self-directed year 7 maths unit
TRANSCRIPT
National Literacy and Numeracy Week 2008 Project Report
Project title: Mass Appeal Project description: A self‐directed Maths unit for Year 7 students on the topic of Volume and Mass Person responsible for project: Diane Gore, Paul Gilchrist & Elizabeth Campbell School, region, diocese: South West Sydney Contact person’s email: ecampbell@strathfieg‐h.schools.nsw.edu.au Number of students, teachers, parents, other community members directly involved:
• Year 7 (approx. 160 students), 6 Year 7 maths teachers & 2 ESL teachers Intended literacy and/or numeracy outcomes:
• students learn how Maths can be applied to everyday situations • students choose from a variety of different learning styles that interest them
(linguistic, logical/mathematical, visual and kinaesthetic) • students choose the level of difficulty of their work. The activities have a ‘star’ rating
based on their level of difficulty ‐ students choose activities which involve remembering, applying, analysing, evaluating and creating. (Students must complete at least 15 stars)
• students’ literacy and numeracy is extended in Maths in a creative way which motivates students of all abilities. A number of activities are literacy‐based and many activities involve hands‐on experiences. Students enjoy the lessons because they have control of their own learning.
• students work at their own level and pace. More able students may choose more difficult activities and they may do more than the 15 stars minimum. Less able students can still do 15 stars, but they have to do more activities with a lower star rating. Often it is found that less able students challenge themselves and opt to do some more demanding activities to get the 15 stars
• students gain the knowledge needed for tests and exams. Some activities are compulsory to ensure that all students have learnt the Maths needed for assessments.
Evidence of achievement of intended literacy and/or numeracy outcomes: • there wasn’t enough time to conduct a test or survey; however, students were
highly engaged in the unit of work and many said they enjoyed it. Some students did 30 stars of work and their standard of work was high. One parent said her daughter enjoyed doing the activities so much that she had to ask her to stop doing her Maths homework!
• many students happily took activity sheets to complete at home • students in the lower ability class needed a support teacher as well as their Maths
teacher to help them with the experiments, as we found they were not very good at reading instructions. With help, they were still able to achieve 15 stars.
• students will be doing a Yearly Exam in Term 4 which will be used to gauge the knowledge they have learnt.
Feedback about making grants available for such projects: The grant was very helpful, but of course we could have used even more! See materials below:
Year 7 Mass Appeal Topic Outline
You will have two weeks to complete this self-directed unit of work. You can choose activities from a variety of different learning styles that interest you. Information about the Activities
• Each activity has a star rating (*). • You should choose activities that total at least 15 stars.
A guide to the time taken to complete each activity is as follows: One star * will take about 20 minutes Two stars ** - 40 minutes Three stars *** - 60 minutes Four stars - more than 60 minutes
• At least one activity must be chosen from each of the four learning styles (Linguistic, Logical/Mathematical, Visual, and Kinaesthetic/Musical).
• You must do the compulsory activities - LR, MR, VP, KR, KP and the Team Investigation. (It is recommended that teachers work through LR and MR with the class first, before other activities are attempted.)
• Each activity must be signed off and dated by you and your teacher. • Keep all activity sheets together in an A4 display folder. This will be your
portfolio. • Your portfolio will be marked by your teacher at the end of the topic.
The mark will contribute towards your final assessment mark. What to do
• Choose the activities you want to do from the Mass Appeal Activities Grid. You must be able to do the following after completing your activities:
Define all the keywords in activity LR Calculate conversions of mass and volume Understand the meaning of gross and net mass Measure the volume of a rectangular prism Measure the mass of an object using a balance
• Tick the boxes above once you have checked that your activities cover the skills listed.
• Complete the Year 7 Mass Appeal Planning Sheet, making sure you have at least 15 stars. (You can change an activity if you find it too hard).
KP Estimating and Measuring Volume
Equipment needed 200 centicubes, calculator 12 different sized containers-some boxes eg cereal, soup, toothpaste, some bottles, cans and small tubs e.g. yoghurt, strawberry, sour cream 375 mL measuring cup 2L bottle to bring water from the tap The Task You will be provided with 12 different containers. Your task is to arrange the containers in ascending order of volume (from occupying the smallest space to the largest space). Then you will work out the actual volume of each container and see whether your order was correct. Instructions A. Putting the containers in order from smallest volume to largest volume
1. Try to arrange the 12 containers in order from smallest volume to largest volume. To help estimate their order, fill the smaller containers with centicubes (each has a volume of 1 cm3). For example, if 10 centicubes fill your container, it has a volume of 10 cm3. There will not be enough centicubes to fill the larger containers, so you will have to estimate which ones take up the most space. Note: Do not calculate the volume of the containers yet! You are simply putting them in order of volume.
2. Complete the first column of the table on the next page.
B. Calculating the actual volume of each container 1. For containers that are not rectangular prisms, (e.g. round tubs,
bottles, etc). Add water to the containers then pour the water into a measuring cup to check the actual volume of the container. The volume of water will be measured in millilitres (mL), but since 1mL = 1 cm3, the volume of the container can be written in cm3. eg if the container holds 10mL, you can write its volume as 10cm3
2. If the container is a rectangular prism, use a calculator to determine the volume using the equation:
Note Measure all lengths in cm, so that the units of volume will be cm3.
3. Record all your answers in the second column of the table on the next page.
V = volume l = length b = breadth h = height
V = l x b x h
Volume of Different Sized Containers
Containers in ascending order of volume-
e.g. yoghurt, milk, cereal, etc)
Actual volume (using measuring jug or
calculations) (cm3)
1. (smallest volume)
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. (largest volume)
Questions 1. How did your estimates of volume compare with your actual volume
measurements? _____________________________________
_______________________________________________________
_____
2. Were there any containers out of order? Why do you think this
happened? _________________________________________
LA Comparing Mass and Volume
1. a.) Which is heavier? A tonne of lead or a tonne of feathers? The answer is easy. Explain._________________________________________
_________________________________________________________________
_________________________________________________________________
b) Which do you think would have the bigger volume? Explain why? _________________________________________________________________
_________________________________________________________________
2. What is the difference between volume and mass? Try to explain it in your own words. _____________________________________________________________________
_______________________________________________________________
3. Are big things always heavy? List three big things that are relatively light.
_____________________________________________________________________
_______________________________________________________________
4. Are little things always light? List three little things that are relatively heavy. _____________________________________________________________________
_______________________________________________________________
5. Look at these objects. They are not drawn to scale. The mass and volume refer to one of each object.
a) Cut and paste these objects [one of each], in ascending order of mass on the back of this page.
b) Now cut and paste these objects [one of each], in ascending order of volume.
c) What is different in the order? (Answer on the back page)
………………………………………………………………………………………………
Anvil Box Safe Mass 450 kg Mass 5 kg Mass 40 kg Volume 0.5 cubic m Volume 0.128 cubic m Volume 0.08 cubic m
Loaf of bread Toaster Gold Bar Mass 500 g Mass 1 kg Mass 6 kg Volume 0.002 cubic m Volume 0.0015 cubic m Volume 0.002 cubic m
LE
Cooking Up a Storm When you write a recipe you often begin with a list of ingredients. Here are the lists of ingredients for several recipes. Each one has been printed incorrectly and has one error. Read each list carefully and circle the error. In the space provided explain why you think it is an error. Chilli Con Carne ½ onion 5 grams of chilli powder 18 kilograms of minced chicken 250 grams of kidney beans 20 milligrams of salt 300 grams of tomatoes What is incorrect about the circled error? ______________________________________ ________________________________________________________________________ Sweet and Sour Noodles 250 grams of egg noodles 60 litres of groundnut oil 125 grams of baby corn cobs 200 grams of tomatoes 1 clove of garlic What is incorrect about the circled error? ______________________________________ ________________________________________________________________________ Quick Quiche 3 eggs 3 rashers of bacon 2 millilitres of milk 125 grams of flour 200 grams of grated cheese What is incorrect about the circled error? ______________________________________ ________________________________________________________________________ Now look carefully at this recipe. The quantities in the ingredients list and the method are not consistent. [That means the amounts are not the same in both.] Circle the inconsistencies. Explain which amounts you think are incorrect. Spaghetti Bolognese
Ingredients 200 grams of minced steak 200 ml chicken stock 200 grams of spaghetti 400 grams of tomatoes 1 onion 1 clove of garlic Method
1. Heat oil in a medium saucepan and fry the onion and garlic until soft. 2. Add the fifth of a kilogram of mince steak and cook until brown. 3. Add the 4 milligrams of tomatoes and the quarter of a litre of stock, and bring
to a simmer until sauce thickens. 4. Cook the 0.02 kilogram of pasta in another saucepan. 5. Drain cooked pasta, place on a plate and top with sauce.
Serves 4 What is incorrect about the circled errors? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
LP Metric Units All Around Us
Instructions
1. Collect 10 advertisements or newspaper articles which include the following metric units for capacity and mass:
a) grams b) millilitres c) kilograms d) litres e) tonnes
2. Glue the advertisements on the back of this page and alongside each
write what the metric unit is and what it is used for measuring (capacity or mass).
3. Match each object on the left with the most suitable measurement on the right.
Object Correct letter
Measurement
a truck _____ a) 820 g
a bottle of Coke _____ b) 15 mL
a tablespoon of butter _____ c) 100 kilograms
a large block of chocolate _____ d) kilolitres
a cup of water _____ e) 2 kg
a large bottle of milk _____ f) 2 L
an egg _____ g) 8 tonnes
an amount of cough mixture _____ h) 30 g
water in a swimming pool _____ i) 250 mL or 250 cm3
a large packet of Sultana Bran _____ j) 60 g
a bag of sugar _____ k) 2 mg
a pinch of salt _____ l) 1.25L or 1250 cm3
a boulder (large rock) _____ m) 250 g
KeY WORD MATCH UP • Match each word with its correct meaning
Key word Correct Letter
Meaning
volume a) the force of gravity pushing down on an object. It is
measured in Newtons
mass b) a prefix meaning one hundredth or 1/100
milli c) units of capacity
tonne (t) d) a unit of volume written as m3 (1 m3 = 1 000 000 cm3)
cubic millimetres e) units of mass
centi f) the amount of matter (or substance) in an object
capacity g) a unit of volume written as cm3 (1 cm3 = 1000 mm3)
litre (L), millilitre (mL) h) a prefix meaning one thousand
cubic metres i) Volume = length x breadth x height
kilo j) a unit of volume written as mm3
gram (g), milligram (mg) k) the amount of liquid a container can hold
weight l) the amount of space that an object occupies
cubic centimetres m) a prefix meaning one thousandth or 1/1000
formula for volume of a rectangular prism
n) a unit of mass equal to 1000kg. It is used for measuring the
mass of heavy objects
KEY WORD MATCH UP ANSWERS
• Match each word with its correct meaning
Key word Correct Letter
Meaning
volume l a) the force of gravity pushing down on an object. It is measured in
Newtons
mass f b) a prefix meaning one hundredth or 1/100
milli m c) units of capacity
tonne (t) n d) a unit of volume written as m3 (1 m3 = 1 000 000 cm3)
cubic millimetres j e) units of mass
centi b f) the amount of matter (or substance) in an object
capacity k g) a unit of volume written as cm3 (1 cm3 = 1000 mm3)
litre (L), millilitre (mL)
c h) a prefix meaning one thousand
cubic metres d i) Volume = length x breadth x height
kilo h j) a unit of volume written as mm3
gram (g), milligram (mg) kilogram
e k) the amount of liquid a container can hold
weight a l) the amount of space that an object occupies
cubic centimetres g m) a prefix meaning one thousandth or 1/1000
formula for volume of a rectangular prism
i n) a unit of mass equal to 1000kg. It is used for measuring the mass
of heavy objects.
Mass Appeal Key words
S G D I R K U R H S C I K L Y
I Y F P C Z I A G B A L P S Q
H T D A E R B L V R P L F O L
E Q N F H H E U O T A I I W Y
I M J E T Y D G M L C M R O E
L V U G C I R N V G I O G R B
U I N L L E W A B Q T T T J T
H E T O O X U T F C Y I R K O
L Q S R K V J C F Z L C I E N
K T Q G E B F E X I U L T U N
I H E I G H T R L B O L E B E
L G U C M I L L I G R A M Q P
O I M A S S I C R M S I R P L
M E Q N F M V A T D W M D Y X
L W H L L X M Z R F H C U T L
BREADTH CAPACITY CENTI
CUBIC GRAM HEIGHT
KILO KILOGRAM KILOLITRE
LENGTH LITRE MASS
MILLI MILLIGRAM MILLILITRE
PRISM RECTANGULAR SOLID
TONNE VOLUME WEIGHT
Created by Puzzlemaker at DiscoveryEducation.com
Year 7 Mass Appeal Planning Sheet
Activity code e.g.
LR
Star rating
(must total 15 stars)
Name of activity
Date completed
Student’s signature
Teacher’s signature
LR 2 Mass Appeal Keywords
MA
Super Specials! $$
Almost every time we buy something from the supermarket, we must decide which brand and size is the best value for money. Soon, all large supermarkets will display the unit pricing for each product under the price label, so that you can easily work out which product is the best value. Unit pricing means the price per unit using equal measures is shown. For example, it could be the price per 100 mL or per 100g or per L or per kg that is shown. Aldi supermarkets already do this. See the Aldi advertisement below: The Barbeque Snacks cost $1.19 for 200g. The unit price is the price for 100g, which is 59.5cents. The unit pricing calculation is shown below:
200g costs $1.19 200g ÷ 2 costs $1.19 ÷ 2 therefore 100g costs 59.5cents
The unit price is 59.5cents per 100g What to do In this activity, you will be given two laminated pages of “Super Specials” from a supermarket called Colesworths. Your job will be to calculate which product in each pair of products is the best buy. To do this:
1. Calculate the unit price for each pair of products. This will help you compare the price of the products.
2. Complete the table on the next page with your calculations and best value products. The first specials have been calculated for you.
unit price
Super Specials $$$$$
Specials Unit price calculation Best value product
1. Maggi super noodles 50g
50g costs $1.19 50g x 2 costs $1.19 x 2 100g costs $2.38 The unit price is $2.38 per 100g Maggi super noodles
100g Maggi super noodles 100g
The unit price is $1.59 per 100g
2.
3.
4.
Specials Unit price calculation Best value product
5.
6.
7.
8.
Specials Unit price calculation Best value product
9.
10.
11.
12.
ME
Crystal Stone Cavities
Introduction Madeleine, a Year 7 Maths student, took a plastic container and filled it with her favourite crystal stones. She noticed that although the stones were packed as close as possible, there were still many gaps between the stones. Madeleine wanted to find out how much space was taken up by the air in the container. How could she do it? The instructions below outline two ways to solve Madeleine’s problem. Follow Methods 1 and 2 to calculate the volume of air spaces in Madeleine’s container and then evaluate (decide) which method gives the most accurate results. Equipment needed large plastic Glad Ware storage container (approx 700 mL) about 70 crystal stones (or rocks of a similar size) 100 mL measuring cylinder 375 mL measuring cup ruler calculator Instructions Method 1
1. Fill the container to the brim with crystal stones. 2. The volume of air spaces can be found out by pouring water into the container. The
water should fill all the air spaces. 3. Pour the water into the measuring cup and record the volume of the water. (The
measuring cylinder could also be used to measure the volume of water). The volume of water will be equal to the volume of the air spaces. (Remember that 1 mL is equal to 1 cm3).
Results Volume of water filling air spaces __________mL
Volume of air spaces in container __________cm3 Method 2
1. Calculate the volume of the container (a rectangular prism) in cm3. 2. Remember that:
volume of container = _________________________ = ________________________
V = volume l = length b = breadth h = height
V = l x b x h
3. Calculate the volume of 1 crystal stone using the displacement of water, then count the
number of stones needed to fill the container. Then the volume of all the stones can be calculated. Follow the steps below:
Steps a) Pour 50 mL water into a measuring cylinder. b) Add 1 crystal stone to the water. c) Record the new volume of water d) Subtract the original volume (50mL) from the new volume to find the volume of 1
stone. Complete the table below: A.
Original volume of water
mL
B. New volume of water (when stone is added)
mL
New volume of water – Original volume of water
(B-A) mL
Volume of 1 stone
cm3
50
4. Calculate the volume of air spaces using the equation below:
Follow the steps
below: a) Count the number of stones needed to fill the container to the brim.
Number of stones needed to fill container ___________ b) volume of stones in the container = number of stones needed to fill container x
volume of 1 stone volume of stones = ______ stones x ______ cm3 = __________ cm3
c) volume = volume of container – volume of stones of air spaces
volume of air spaces = __________ - __________ = __________ cm3
Questions 1. How close were the two methods for calculating for the volume of air spaces
_________________________________________ __________________________________________________
2. Which method (1 or 2) do you think gave the more accurate results? Explain why. __________________________________ __________________________________________________ __________________________________________________ __________________________________________________
volume of air spaces = volume of container - volume of stones
Learning Style Remembering Applying Analysing Evaluating Creating
Linguistic
I enjoy reading, writing & speaking
Keyword Match Up (teacher to revise keywords first) Match “mass appeal” keywords with their correct meaning + a word search ** Compulsory LR
Metric Units All Around Us Collect newspaper ads with mass and volume units. Match objects with suitable measuring units ** LP
Comparing Mass & Volume Cut & paste objects according to their mass & volume. . ** LA
Cooking up a Storm Find the mistakes in a cooking recipe. ** LE
Mr Archimedes’ Bath Use pictures from, “Mr Archimedes' Bath” by Pamela Allen to write a children’s story about Archimedes’ brilliant idea. ** LC
Logical/ Mathematical
I enjoy working with n numbers & science
Conversion Capers Calculate conversions of mass and volume *** Compulsory MR
Being Water Wise Use information given to calculate water use around the home. ** MP
Super Specials Calculate which specials are the best value for money. ** MA
Crystal Stone Cavities Evaluate the volume of air spaces in a container filled with crystal stones *** ME
The Coke Creation Create a Coca Cola container out of cardboard in the shape of a rectangular prism. It must hold a volume of 500 mL. Don’t forget to colour it! The teacher will test it with sand! *** MC
Visual
I enjoy painting, drawing & visualising
Balancing Act Cut & paste pictures of objects of different mass to balance a set of scales ** VR
Estimating & Measuring Mass Estimate & then measure the mass of various objects. Then play a “Sand Competition” with the class. ** Compulsory VP
Making & Drawing 3‐Dimensional Shapes Use centicubes to make & draw different shapes with the same volume *** VA
Water, Water Everywhere Use displacement of water to evaluate the volume of a number of irregular shaped objects. *** VE
Saving Water Pamphlet Use information provided to design a pamphlet which shows how to save water. **** VC
Mass Appeal Activities Grid This matrix was devised by Ralph Pirozzo in 1997. Approximate time to do the activity: * 20min , ** 40 min , *** 60 min, **** > 1 hour
Kinaesthetic
I enjoy doing hands‐ on activities, sports, experiments, etc.
A Gross Problem Find the gross and net mass of a number of different objects ** Compulsory KR
Estimating & Measuring Volume Estimate & then measure the volume of various objects. ** Compulsory KP
Don’t be a Drip! Find how much water is wasted from a dripping tap. *** KA
Density of Cubes Evaluate the relationship between the mass and volume of cubes. *** KE
Packing Stock Cubes Construct the cheapest box which could hold a certain number of stock cubes. *** KC
Interpersonal I enjoy working in a group
Team Investigation – “Popping the Question” Your group will investigate what happens to the mass and volume of corn when it is popped! Compulsory