mathsweb.ieapng.netmathsweb.ieapng.net/.../2015/04/L3b_MTP_T3.docx · Web viewUse, read and begin to write vocabulary related to place value and properties of number

Medium Term Plan Level 3b Term 3 Class:

Problem Solving Strategies: Guess & Check

Unit Days Outcomes Overview of Key Learning Activities Assessment ResourcesL.I. We are learning to…

INTERACTIVE TEACHNG STUDENT ACTIVITES

Unit 1: Place Value & Decimal Numbers

83bNN01 Use, read and begin to write vocabulary related to place value and properties of number

3bNN08 Multiply and divide whole numbers to at least 4-digits by 10 and 100 (whole number answers)

3bNN06 Compare and order whole numbers to at least 5-digits

3bNN09 Round numbers to at least 5-digits to the nearest 10, 100 or 1000

3bNF05 Recognise and apply decimal notation to express whole numbers, tenths and hundredths as decimals e.g. 0.1 is the same as 1/10, within contexts

3TM 01 Describe and explain mathematical thinking and solutions orally and in writing using mathematical vocabulary, symbols, diagrams appropriately for an audience

Compare and order whole numbers

Problem: The population of Madang is 29 339. The population of Wewak is 25 143. Which has more people living in? How do you know?

Model writing numbers into place value chart and comparing the digits. Start on the left because these digits are worth more. Compare more than 2 numbers. Discuss the terms ascending and descending.

Compare pairs of 5-digit numbers in a range of contexts.

Order sets of numbers from smallest to largest (ascending) and largest to smallest (descending) order.

Can students compare two or more 5-digit numbers?

Can students find the midpoint of two numbers?

Can students round to the nearest 10, 100, 1000?

Can students place decimals on a number line?

Can students create patterns using decimals?

Can students represent decimals using base ten materials?

Place Value Charts

Number word poster

Number line

Base ten materials

Place Value Charts with decimals

Compare and order whole numbers

Problem: Which number is halfway between 740 and 750? Model using a blank number line to help work out which number is halfway. Repeat with a range of examples: 4000 and 4100, 2350 and 2380. Extend to higher numbers e.g. 27 400 and 28 000

Find the midpoint between numbers. Mark a number in the correct place on a partially numbered number line.

Order a group of 4 and 5 digit numbers.

Round numbers to the nearest 10, 100 or 1000

Problem: A store takes K7 458 on Saturday. How much is this to the nearest K100? Show 7 458 on a number line, with 7 400 and 7 500 marked. Which is it closer to? Write the number in a place value chart and model looking at the place value to the right (the tens column) to decide. In this case the

Round numbers to the nearest 10, 100 and 1000.

Solve puzzles such as: a number rounded to 12 350. What could it have been?

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digit is a 5 so the number is rounded up. Model rounding a range of 3, 4, and 5 digit numbers to a variety of places.

Round measurements to the nearest 10, 100 or 1000

Problem: Lucy measured the length of the field. It was 1 345m. Round it to the nearest 10m, 100m, 1000m.

Take a range of measurements and round them to the nearest 10, 100 and 1000.

Solve puzzles such as: rounded to the neares100 litres the swimming pool holds 13 400 L. What is the most amount of water that the pool could hold?

Position decimals on a number line

Count from zero in steps of 1/10. Label the number line using decimals and fractions.

Ask students what the value of the 4 in 0.4 is – write in a place value chart. To assist, check by referring to the labelled number line.

Position decimals on a number line.For example: Place these decimals on a line from 0 to 2: 0.3, 0.1, 0.9, 0.5, 1.2, 1.9

Identify the value of different digits in decimal numbers e.g. What is the value of the 4 in 3.4?

Create patterns using decimals

Continue the patterns:

1.2, 1.4, 1.6, 1.8, 2.0, 2.2…

1.1, 1.6, 2.1, 2.6

1.2, 1.5, 1.8, 2.1.

What do students notice about the different patterns? Use knowledge of whole numbers to help solve. Model describing the difference between terms using tenths e.g. 1.4 has increased by 2 tenths to

Extend a range of patterns. Identify missing values within patterns. Create their own patterns

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become 1.6

Represent decimals using base ten materials

Take a flat from the base ten materials and explain to students that this is worth one whole.

Take the longs and ask them to think about how many longs make a flat (10). What fraction is one long of the flat? (1/10 or 0.1)

Ask for a student to volunteer and make the number 3.2 using flats and longs. (3 flats, 2 longs). Place the base ten material in a place value chart and record in digits.

Ones . Tenths

3 . 2

Represent a range of decimals (to one decimal place) using base ten materials.

Represent decimals using base ten materials

Recap on the use of base ten materials to model decimals. If appropriate extend to hundredths.

Discuss with students that hundredths are smaller than tenths, they are the result of chopping one whole into one hundred pieces.

Ones . Tenths

Hundredths

Consolidate learning Represent a range of decimals (to one decimal place) using base ten materials. Order a range of decimals to one decimal place, using base ten materials to help.

Extend learningRepresent a range of decimals (to two decimal place) using base ten materials.

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3 . 2 5

3bNN08 will be a focus during the mental starters.

Continuous assessment throughout this unit should provide sufficient evidence to assess student progress towards achievement of learning intentions.

Unit 2: Money & Financial Mathematics

83bNMF01 Use, read and write, spelling correctly, vocabulary related to money

3bNMF02 Solve problems involving purchases and the calculation of change to the nearest five toea/cents, with and without digital technologies

3bNA05 Use a range of mental strategies to solve addition and subtraction problems involving numbers with up to 4-digits; use informal jottings to explain solutions orally

3bNA06 Refine and use efficient written methods to solve addition problems involving numbers with at least 4-digits

3bNA07 Refine and use efficient written methods to solve subtraction problems involving numbers with at least 4-digits

3TM 02 Select and apply appropriate calculation and problem solving strategies to solve problems involving one and

Add groups of numbers by looking for pairs which make 10

Mental Strategy: Re-ordering: add several single digit numbers or multiples of ten, using strategies such as looking for pairs that make ten and adding these first or starting with the largest number.

Price List: Show students a group of single digit kina prices for items in a shopping trolley. What is the most efficient way to add these together? Model looking for pairs of numbers which add ten.

Repeat with prices with multiples of 10. Model looking for pairs which add to make 50 or 100.

Card Trick. Deal 5 cards to each student. Move the cards to pairs which make 10 if possible. Check and discuss with a partner.

Shopping Prices – multiples of 10, find pairs which make 50 or 100 to make adding easier.

Can students reorder numbers to add more efficiently?

Can students find a difference by counting up?

Can students add by partitioning?

Can students write related addition and subtraction facts?

Can students use efficient written methods for addition?

Can students use efficient written methods for subtraction?

Can students select the correct operation when problem solving?

Cards

Prices tags

Base ten MAB materials

Find a difference by counting up

Mental Strategy: Partitioning - Bridging through multiples of 10 and 100: find a difference by counting up from the smaller number to the larger number, bridging through the next multiple of 10, 100 or 1000 e.g. 403 – 386, 4003 – 3993

Steven has saved $297. The computer he wants to buy cost $303. How much more does he need?

Solve a range of problems in a money context which require counting up.

E.g. How much money is left?Originally costs K605, New price is K598. How much was the price reduced by?

Use a number line to help record the landing points when bridging through 10, 100 or 1000.

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two steps, using technology as appropriate; estimate before calculating and check the reasonableness of solutions; begin to formulate problems and suggest extensions to investigations

297 + 3 + 3 = 303. The difference is 3 + 3 =6

Add by partitioning into tens and ones

Mental Strategy: Partitioning – Multiples of 10: partition into tens and ones, adding the most significant digits first e.g. 24 + 58

Sarah saved K34 and her little sister saved K28. How much money have they saved altogether?

Model 34 + 28 = 30 + 20 + 4 + 8 = 50 + 12 = 62

Solve a range of addition problems using partitioning. Students may need to make rough notes to support their calculations as they work. Remember it is a mental strategy so as confidence develops, students should move away from writing things down.

Use a known fact to work out related addition and subtraction facts

Mental Strategy: write 3 related addition and subtraction facts, given one fact.You know 56 + 14 = 70. What else do you know?

Model working out the other facts. It may help to show with practical models or with simpler examples e.g. if I know 3 + 2 = 5 what else do I know?

Create a table and fill in the missing statements. Should end up with 2 columns of addition and 2 of subtraction. Discuss with partner how to find all 4 facts.

23 + 38 = 61

38 + 23 = 61

61 – 23 =38

61 – 38 =23

Use the numbers 25, 37, 52, 77, 87 to write as many addition and subtraction facts as you can. Encourage students to use the partitioning strategy which was yesterday’s focus.

Use written calculation methods to solve addition problems

Problem: A cake cost K6.75 and the lollies to decorate it cost 45t. How much did I spend altogether?

Model using the expanded method of addition (Stage 3 in Guidance on Teaching Written Calculation).

Focus on adding the ones (rather than the hundreds) first.

Solve a range of problems using efficient written methods. Add HTO + HTO, including examples where the answer has ThHTO.

Students use MAB, as appropriate, to explain calculations. Some students may need further time to consolidate the method, rather than moving on to questions involving

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Focus on lining up the decimal points.

decimals. See assessment records from T2.

Use written calculation methods to solve subtraction problems

Problem: Lucy had K342 in her bank and spent K185. How much does she have left?

Model using the expanded method of subtraction (Stage 3 in Guidance on Teaching Written Calculation). Include decomposition from the hundreds to the tens, and the tens to the ones.

Solve a range of subtraction problems using efficient written methods.

Students use MAB, as appropriate, to explain calculations.

Solve addition and subtraction problems

Range of contexts over 2 days

Harry buys a book for $4.45 and a game for $6.90. How much change from $20?

Mixed problems – range of subtraction and addition worded problems.How can we decide which operation is needed? Which method will be most efficient?

Work with a partner to decide whether addition or subtraction is needed.

Make decisions about using mental or written methods to solve problems efficiently and accurately.

3bNA05 will be a focus during mental starters.

Unit 3: Multiplication & Division

53bNM01 Use, read and begin to write related vocabulary for multiplication and division to respond rapidly to oral questions phrased in a variety of ways

3bNM05 Recall multiplication facts to 10 x 10 and related division facts (focus on learning multiplication facts: x6, x7, x9)

3bNM07 Multiply and divide whole numbers by 10 and 100 (whole number answers)

Use written calculation methods to solve problems involving multiplication

Introduce the expanded method for short multiplication (Stage 4 in Teaching Written Calculations: Guidance for Teachers).

Link to the grid method so that students are able to see where the calculation comes from.

Use rounding to estimate an approximate answer before calculating.

Repeat over 2 days using different

Round, estimate, use expanded method to solve TO x O

Some students may need further time to consolidate the grid method.

Repeat over 2 days using different contexts.

Can students use rounding to approximate?

Can students use the grid method to record multiplication?

Can students use the expanded method to record multiplication?

Can students divide a 2

Tables square

Laminated grids to practise grid method

Laminated layouts to practise the expanded method for short multiplication.

Word banks to help decide whether to

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3bNM08 Use efficient mental strategies to solve problems involving multiplication of a 2-digit number by a 1-digit number

3bNM09 Solve problems involving division, including division with remainders, using mental strategies (2-digit number by a 1-digit number)

3bNM10 Develop and use informal written methods to explain problems involving multiplication of 2-digit numbers by a 1-digit number

3bNM11 Solve problems involving division, including division with remainders, using informal written methods (2-digit number by a 1-digit number)

3TM 02 Select and apply appropriate calculation and problem solving strategies to solve problems involving one and two steps, using technology as appropriate; estimate before calculating and check the reasonableness of solutions; begin to formulate problems and suggest extensions to investigations

contexts. digit number by a single digit number?

Can students use expanded short division to record division calculations?

Can students decide whether to divide or multiply when solving a range of worded problems?

Can students decide on an appropriate method of calculation i.e. mental or written, when solving problems?

multiply or divide

Use mental strategies to solve problems involving division

Problem: There are 77 students in Grade 4. 6 can go in each car. How many cars are needed to take the whole year group?Mental Strategy: TO ÷ 0 Partition into multiple of 10 and extra ones: 60 + 17÷6 gives 10 + 2 r 5 = 12 r 5

Round up or down? Need 13 cars to move everyone, but one will only have 5 students in.

Interpret and solve a range of worded problems to practise the skill.

Include examples with remainders.

Include examples where decisions about rounding up or down need to be made. E.g. how many boxes will be full? How many cars do I need to take the whole class?

Use written calculation methods to solve problems involving division

Model division problems TO ÷ OUse expanded short division (chunking) to record. (Stage 3 in Teaching Written Calculations: Guidance for Teachers).

Use expanded short division to record when solving TO ÷ O

Solve problems involving multiplication and division

Interpret and solve a range of worded multiplication and division problems. Focus on reading and understanding the problem, act it out if appropriate. Make decisions over whether a written or mental method is required to solve the problem.

Solve a range of problems TO x O and TO ÷ O.Work in pairs and decide which operation is needed and whether a mental or written method is required.

3bNM05, 3bNM07, 3bNM08 will be a focus during mental starters.


Day to Assess and Review – Summative Assessment to cover concepts from Units 1, 2, and 3.

Unit 4: Capacity

83bMM01 Use, read and write

Measure capacity using

What is the capacity? Show students a scale with some of

Read a range of scales, with different sized divisions.

Can students read a partially marked scale?

Measuring cylinders – with a range of

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vocabulary related to measurement

3bMM02 Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, mass and capacity; use appropriate scaled instruments to measure length, mass, capacity

3bMM03 Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit

3bNN07 Make and justify estimates of numbers and measurements in a range of practical contexts

3TM 02 Select and apply appropriate calculation and problem solving strategies to solve problems involving one and two steps, using technology as appropriate; estimate before calculating and check the reasonableness of solutions; begin to formulate problems and suggest extensions to investigations

partially numbered scales

the divisions unmarked. How can we calculate the missing value?In the example below, there are 5 divisions between 300 and 400 so each division muse be worth 20ml. The marked position is therefore 320ml. Check by counting in 20s.

Range of activities involving reading of scales over 2 days.

Identify the value of each division, use skip counting to test they are correct.Work out what the marked place on the scale is.

Range of activities involving reading of scales over 2 days.

Can students estimate the capacity of a container?

Can students measure the capacity of a container?

Can students order a group of containers according to the size of their capacity?

Can students use an appropriate calculation method?

Can students convert between ml and l?

Can students select the correct operation when solving word problems involving mass?

marked scales

Items of food with capacity marked on

Range of containers for students to estimate and measure capacity

Estimate the capacity of containers

Can you estimate? A teaspoon is about 5ml. A glass of water is about 250ml. A carton of milk is 1l Estimate and measure the capacity of a range of containers using scales. Use the strategies from yesterday to help read accurately.

Estimate and measure a range of capacities – does their estimation improve throughout the activity?

Estimate the capacity of containers

Measure and record the capacity of five different objects that you estimate to have a total capacity of 2l.

Ask students to read the questions and interpret what it means – need

Work in pairs to agree a collection of 5 containers – make an estimate for each, measure and then calculate how close they were. Encourage discussion about the estimates – what are they comparing it to when they estimate

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5 containers which in total make 2l, not 5 containers which each hold 2l.

the capacity? Can they improve with 5 different containers?

Compare and order capacity of containers

Order these containers objects from smallest to largest.Medicine spoon, yoghurt pot, drinks can, milk carton, bucket. Estimate and then check by measuring the capacity.

Students have different collections of objects to order by estimating and measuring.

Convert between units of measurement

Q: A coke bottle holds 500ml. What is that in litres? Ask students how many ml there are in a litre.1l= 500mlConvert from ml to l and vice versa. Record in l and ml. For example, 1l 500ml if needed.

Range of activities over 2 days.

Convert a range of mass from l to ml and vice versa. Include key fraction values such as: ½ l, ¼ l, ¾ lUse capacity equipment to check conversions.


Solve word problems involving capacity

There is 500ml of juice. Sam drinks 125 ml. How much is left over?How can I solve this problem?

Solve a range of problems, using all four operations, modelling a range of mental and written methods.

Solve a range of problems, focus on selecting correct operation and an appropriate mental or written methods.

Continuous assessment throughout this unit should provide sufficient evidence to assess student progress towards achievement of learning intentions

Unit 5: Data 83bSD01 Use, read and begin to write vocabulary related to data

3bSD02 Select and trial methods for data collection, including survey questions and recording sheets

3bSD03 Construct suitable data displays, with and without the

Display data on bar charts

Show students a bar chart with a scale where the axis is marked in

Present students with a tally chart showing province of origin for students in the school. Discuss with students the need for the scale on the side to be in 2s, 5s or 10s. Students draw the bar chart from the data. What does their graph show?

Can students represent data using a bar graph?

Can students represent data using a pictogram?

Can students draw conclusions using data to support their ideas?

Range of data and graphs from newspapers, sports matches etc

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use of digital technologies, from given or collected data: tables, bar charts and pictograms with one-to-many correspondence

3bSD05 Evaluate the effectiveness of different displays in illustrating data features including variability

3TM 03 Investigate and check the accuracy of a statement; explain the reasoning used and give an example to justify the conclusion; make and check conjectures and begin to form generalisations based on results of investigations

multiples of 2, 5, 10 or 20.

Write statements about the graph and what it shows.

Write a list of features including: Title, labelled axes, bars drawn with a ruler, scale on axis.

What would they expect the bar at 1:00 to show? Would the graph be different on a Saturday?

Can students design questions to collect useful information?

Can students collect data?

Can students pose questions about data?

Can students create a survey with a scale?

Can students interpret a range of data displays?

Can students identify elements of a graph which may be misleading?

Display data on pictograms

Show students a pictogram with a scale of many to one correspondence.

E.g. Five people = one face.

Answer a range of questions on this chart, referring to the scale and how this affects the answers.

Pose a statement such as: Snax chicken crackers are the favourite biscuit in Papua New Guinea.

Students use given data to draw a pictogram. Ensure that the data requires many to one correspondence.

Students respond to the statement, using pictogram to support their comments.

Design and carry out a survey

Create a survey to find out the most popular playground game for Grade 3 students.

Introduce the idea to students and discuss ways they could approach this.

Discuss the advantages and/or disadvantages of open-ended questions in a survey, compared to questions with predetermined categories.

In pairs, decide which questions they will ask? How will they ensure the information is useful? Trial questions on each other. Design a table to record the information and decide upon an appropriate method of recording the results table.

Display data using bar charts and pictograms

Remind students of the features of a bar chart and pictogram.

One partner draws a pictogram, one draws a bar chart. Use data from own survey and represent it on a bar chart.

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Compare the charts and decide which they think is more useful.

Write a range of questions to use with their graph and ask a different group to answer in the plenary.

Design and carry out a survey

Create a survey with a scale for students to indicate their preferences for food items from the canteen menu.

Scale of 1 to 5 to indicate preferences (1 = don't like, 2 = like a little, 3 = don't know, 4 = like, 5 = like a lot).

Students prepare a table to collect the tally when they conduct the survey. Sketching one out on a whiteboard will enable them to trial different formats.

Conduct survey.

Use digital technology to represent data

Model how to create a bar graph using a spreadsheet program.

Present data to students. Use the spreadsheet program to create a bar graph. Write statements to describe what the graph shows.

Analyse a range of data and displays

Show students the graph and pose a range of questions. For example:

http://www.topmarks.co.uk/Flash.aspx?f=barchartv2 Use the website to generate a range of graphs.

Show students a range of graphs. Answer questions, write statements about the graphs.

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http://www.topmarks.co.uk/Flash.aspx?f=barchartv2

http://www.topmarks.co.uk/Flash.aspx?f=barchartv2



Which was the most popular genre? How many fewer people liked fantasy than adventure? How many children were asked altogether? Model how to use the scale to help calculate the different values.

Identify misleading features of graphs

Show students the graph below. How would they describe the sale of biscuits?

Why is looking at the graph a bit misleading?

Discuss how the final bar is wider than the others so it seems that 2001 is much larger than the rest.

Analyse a range of graphs with issues which make them misleading. Discuss with a partner and consider how they should be redrawn. For example, the graph below only starts at 106 on the axis. Why would this be negative the government?Suggests job levels have halved over the year, whereas only gone down by 1%.


Unit 6: Time 5 3bMM01 Use, read and write vocabulary related to measurement

3bMM06 Convert between units of time; use am and pm notation and solve simple time problems

Relate digital and analogue time

Show students a selection of clocks and model writing in digital time – am and pm. Write in words for analogue time.


Match times cards showing clock faces, digital times, analogue times.


Can students relate digital and analogue times?

Can students estimate and measure time?

Can students solve problems involving

Mini clocks

Picture cards showing clock faces, digital times, analogue phrases.

StopwatchesEstimate and measure time

Ask students to sit quietly with their eyes closed. When they think

Use a stop watch to estimate and measure a range of events.

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3TM 01 Describe and explain mathematical thinking and solutions orally and in writing using mathematical vocabulary, symbols, diagrams appropriately for an audience

30 seconds is over open their eyes.

Measure the time for a partner to count to 50, write their name etc. using a stopwatch.

Estimate and measure the time it takes a partner to run across the oval.

time?

Can students solve problems using a calendar?

Calendars

Solve a range of problems involving time

Problem: Raiza got into the pool at 2:26. She swam until 3 o’clock. How long did she swim?

Model using an empty number line to calculate the amount of time.

Solve a range of problems involving time.

For example:

Mary got up at 7:35. She left for school 45 minutes later. Her journey took 15 minutes. What time did she arrive at school?

Lunch takes 40 minutes. It ends at 1:10 pm. What time does it start?

Solve a range of problems involving time

Problem: The swimming pool shut for repairs on Friday, 20 March. It opened again on Friday, 10 April. For how many weeks was the swimming pool shut?

Model using the calendar to count the number of days, then working out the number of weeks.

Use this year’s calendar to work out, for example: which day of the week is 22 June; the date of the third Thursday in May; the number of days from 27 February to 10 March; the number of weeks from 18 September to 13 November.

Solve similar problems to the main teaching.


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