L.O.1To be able to read and write wholenumbers and know what each digitrepresents.
347 256In your book write the value ofeach digit as it is pointed to.
347 256Use the last answer you made to start each calculation andwrite the new answer in your book each time.1. Add 40 000 to 347 256.2. Add 3003. Subtract 100 0004. Add 60005. Subtract 46. Subtract 50 0007. Add 7008. Add 20
L.O.2To be able to solve a problem byrepresenting and interpreting data in tallycharts and bar charts.
Q. Which number is most likely to turn upwhen a normal 1 – 6 die is rolled?I will roll this die until I reach 20 or more andyou will need to keep a record in your booksof the running total.Before I begin you will need to predict andwe will record how many times you think Iwill need to roll the die to reach my total.
Now we’ll try again.First we will record your predictions.And again!
Q. Is it possible to predict the number of rollsneeded to get a total of 20 or more?Q. Suppose I put a number 3 on each face,could we predict how many rolls we wouldneed to get a total of 20 or more?Q. How accurate would our prediction be?Why?
This time the target is 24 or more and there willbe a normal 1 – 6 die.Q. What could be the greatest number of rollsneeded to score 24 or more? What couldthe fewest number of rolls be?Work with a partner and conduct this experiment10 times. Each time record the number of rollsyou needed to reach 24 or more.
Q. Did anyone get a 24 in exactly 24 rolls or inexactly 4 rolls?I want to collect the class results andput them on a chart.Q. How can we collect and display the class’results?Would a tally chart or a bar chart be useful?
Work with the people on your table tocollect all your experiment resultsusing tallies and counting thedifferent numbers ofrolls taken.
In order to collect the class’ results we aregoing to write the results from each groupin the middle column of OHT 8.1.thenworkout the totals.
REMEMBER…The total in the final column is called theFrequencyof the number of rolls taken.
Q. Which number of rolls was the mostfrequent? Which was the least?Answer these:1. Which frequencies occurred more than ¼ the time?2. Which occurred less than 1/3 the time?3. Which occurred exactly half the time?4. Which occurred twice as much as any others?
OHT 8.1 can be turned round so the totalscan be shown as aBAR CHARTwith the horizontal axis showing theNUMBER OF ROLLSand the vertical axis showing theFREQUENCIES.
Q. If we are to draw this bar chart what scaledo we need on the vertical axis?When the scale has been decided you mayeach draw the bar chart on your squared paper.
By the end of the lesson the childrenshould be able to:Test a hypothesis from a simpleexperiment;Discuss a bar chart showing thefrequency of the event;Discuss questions such as “Whichnumber was rolled most often?”
L.O.1To be able to order a set of positive andnegative integers
Place the numbers in their correct position onthe number line. – Volunteers!-10 18 - 4 - 164 - 11 17 - 99 -14 2 15-20 200
Write the numbers in order in your bookstarting with the lowest.- 10 18 - 4 - 164 - 11 17 - 99 - 14 2 15
Now try these - starting with the lowest.- 16 11 - 6 - 1714 - 8 17 - 107 - 19 1 -15
Prisms and spheres only.Order these starting with the highest:23 -19 18 -7-5 -22 -11 29 -4-13 6 25 -28 34-17 -30 16 27 -1
L.O.2To be able to solve a problem by representingand interpreting data in bar line charts whereintermediate points have no meaning, includingthose generated by a computer.
Yesterday we rolled dice to make 24 or more.Rolling 24 1’s to make 24 wasVERY UNLIKELY.Which numbers of rolls of the dice appear to beMOST LIKELY …. LEAST LIKELY ?
We are going to do some moreexperiments using dice.What is happening in this sequence ofnumbers?2, 3, 5 (3)What is happening now?2, 3, 5, 1 (4)
Q. What is happening in these sequences?3, 3, 5, 6, 2 (5)1, 2, 4, 2, (4)3, 4, 5, 6, 3 (5)1, 5, 1 (3)Q. What is the rule here?
The rule is to continue rolling until thenumber decreases, then stop.Write down 3 sequences we might get whenrolling a die and abiding by the rule.Q. What is the shortest sequence we couldhave?Q. What is the longest?
The shortest sequence we could have hasonly 2 terms e.g.6, 1 (2)4, 2 (2)The longest sequence of terms would haverepeats e.g.1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 1 (11)1, 3, 3, 3, 3, 4, 4, 6, 5 (9)
I have read this in a book:“more than half the time the sequenceswill have 4 or less terms.” (copy onto board)Q. Do you think this is true??Using your dice each of you is to generate 20 sequencesusing the stopping rule “when it decreases stop.”List your sequences and the number of terms in each.
In groups of 5 pool your results usingtallies for the number of terms.Q. What was the longest sequence of terms inyour group?Q. Do the results in your group suggest that thestatement on the board is true?Q. What table should we use to collect anddisplay the results to the whole class?
Our table needs to cover the numbersfrom 2 to the largest number of termswe have.The graph will be shown as a bar-linegraph.Q. Will there be gaps between the lines?
Frequency / Number of TermsNumberofTerms2 4 6 8 10 12 14 16 18 20 22 24 26 28Frequency23456789101112131415161718192021222323
On your squared paper draw the bar-linechart using the whole-class data set.
Q. Is this graph similar in shape to the barchart you drew yesterday?Q. How many data items are there in thegrand total?Q. Were there 4 or less terms in oursequences in more than half our data items?Q. Is this more than half our data?Do we think the claim is true or false?
With a partner work out some statementsabout the behaviour of the sequences.Be prepared to share your ideas.
By the end of the lesson the childrenshould be able to:Test a hypothesis about the frequency of aneven number by collecting data quickly;Discuss a bar chart or bar line chart andcheck the prediction.
L.O.1To be able to recognise which simplefractions are equivalent.
½ ¾ ¼Q. Which figure is the NUMERATOR?Q. Which is the DENOMINATOR?Q. Are the fractions in order of size,smallest first?
The order should be : ¼ ½ ¾We will list some fractions which are equal to½. Volunteers!Q. Can you describe the relationship between thenumerator and the denominator?
Here are some fractions equivalent to ½ :2/4 8/16 3/6 4/89/18 5/10 7/14 11/2250/100 12/24 15/ 42/Q. If the numerator is 15 what must thedenominator be to go with these equivalentfractions? What if the numerator is 42?
We will list some fractions which areequivalent to ¼. Volunteers!Q. What is the relationship between thenumerator and the denominator?
: Here the fraction is ¼.Here are some equivalent fractions:¼ 2/8 4/16 20/805/20 3/12 7/28 6/249/36 11/44 14/ 27/Q. If the numerator is 14 what must thedenominator be to go with these equivalentfractions? What if the numerator was 27?
We will list some fractions which areequivalent to ¾.One is 15/20.How does this work?Q. What is the relationship between thenumerator and the denominator?
: Here the fraction is ¾ .Here are some equivalent fractions:3/4 6/8 12/16 60/8018/24 9/12 21/28 18/2427/36 33/44 21/ 27/Q. If the numerator is 21 what must thedenominator be to go with these equivalentfractions? What if the numerator was 27?
L.O.2To be able to solve a problem byrepresenting and interpreting data in barline charts where intermediate points mayhave meaning.
This table shows the temperature in °C of a surfaceexposed to the sun over a 24 hour period.Q. When was it hottest / coldest?Q. If we are going to put the data onto a graph whichnumbers should we put on the time axis and which onthe temperature axis?
The time axis must be 0 to 24and the temperature axis must be 0 to 60.Q. Which way round shall we place the graph paper?Q. Where should we place the first X on our record.
Temperaturein°C6055504540353025201510500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Time in hoursIs this a sensible way round?
Temperaturein°C605754514845423936333027242118151296300 2 4 6 8 10 12 14 16 18 20 22 24Time in hoursIs this moresensible?
Complete your own graph.Q. Can you work out at what times of day the differenttemperatures were taken?Q. What time of day were the 7th, 8thand 9thtemperatures taken?What about the 19th, 20thand 21st?Q. How could we estimate the temperature at 3.5 hours?Q. Are there values in the spaces between the X ‘s ?
Use a ruler to join the points you haveplotted.If we had more detailed measurementswould the points make a smoother curve?
REMEMBER…Time and temperature are MEASURESand not COUNTS or FREQUENCIES sothe intermediate points have meaningand we can join the X ‘s and use them toanswer different questions.Q. For how long was the temperature greater than 40°C?Less than 20°C?Work out some questions about your graph for yourpartner to answer.Prisms – 10; Spheres – 8; Tetrahedra – 5.
Here is another set of measurements collectedover the same 24 hours. These show the intensityof the light and are measured in lux.Q. Why are there 0’s for hours 8 to 12?Q. When was the light strongest?
There are 0’s for hours 8 to 12 becausethere was no light so it must have beennight time.The light was strongest at hour 21 – thismust have been close to midday.
By the end of the lesson the childrenshould be able to:Draw and interpret a line graph;Understand that intermediate points mayor may not have meaning.
.0 1 2 3 4 5 6 7 8 9 1050484644424038363432302826242220181614121086420Use thesegraphs tofind:4.5 x 2 =4.5 x 3 =4.5 x 4 =4.5 x 5 =
.0 1 2 3 4 5 6 7 8 9 1050484644424038363432302826242220181614121086420Tetrahedrasfind3.5 x 2 =3.5 x 3 =3.5 x 4 =3.5 x 5 =5.5 x 2 =6.3 x 3 =7.5 x 4 =9.2 x 5 =Spheres find2.7 x 2 =4.3 x 3 =5.7 x 4 =7.2 x 5 =Prisms find3.9 x 2 =8.1 x 3 =4.7 x 4 =5.9 x 5 =
Q. Whichtimes tabledoes thisrepresent?Themultiplication by10 gives 25.10 x ? = 25Q. Whatnumber x 10gives 25?
2.5 x 10 = 25Findestimates for3 x 2.54 x 2.57 x 2.58 x 2.5Which linewould we needto draw to getestimates ofmultiplication by3.8?
We would needa line whosecoordinates are0,0 and 10,38Draw the line onyour graphsUse the graph tofind estimatesfor 5 x 3.83 x 3.87.5 x 3.8
What strategies did you use to obtain yourestimates?Did you use approximations e.g.5 x 3.8 ~ 5 x 4.0 = 20Exact answers are: 5 x 3.8 = 19.03 x 3.8 = 11.47.5 x 3.8 = 28.5What are the limitations of the graph method?
By the end of the lesson the childrenshould be able to:Draw and interpret a line graph whereintermediate points have meaning.