the names of any measuring instruments?
What quantities do they measure?
 Record a few of the learners’ ideas to show a web of thoughts emerging:
Give individuals a mini-whiteboard or a sheet of paper and give them five minutes to develop
the poster further urging them to think of as many different things as they can. This gives the
teacher the opportunity to see what the class knows and where misconceptions lie.
 Give pairs of learners a set of Card Set A – Measuring instruments.
Ask pairs to sort them into groupings of their choice. (classify)
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When learners have sorted the cards ask them if they can think of a different way of
categorizing them.
Discuss with the class how they chose to sort their cards and the different groups they
made. It is likely that they will have chosen to sort the cards according to what sort of
quantity they measure, such as distance or time.
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If they haven’t already done so, ask each pair to sort the cards according to the sort
of quantities they measure. Discuss their decisions,
Where are you likely to find these instruments?
Can you think of another measuring instrument that could go into each category?
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Now give pairs Card Set B – Units of measurement. Ask pairs to match Card sets A
and B, matching the units cards to the measuring instruments. Pairs must agree on
how the cards should be matched and explain to each other why they think cards
should be placed together.
 Extension If any learners finish quickly they could be asked to create their own
measuring instrument cards and then agree on which units would match them.
Reading Dials.
Go through power point with class get them to answer questions on white boards.
Measuring length.
On mini white boards get learners to estimate the
 height of the room,
 your height,
 their own height
 the length of the desks
 An item of their choice
Get learners to raise their hand to where they think 1 metre is from the ground. Use a
metre rule to go round to each hand. Then get them to re estimate the previous lengths.
Get them to estimate where they are in height in the class (eg 6th tallest)
While they are doing this measure and record their heights onto a spread sheet.(TA)
Use their heights to find their position in the class go over the measurements they estimated.
Are they taller than fish are long?
Using Fish sheet make life size pictures of fish in pairs. (Make sure some do the Halibut and
Cod)
Lesson 3
Resources 5 squares each, OHT S1.1c
Measuring Perimeter.
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Give the class 5 squares each. How many ways can they put them together to make
a shape, record results (you can only fit them together with whole sides touching
whole sides, 12 pentominoes).Which of their shapes has the largest perimeter?
 Display OHT S1.1c. Explain that the grid is in centimetres.
Q What is the name of shape A? (a rectangle) And of shape D? (a square)
Q How do we find the perimeter of shape A?
Establish that perimeter is the distance around the shape. Ask pupils to work out the
perimeters of rectangles A, B, C and D and to write the answers on their whiteboards in
centimetres. Discuss the answers, writing on the board:
perimeter of A is 5 + 3 + 5 + 3 = 16cm
perimeter of B is 2 + 10 + 2 + 10 = 24cm
perimeter of C is 4 + 6 + 4 + 6 = 20cm
perimeter of D is 5 + 5 + 5 + 5 = 20cm
Establish that another way to find the perimeter of a rectangle is to add together the length
and width, and multiply by 2. Record on the board next to the above:
(5 + 3) x2 = 16cm
(10 + 2) x2 = 24cm
(6 + 4) x2 = 20cm
(5 + 5) x2 = 20cm
 Tell the class you are going to sketch a rectangle with a perimeter of 10cm.
Q What could be the length and the width of my rectangle?
Establish that half the perimeter is 5 cm, so that the length plus the width must be 5cm. The
possibilities (for whole numbers of centimetres) are 4cm and 1cm, and 3cm and 2cm. Sketch
both the rectangles and label the length and width in each case. Explain that your drawings
do not show true measurements.
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Ask pupils to sketch on their whiteboards a rectangle with a perimeter of 12
centimetres, and to label the length and the width of the rectangle.
Now sketch on the board a series of shapes, one by one. Label each side with a suitable
length, in metres, centimetres or millimetres. For example: Ask pupils to calculate the
perimeter of each shape and to write the answer on their whiteboards.
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What is the perimeter of the classroom called?
What is a round the perimeter of the school?
What is a round the perimeter of the UK?
Lesson 4
Resources Centimeter square paper, OHT S1.2b
Area.
 Get class to draw round their hands on centimetre square paper.
How much space does you hand take up?
This is the area of your hand in cm2
Area is how much flat space something takes up (2 Dimensional)
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OHT S1.2b Get class to find the areas of the 5 shapes.
Tell the class you are going to sketch a rectangle with an area of 20 square
centimetres. Each side is a whole number of centimetres.
Q What could be the length and the width of my rectangle?
Establish that the length multiplied by the width must be 20 square centimetres. The
possibilities are 1cm by 20cm, 2cm by 10cm, and 4cm by 5cm. Sketch all three rectangles
on the board and label the length and width in each case. Explain that your drawings do not
show true measurements.
Ask pupils to sketch on their whiteboards a rectangle with an area of 12 square centimetres,
and to label the length and the width of their rectangle. Point out the three possibilities: 1cm
by 12cm, 2cm by 6cm, and 3cm by 4cm.
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Find the area of a classroom using the carpet tiles.
Lesson 5
Resources S1.2c sheet, centimetre square paper
Area
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Get class to define area. Put ideas on board and refine, to give them a definition.
Resource S1.2 c Find the areas of the shapes.
What do you notice about the triangles?
Get class to draw 5 right angled triangles onto centimetre squared paper and then
find the areas. Can they discover the relationship between the area of a triangle and
the rectangle it would fit into.
Give definition of an area of a triangle to those who did not find it.
Lesson 6
Resources Lego, S3.3e
Volume (Capacity)
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Volume of a cuboid. Using lego make different cuboids that all have the same
volume. Define what volume and cuboid means.
S3.3e Copy shapes from sheet onto isometric paper and then work out the volume of
each shape. Remember to mention units cm3 etc.
In groups devise a method for finding the volume of an irregular shape (for example
the space a boy/girl takes up).
What do we use to measure the capacity of liquids? Units used
Lesson 7/8
Resources 2 Fish sheets
Mini project
 Which is the biggest fish?
In groups of up to 4 people.
Look at the length the area and the volume of 3 types of fish and decide which is the
biggest.
You will need to
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choose the fish (use ones that you can find lots of information about)
Draw full size models
Decide what you mean by biggest (Longest, biggest perimeter, biggest area, largest
volume).
Present your findings, with the maths involved. (the more able should look at all ways of
measuring to get their answer).
PHASE 3 : TEMPERATURE AND DEPTH OF THE OCEANS
LO:
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Relate whole and decimal numbers to their position on a number line
Find the difference between a positive and a negative integer, or two negative integers in
context
Find percentages of numbers and quantities
Use all four quadrants
Read and interpret scales on a range of measuring instruments
Compare readings on different scales
Solve problems by selecting, processing, presenting and interpreting data
Construct and interpret line graphs
Describe and interpret results and solutions to problems using the mode, range, median and
mean
Possible outcomes for assessment:
Level 3
 Use standard units of time
 Construct bar charts
 Extract and interpret information presented in simple tables, lists, bar charts
 Recognise negative numbers in contexts such as temperature
Level 4
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Present information and results in a clear and organised way
Search for a solution by trying out ideas of their own
Interpret, with appropriate accuracy, numbers on a range of measuring instruments
Construct and interpret frequency diagrams and simple line graphs
Understand and use the mode and range to describe sets of data
Use and interpret coordinates in the first quadrant
Level 5
 Draw simple conclusions of their own and give an explanation of their reasoning
 Use the sum of angles at a point
 Read and interpret scales on a range of measuring instruments, explaining what each
labelled division represents
 Understand and use the mean of discrete data and compare two simple distributions, using
the range and one of mode, median, mean
 Use and interpret coordinates in all four quadrants
 Order, add and subtract negative numbers in context
 Use a calculator where appropriate to calculate percentages of quantities
Activity 1
NRICH: Tug Harder (http://nrich.maths.org/5898)
Activity 2
Resources: Sea Surface temperature maps, picture of globe with lat & long Lines, world map with
countries marked, sea surface temp question sheet
Show students the picture of the globe on the IWB.
Ask:
 Can you find Great Britain?
 What other countries can you see? (students could come up and point them out. Make a list
on the board)
 What are the lines on the globe? (See how much they know. Cover: Latitude is how far
north or south you are. The measurements are in degrees to represent the degrees round
the circle Zero degrees latitude is the equator. Longitude is how far east or west you are.
Where is the zero degrees line? It goes through Greenwich and is called the meridian.
Give students the map of sea surface are. Explain that the globe has been cut down the back and
folded out to a flat surface to give this picture.
Ask them to identify the meridian and draw it in on the map in bold. Ask them to find the equator
and draw that in bold. Label the vertical numbers with Latitude and the horizontal numbers with
Longitude. Tell them we now have a four quadrant coordinate grid that we are used to seeing in
maths.
Ask:
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Why do the longitude numbers go from –180 to +180? (360 degrees all the way round a
circle)
Why do the latitude numbers go from –70 to +70 ( 180 degrees from south to north, the last
20 degrees not shown on the map)
Using the map can anyone tell me what the coordinates for Greenwich would be?
(about(0,51)). Make sure everyone knows that the horizontal axis is written first.
Explain that on their map the seas are coloured to reflect the temperature they are. There is a key
at the bottom that we will look at later.
Give a list of about 8 coordinates that everyone has to mark on their maps (start with coordinates in
the first quadrant). They should try and identify which country each one is in. (you may need to put
the country map up on the board) They can then find coordinates for the countries they recognised
at the beginning of the lesson.
In pairs or threes students should try and answer the questions on the sea temp question sheet.
Groups pass their answers to another group to check and the teacher answers any queries.
Take feedback from groups on the descriptions in Q1 and 2.
Activity 3
Resources: Thermometer cards
In pairs or threes, students sort the thermometers into 3 piles. Thermometers they can definitely
read, thermometers they think they can read, thermometers they definitely can’t read.
Taking the pile they CAN read, sort them into order of temperature. Then try and add in the ones
they were not sure about using the ones they have sorted to help. Teacher can help each group
through questioning when necessary.
Using one of the most difficult examples from the pack, ask students what strategies they would use
to try and work out the temperature. Discuss and then ask students to try to add their third pile to
line.
Activity 4
Resources: Light house pictures and questions, elevation map
Put the lighthouse picture on the IWB. Teachers exlains about the scale markings being Im apart.
Ask students what number should go on the scale at sea level. Ask them about the depth of some
fish to make sure they understand the scale. In pairs, students complete the questions.
Put elevation map on the board. Can they find Great Britain? Ask students what they think it shows.
Brief discussion to ensure they understand the map. In pairs, students have 5 minutes to come up
with three questions to share with the class. Put questions on a piece of paper. Teacher chooses
one question from each list to ask the class. Students put answers on the miniwhiteboards. Discuss
answers if necessary.
Activity 5
First Connect Three from NRICH (http://nrich.maths.org/5865)
Activity 6
Resources: Monthly mean sea temperature data.
In threes, brainstorm “What could we find out from this data?” Collect best ideas from each group
on the board. In threes, brainstorm “ What sorts of things could we do with the data to help us find
the answers. Go through all suggestions talking about relevance. Give examples of calculating the
mean and drawing line graphs. ( for weak students, scaffolding might include giving them data
rounded to the nearest whole number and providing axes with ready drawn scales )
Students work in threes,decide what they want to find out from the suggestions on the board
thenidentify which data would be best to use and allocate one task per person. (eg Calc means,
draw line graph). Students then work together to use their evidence to draw a conclusion. Put all
together on a poster to put up in classroom.
The Sea
Phase 4: Interpreting Data (six lessons)
LO
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Answer a set of questions by collecting, selecting and organising, relevant data: draw
conclusions.
 Use tally charts, frequency tables pictograms to show results.
 Use ICT to create graphs.
 Use measurement tools (ruler, metre stick, tape measure, scale) to perform
measurements and determine sizes for their scuba gear rentals.
 Read and interpret a schedule and table/chart
Possible outcomes for assessment.
Level 2
 Record and collect data in lists and tables.
 Use lists tables and diagrams to sort objects.
Level 3
 Use ICT to create a simple bar chart.
 Answer a question by collecting and recording data in lists.
Level 4
 Find the mode of a set of data
 Answer a set of questions by collecting, selecting and organising relevant data in lists.
 Describe and predict outcomes from data.
Level 5
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Level 6
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Describe and interpret results and solutions to problems using mean median mode and
range.
Explore hypothesis by planning surveys or experiments.
Calculate statistics for sets of discrete and continuous data.
Recognise when it is appropriate to use mean, median, mode and range of sets of data.
Lesson 1
Resources
Spread sheet of class on electronic white board with all their heights in cm on. (Created during
measuring topic).
Collecting data.
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Discuss the data collected so far. Get them to write five statements about the data. E.g .Who
is tallest/shortest, where they come in the list etc.
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Discuss what other data they could add easily, direct them towards shoe size (no ½ sizes)
and DOB. Collect this data.
Get them to write five more statements about each type of data.
Draw a graph of their own choice to represent one of the types of data. Use ICT to do this
from spreadsheet of data.
Compare with others in class.
Lesson 2
Resources
Printed copies of sheet of data collected last lesson. Calculators.
Finding averages.
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Give definitions of mean, median and mode.
Class to find averages of the data they have collected. (More able will be able to do all
three). Use ICT as appropriate to students.
Why could they not find the mean of the DOBs?
All to find range of all three sets of data. Emphsise that range is not an average.
Lesson 3
Resources
Printed copies of Data sheets. Paper for posters.
Displaying data.
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Using white boards students to remember as many types of ways of displaying their data as
possible. (They should include: Tally charts, frequency tables, bar charts, pictograms and pie
charts.)
Choose some of these and display the data they have collected using them. (more able to do
grouped frequency tables for height and DOB. Again use ICT as appropriate).
Make a poster of these graphs etc.
Lesson 4
Resources
Mymaths, whiteboards, dice.
Probability
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Mymaths on white board - bexleyheath -alpha to log in then Data –Probability-Probability
intro- lesson. Students can use their own logins to work on individual computers if
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appropriate for some individuals (higher level students will be able to cover more). (Get class
to put their answers onto white boards before entering them into lesson so they all
contribute).
In pairs or groups make up a FAIR game using 2 dice.
Demonstrate game.
Phase 5
EITHER Mini project on Scuba Diving OR Coral reef project :
Mini project on scuba diving
Resources
Scuba Gear rental sheets. Measuring equipment.

Students are to imagine they are going on a holiday which will involve Scuba Diving in the
sea. They need to order the correct equipment for this holiday.

For the next portion of the lesson, students will be taking measurements to determine
the size of gear they will need. Ask students, "What equipment will you need for the
dives?" Have students Think, Pair, and Share, and chart their responses. After
allowing students to brainstorm, give out Scuba Diving sheets.
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In pairs complete Scuba Gear rental sheet. (You may chose to estimate weights if scales are
not available or if class is too self conscious).
Before you start, it is important that students understand the following:
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How to round their measurements [Note: The physical tools in this lesson provide a good
opportunity to teach basic rounding skills. If an actual measurement occurs between two
numbers on the ruler, the student should choose the number that is closer to the actual
measurement.]
What "head circumference" means
Go over the instructions with students, and pass out the rulers and yardsticks. Set up the
bathroom scale, and remind students that they can do their measurements in any order (to
eliminate wait time at the scales). Circulate as students work to be sure students are choosing
the correct tool and using it accurately. Assess students as they work, with questions such as:
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How did you figure out that you needed to order that particular size?
If my shoe size is 7 1/2, what size fins would I need to rent? How do you know?
You may want to have students share their data with the group (however, let them volunteer
to share, as some students may be self-conscious in sharing this type of information). Ask
students why they have different measurements.
1. Create a bar graph showing the number of wetsuits for each of the sizes. Let students create
questions for their partner to answer using the graph.
2. Let students set a fair price for each piece of scuba gear, and calculate the total price for
their rental equipment.
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Conclude this mini project by; getting them to say what the mode size of each piece of
equipment would be for the class; how good their estimates were; cost of equipment hire;
displaying results.
Coral Reef Project
This can be based around the following resources:
Introduction: Map to locate Belize, Letter setting scenario, Scuba diving video.
Where in the World is Belize? Offers work on estimation, distance and speed.
Arriving in Belize City. Offers work on time.
Scuba Gear Rental. Offers work on measuring and reading tables.
Ready to take the plunge. Offers work on time, distance, speed and simple percentages.
Dive Data. Offers work on drawing line graphs and analysing trends.