hamiltontrust-live-b211b12a2ca14cbb94d6-36f68d2.divio-media.net… · Web viewPuzzles Unit 1. Whole Class Teaching Input DAY 1. Objectives : Use a calculator to convert fractions

$Page 1: hamiltontrust-live-b211b12a2ca14cbb94d6-36f68d2.divio-media.net… · Web viewPuzzles Unit 1. Whole Class Teaching Input DAY 1. Objectives : Use a calculator to convert fractions$
Puzzles Unit 1

Whole Class Teaching Input DAY 1

Objectives Use a calculator to convert fractions to decimals.Read and understand recurring displays. Round to two decimal places.

Resources Calculators, IWB calculator, whiteboards and pens

Teaching Children work in pairs, using a calculator. Ask children to enter 1 ÷ 3 =. What’s the answer? What fraction is this decimal equivalent to? Explain that if we divide 1 into 3 equal parts, each part is one third (1/3), which we can write as 0.333333 as a decimal. This decimal repeats 3 forever; we call it a recurring decimal. Children write a short division calculation for 1 ÷ 3 to discover this for themselves.

While there is no universally accepted notation for recurring decimals, in the UK it is usually written as 0.3 with a dot above the 3:

What do you think we will get if we divide 2 by 3 on the calculator? Agree that you get 0.666667 (depending on the number of decimal places in the calculator display), which can shortened to:

Really this is 0.6666666 going on forever, but the calculator rounds the last digit. What would this decimal be if we rounded it to two decimal places? (0.67). Remind children that 2/3 is approximately equivalent to 67%.

Use an IWB calculator to do the same calculation, showing the greater number of digits. Then use the IWB calculator to divide 1 by 7. This is the decimal equivalent to one seventh (1/7). This is a recurring decimal too, but this time it’s a pattern of six repeating digits. Dots are used to show the ends of the repeating sequence of digits:

Sketch a line from 0 to 1. Mark on tenths and ask children to help to mark on 1/7. Discuss its position. So, this fraction is between 0.14 and 0.15, and closer to 0.14 than 0.15. How can we tell? So, which is more 14/100 or 1/7?

Let children try dividing 1 by all numbers less than 10 to find other recurring decimals (1/6 and 1/9).

Help children to round them to two decimal places and to mark them on the number line (1/6 ≅ 0.17, 1/9 ≅ 0.11).

© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.teach-activs_puzzles_6709

You’ve worked out the answer to a calculation in a problem and the calculator shows 52.14285714. What answer would you give if the question related to pounds? Centimetres? Metres? Litres? Help children to round this answer to one, two and three decimal places. What if the question was asking for the number of weeks in a year?


Group activity notes DAY 1 Use a calculator to convert fractions to decimals by division and place the fractions on a 0–1 (or 0–2) line. Aim to get three fractions in a line without an opponent’s fraction in between.Objective: Use a calculator to convert fractions to decimals. Read and understand recurring displays. Round to two decimal places.You will need: ‘Three in a row’ sheets 1, 2 and 3 (see resources), calculators, flipchart and two different coloured pensGroup of 6 – with T or TA Working at ARE

Enlarge a copy of ‘Three in a row’ sheet 2 (a 0–1 line landmarked in tenths, with 0, 0.5 and 1 labelled). Divide the group into two teams. Give a different colour marker pen to each team. Each team take it in turns to choose a numerator and denominator from numbers 1 to 10 to enter into the calculator as a

division. They use this decimal equivalent to the fraction to help to place the fraction on the 0–1 line in their colour marker pen. The aim is to get three fractions in a line without one of the other team’s fractions in between. Support the discussion about which divisions might give useful fractions, but let children test out their ideas. After a while, ask

questions such as: What do you know about comparing the numerator with the denominator to give a number which will fit on this line? (The numerator must be less than the denominator.) If you want to get a decimal less than 0.5, what can you say about the numerator and denominator? (The numerator must be less than half of the denominator).

Working towards ARE Using a copy of ‘Three in a row’ sheet 1, children choose numerators and denominators from 1, 2, 3, 4, 5, 8, 9 and 10.

Greater Depth Using a copy of ‘Three in a row’ sheet 3, children choose numerators and denominators from 1 to 12 on a 0–2 line.

If you want to place a decimal between 1 and 2 on the line, what do you know about the numerator and denominator? The numerator must be greater than the denominator, but less than double the denominator.

Outcomes: I can use a calculator to convert fractions to decimals. I can read recurring displays.



Objectives Use a calculator to convert fractions to decimals.Realise when a calculator has produced a rounding error.

Resources Calculators, IWB calculator

Teaching Ask children to enter 1 ÷ 3 into the calculator and not to clear it. If you multiply this answer by 3, what should you get? Try it. What happens? The calculator is wrong! This is called a rounding error. Explain that we know that 1 divided by 3 gives a recurring decimal that goes on forever, but the calculator only thinks the actual answer is 0.33333 (or however many places it shows/stores) so when it multiplies this by 3, it gets an answer of just under 1.

Use the WindowsTM calculator (or the one on your phone) to carry out the same key sequence. But this calculator gets 1 as an answer, why do you think that it is? Explain that some calculators display more digits, and some keep more in their memories that aren’t displayed – this means that they produce fewer rounding errors.

Ask children to divide 1 by 4, then multiply by 4. The calculator is right this time.

Do you think the calculator will give the correct answer when dividing, then multiplying by 5? Why? What about dividing by 6? Try it!


Group activity notes DAY 2 Group activity notes DAY 2

Investigate divisors 2 to 10 that will give rounding errors on the calculator. Investigate divisors 2 to 20 that will give rounding errors on the calculator.Objective: Realise when a calculator has produced a rounding error. Objective: Realise when a calculator has produced a rounding error.You will need: Calculators You will need: CalculatorsIn pairs – independent or with TA Working towards ARE

Children divide 1 by 2, 3, 4, 5, 6, 7, 8, 9 and 10 on the calculator and then multiply back again, first predicting which ones they think will give rounding errors.

Does the same thing happen when you divide other numbers by these same divisors? e.g. is there a rounding error when we do 2 ÷ 9 or 5 ÷ 6?

In pairs – independent or with TA Working at ARE

Children enter 2 ÷ 3 = × 3 = and 1 ÷ 9 = × 9 = on calculators and see what happens. They also record what the answer should be.

Next, they work in pairs to find other divisors that will give similar rounding errors (those which give recurring decimals, e.g. 6, 7, 11, 13 etc).

They write what they found, including which divisors gave same-digit recurring decimals, e.g. 6 and 9, and which gave recurring decimals with different digits, e.g. 7 and 13.

Outcomes: I realise that a calculator can produce rounding errors.

Outcomes: I realise that a calculator can produce rounding errors.


Group activity notes DAY 2


Given the answer 1.181818 (13 ÷ 11), use a calculator to work out the mystery division. Set further similar problems for the group.Objective: Use a calculator to convert fractions to decimals.You will need: Calculators, cardsGroup of 6 – with T Greater Depth

Secretly enter 13 ÷ 11 = into the calculator and show children the display (1.181818…).

I’ve divided 2 numbers less than 20 to give this answer. Which number was bigger, the first or second? How can you tell? Could I have divided by 5? Why not? Which other numbers could I have not have divided by?

Children work in pairs to use a calculator to try and work out which 2 numbers you entered.

Challenge! Set a similar problem (using numbers <20) for the group to solve. Write it on a card to share with the others.

Outcomes: I can use a calculator to solve problems involving conversion of fractions to

decimals.


Objectives Use a calculator and reasoning skills to aid problem solving.

Resources

Teaching Write on the board the following questions:675 + = 1000, 47.2 × = 283.2, 586.1 ÷ = 24.7, 84 ÷ = 7, – 6.795 = 4.615, 25 × = 1000;Find two consecutive numbers with a product of 2070;Find two numbers greater than 1000 with a difference of 75. Children work in pairs. They discuss each question and

decide whether or not they would need to use a calculator. Take feedback, writing C next to those where most children

would use a calculator. Encourage children to explain their reasoning.

Also discuss how inverse operations can be used to solve some of the questions, using one or two to exemplify this, e.g. 47.2 × = 283.2, agree that we can divide 283.2 by 47.2.

Discuss how to solve the calculation involving subtraction e.g. − 6.795 = 4.165. Agree that we need to add the two numbers not subtract! Encourage children to test out their answer if they are not sure, by substituting their answer for the box in the equation.

Let’s have a go at Find two consecutive numbers with a product of 2070. What skills do we need to use? (Estimating, tables facts, trial and improvement.)


Group activity notes DAY 3 Group activity notes DAY 3

Use a calculator to solve multiplication problems. Use a calculator, trial and improvement, and reasoning skills to aid problem solving.

Objective: Use a calculator and reasoning skills to aid problem solving. Objective: Use a calculator and reasoning skills to aid problem solving.You will need: Calculators You will need: CalculatorsGroup of 6 – with T or TA Working towards ARE / Working at ARE

Work as group to find two consecutive numbers with a product of 552 (23 and 24). Firstly, encourage children to make a few guesses using the calculations, and then use these guesses to inform future estimates.

Next ask children to work out three consecutive numbers which might have a product of 120. (4, 5 and 6).Can you find a set of three non-consecutive numbers with the same product?

Why has it been good to use the calculator to work on these challenges?

In pairs – independent or with TA Greater Depth

Children work in pairs. They solve their choice of these problems:1. Find two consecutive numbers with a product of 5402 (73 and

74). What could the ones digits be?2. Find a number whose square root is between 22 and 23.3. Which unit fraction is equivalent to the decimal 0.0625?4. What fraction has the decimal equivalent 1.5555555?5. What are the values of A and B, and P and Q in the following

equalities:AB = 32 (25) PQ = 0.001 (10−3)

Outcomes: I can use a calculator to try different solutions and then use these to

inform problem solving.

Outcomes: I can use a calculator to try different solutions and then use these to

inform problem solving. I can decide when it is appropriate to use a calculator and when it is

not.



Objectives Begin to use a calculator’s memory keys (M+, M− and MR).

Resources Calculators

Teaching We’re going to learn how to use the memory buttons on a calculator today.Write on the board the following key sequence: 3 + 2 = M+ 3 × 4 = M+ MR Ask children to enter it and discuss what is happening: What did the calculator do? Did you notice the little M in the display? Agree that it has put the answer to 3 + 2 in its memory, then added the answer to 3 × 4, and displayed the total when they pressed MR (memory recall), i.e. (3 + 2) + (3 × 4). The M+ button adds what is in the display to its memory, the MR button shows what’s in the memory.

Ask children to press the MC button, explaining that this clears the memory.

Write: 10 × 2 = M+ 2 × 4 = M− MR and ask children to work out what happens (12 should be displayed). What happened this time? Agree that the calculator subtracted the answer to 2 × 4 from 10 × 2, i.e. (10 × 2) – (2 × 4). The M− button subtracts the displayed answer from what’s in the memory.

Write (47 × 56) + (29 × 83). How would you normally enter this calculation into a calculator? We usually do two multiplications separately, then add these together. However, we can do this using the calculator's memory buttons. Ask children to enter 47 × 56 = then press the M+ button. The calculator has stored the answer to 47 × 56 in its memory. Clear the display then Press MR to see it. Ask children to enter 29 × 38 = followed by the M+ button. Now press MR. There’s our answer! The calculator has added the answer to 29 × 38 to the first product.

Repeat with (89 × 24) – (34 × 27), this time pressing the M− button after the second multiplication to subtract this product from the first.


Group activity notes DAY 4 Group activity notes DAY 4 Practise using the memory functions in multi-step calculations, including word problems.

Use the memory function to help solve a shopping-related multi-step calculation.

Objective: Begin to use the memory (M+, M− and MR) keys. Objective: Begin to use the memory (M+, M− and MR) keys.You will need: Calculators, ‘Using the memory function’ activity sheet (see Practice worksheets)

You will need: Flipchart and pens, calculators

Group of 6 – with TA or T Working towards ARE As a group, discuss each calculator key sequence in

questions 1 to 4 (see Practice worksheet), first predicting what the calculator will do and what the answer might be.

Look at question 5. Support children in using calculators to work out the answer to the multiplication in the first bracket, adding to the memory, and doing likewise for the second bracket before recalling the answer to the whole calculation.

Can we do the same for question 6? No. Why? Point out that the calculator needs to work out the answer the calculation in the second bracket, then children subtract from the memory by pressing M−. This didn’t matter with question 5 as addition is commutative.

Children work in pairs on questions 7 and 8. Compare answers.

They then follow the key sequence for questions 9 and 10. Challenge them to talk through what the calculator is doing at each stage.

Group of 6 – with T or TA Working at ARE / Greater Depth Here is a chef’s order for the

ingredients she needs to make a large chicken and broccoli pasta bake. Display the following as a list.

We could enter each multiplication separately, make a note of each answer, then add them up, but let’s try this using the memory functions. Remind children that if they enter a wrong digit, they can use the clear last entry button rather than starting again – very useful when working out long calculations!

Children work in pairs. They use the calculator to work out each multiplication then add to the memory. Press MR to find the total cost. Have you all found the same answer?

The memory button can help us with lengthy calculations like this, but there are lots of opportunities to make mistakes, so making an estimate is important! Agree an estimate and repeat the calculation.

Double all the amounts and repeat. Did children get double the cost? Children work in pairs to make up their own string of calculations.

Each child finds the total answer and compares with their partner.Outcomes:

I am beginning to use the calculator’s memory (M+, M− and MR) keys to solve problems.

Outcomes: I am beginning to use the calculator’s memory (M+, M− and MR) keys. I can use knowledge of order of calculations and memory function to enter

a series of calculations into a calculator.


8 chickens at £3.75 each5kg broccoli at £1.29 per kg7kg cheese at £6.49 per kg3 dozen eggs at £2.50 per dozen5kg of flour at 79p per kg


Objectives Begin to use the memory (M+, M− and MR) keys.

Resources Calculators

Teaching Write on the board this sequence of keys: 6 + 4 = M+ 4 + 2 = × MR = and ask children to work out what happens. Agree that the calculator adds 6 and 4, and then multiplies this by the answer to 4 + 2. Note that we didn’t add the answer to 4 plus 2 to the memory, but pressed multiply and then the MR button to multiply the number on the display (6) by what was in the calculator’s memory.

Ask children to use the memory function to help them to work out: (68 + 27) × (56 + 29).

Write this sequence on the board: 5 − 3 = M+ 6 + 4 ÷ MR =. What do you think will happen this time? Talk to your partner and then try it. Remember to clear the memory before you begin. Was the answer what you expected? Agree that the calculator works out 10 ÷ 2, the number in its memory. (Some children may have thought that the calculator would work out 2 ÷ 10.)

Write (32 + 35) ÷ (42 + 19). How could you use the memory buttons to work this out? Establish that the second addition would need to be entered first and the answer entered into the calculator’s memory. Next we enter the first addition, then divide by the number in the calculator's memory. This is more complicated than when we multiplied the answers to two calculations, why? (Multiplication is commutative, the order of multiplication does not matter, but this is not the case with division where the order matters).



Discuss given calculator key sequences. Compare estimates of answers with actual answers.Objective: Begin to use the memory (M+, M− and MR) keys.You will need: Calculators, ‘Using the calculator’s memory’ sheet 1 (see Practice worksheets), flipchartGroup of 6 – with TA or T Working towards ARE/ Working at ARE

As a group, look at ‘Using the calculator’s memory’ sheet 1 (see Practice worksheets). Discuss what you expect the answers to be for questions 1 to 6. Write them on the flipchart.

Children work in pairs to enter the key sequences and compare answers with the ideas on the flipchart. Were there any surprises? Have children now worked out what the calculator was doing?

In pairs, children use what they have learnt to answer questions 7 to 10, first agreeing a key sequence for each. Encourage children to estimate the answers so they can see if are using the memory function correctly or not.

Outcomes: I am beginning to use the memory (M+, M− and MR) keys. I can use knowledge of order of calculations and memory function to enter a series of calculations into a

calculator.

© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. teach-activs_puzzles_6709


Use the memory function to help solve an area-related multi-step calculation.Objective: Begin to use the memory (M+, M− and MR) keys.You will need: Flipchart and pens, calculatorsGroup of 6 – with T Greater Depth

A lawn measures 7.6m by 3.7m, there is a 1.2m border on 3 sides, and a patio which is 2.7m deep on the fourth side (see diagram). What is the total area of the garden? Draft out the calculation needed…

Agree a calculation, e.g. (1.2 + 7.6 + 1.2) × (1.2 + 3.7 + 2.7). What do you think the answer will be, roughly? Children work in pairs to use the memory function to help find the

answer. Does your answer look about right? Children sketch other gardens making up their own dimensions; then find

the area.

Outcomes: I am beginning to use the memory (M+, M− and MR) keys. I can use knowledge of order of calculations and memory function to enter a series of calculations into a calculator.


ADDITIONAL RESOURCES:

Calculators IWB calculator Whiteboards and pens ‘Three in a row’ sheets 1, 2 and 3 (see resources) Flipchart and pen Coloured pens Cards ‘Using the memory function’ (see Practice worksheets) ‘Using the calculator’s memory’ sheet 1 (see Practice worksheets)

The links to the websites and the contents of the web pages associated with such links specified on this list (hereafter collectively referred to as the ‘Links’) have been checked by Hamilton Trust (being the operating name of the registered charity, William Rowan Hamilton Trust) and to the best of Hamilton Trust’s knowledge, are correct and accurate at the time of publication.

Notwithstanding the foregoing or any other terms and conditions on the Hamilton Trust website, you acknowledge that Hamilton Trust has no control over such Links and indeed, the owners of such Links may have removed such Links, changed such Links and/or contents associated with such Links. Therefore, it is your sole responsibility to verify any of the Links which you wish you use.

Hamilton Trust excludes all responsibility and liability for any loss or damage arising from the use of any Links.


Documents

hamiltontrust-live-b211b12a2ca14cbb94d6-36f68d2.divio-media.net… · Web viewPuzzles Unit 1. Whole Class Teaching Input DAY 1. Objectives : Use a calculator to convert fractions