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Medium Term Plan Level 5a Term 3 Class:

Problem Solving Strategies: Act It Out, Guess & Check

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

INTERACTIVE TEACHNG STUDENT ACTIVITES

Unit 1: Calculations & Units of Measurement

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Convert units of measurement

Convert units of measurement and solve problems involving length. Revisit the different conversions for km to m, m to cm, cm to mm and vice versa. Show in a place value chart. Extend this to word problems.

Rita measures her plot of land and discovers it is 0.85km. Fencing costs K15 per metre. How much will it cost to put a fence along the land?

Convert units and solve word problems.

Can students convert between units of length?

Can students convert between units of mass?

Can students convert between units of capacity

Can students use an appropriate method to solve addition and subtraction problems?

Can students select the correct operation when solving word problems?

Can students use the distributive law when multiplying?

Can students decide how to express a quotient depending on the context?

Convert units of measurement

Convert units of measure and solve problems involving capacity and mass. L to ml, cl to ml, g to kg vice versa.

A bottle for a water cooler holds 25L How many cups of water holding 300ml can be filled?

Convert units and solve word problems.A box contains bags of crisps.Each bag of crisps weighs 25 grams. Altogether, the bags of crisps inside the box weigh 1 kilogram. How many bags of crisps are inside the box?Each booklet weighs 48g.How much do 220 booklets weigh altogether?Show your working. Give your answer in kg.

Use efficient strategies to solve problems

Addition or Subtraction? Written or Mental? Investigate different calculations, when is a mental method appropriate? When do students need to use written methods? Include decimals.

Students work in pairs to answer a range of calculations, discuss and name mental method/opt for written calculation.

Use efficient strategies to solve problems

Problem: In 2005, about 60.2 million people lived in the UK.Look at the information about these people.■ 50.4 million lived in England.■ 5.1 million lived in Scotland.■ 3 million lived in Wales.■ The rest lived in Northern Ireland.

Students work in pairs to answer a range of calculations, discuss and name mental method/opt for written calculation.

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(a) In 2005, about how many people lived in Northern Ireland? Can students

solve multi-step problems?

Can students compare the value of different products?

Use the distributive law

Investigate the distributive law3.7 × 99 = 3.7 × (100 – 1)= (3.7 × 100) – (3.7 × 1)= 370 – 3.7= 366.3Relate this to the mental strategy of compensating. Find the cost of 38 items at $1.99 each. Conclude it is easier to calculate $2 × 38 then compensate by 38 cents than to add $1.99 a total of 38 times, or calculate 1.99 × 38.

Students investigate a range of calculations – how can they express the numbers in different ways to make calculation more efficient?

Solve problems involving quotients and remainders

Discuss with students how the context of a problem affects how to express and interpret a quotient – that is: whether to express it with a remainder, or as a fraction, or as a decimal; whether to round it up or down; what degree of accuracy is required.

For example:Four small cars cost a total of K97 246. What should a newspaper quote as a typical cost of a small car?An appropriate answer is rounded: about K24 000 each.

107 students and staff need to be taken to the inter-school sports competition. How many 15-seater minibuses should be ordered?7 2⁄15 minibuses is not an appropriate answer for this example.To round 7 2⁄15 down to 7 would leave 2 people without transport. 8 minibuses is the appropriate answer.

Solve problems where students have to evaluate a remainder, how to express it and how to round up or down. For example: A football club is planning a trip. 12100 fans want to travel. Each coach holds 52 passengers.How many coaches are needed?

The club wants to put one first aid kit into each of the 234 coaches. These first aid kits are sold in boxes of 18.How many boxes does the club need?

Solve multi-step problems

Problem: A number of bars of soap are packed in a box that weighs 850g. Each bar

Solve a range of multi-step problems.

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of soap weighs 54g. When it is full, the total weight of the box and soap is 7.6kg. How many bars of soap are in the box?

Strategy: Act It Out – act out the problem to help understand what it is asking. Model the conversion and different operations needed to solve the problem.

Encourage students to act out the problems to help solve it if appropriate.

Compare the cost of different products

Problem: Which pack gives better value for money? Model calculating the unit value and comparing this figure. Discuss the appropriate written or mental strategy.

Multi-pack of 9 Twisties at K6.90ORMulti-Pack of 6 Twisties at K4.50

Compare a range of products and the different values involved in each.

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Unit 2: Algebra 55aNP01

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Add and subtract like terms

Problem: How can we simplify 2a + 4b + aModel using pictures of fruit to help students understand the process. 2 apples and 4 bananas and another apple becomes 3 apples and 4 bananas. So 3a + 4b.

Simplify a range of expressions which involves adding and subtracting terms.

Sample Problem:

The number in each cell is the result

Can students simplify algebraic expressions?

Can students write equivalent algebraic expressions?

Can students use inverses to rearrange

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of adding the numbers in the two cells beneath it.Write an expression for the number in the top of the cell.Write the expression as simply as possible.

expressions?

Can students evaluate expressions using the correct order of operations?

Simplify terms with multiplication and division

2ab x 3 – remind students that the order of multiplication does not affect the answer – commutative law so that we can say

2 x 3 x ab = 6ab

12a ÷ 3 this can be solved by thinking of it as a fraction and simplifying so 12a = 4a3

Simplify a range of expressions which involve division and multiplication.

Identify equivalent expressions

Show studnets a range of cards with algebraic expressions on. For example: n + 2, 2+ n, n÷2, 2n – n, n, n/2, n + n etc. Ask students to identify cards which have the same value. Students could also write extra cards which would have the same value as 3n +2n; how many ways can the class come up with?Include a discussion about statements with division in e.g.a ÷ bc is equivalent to a / bc and a ÷ (b x c)it is not equivalent to a ÷ b x c or a/b x c

Match pairs of cards with the same value.

Simplify expressions to find those expressions which are equal.

Write puzzles for a partner. For example, here are 5 expressions. There are 4 expressions which are equivalent, which is the odd one out? Why?

Use knowledge of inverses to rewrite algebraic expressions

Explain that sometimes we may need to rewrite algebraic expressions. Model using ‘fact families’ to help do this. e.g.a + b = 5 so b + a = 55 – b = a so 5 – a = bab = 24 this implies that ba = 24, b = 24/a, a

Create fact families for a given expression.

Solve equations using a given value for one of the unknowns.

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= 24/bThe expression ‘change the side, change the sign’ can be useful.

Use order of operations with algebraic expressions

The order in which we perform operations in mathematics matters. Show students the function machines below and see what happens when we change the order.

2 > - 2 > x 5 > + 5 = 52 > +5 > - 2 > x 5 = 352 > x5 > + 5 > - 2 = 13

Introduce students to the idea of BODMAS –

Now instead of 2 imagine we want to use a letter to represent the input, we will use x.To say subtract 2 and then multiply by 5 and then add 5 we would write

. What would the other expressions be?

Write expressions to illustrate statements such as:First add 6 then multiply by 2First divide by 3 then take away 7

Substitute values for x into the expressions below and evaluate the values of the expressions.For example, if x is 3 what is the value of the following expressions? 2x + 3, x – 5, 2(x + 3), 3(x + 1) – 4, 5 – 2x, 2(3 – x),2x + 3x – 1

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Day to Assess and Review – Summative Assessment on Units 1 and 2.

Unit 3: Geometric Reasoning

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Calculate the missing angle in a triangle

Teach over 2 days

Model rearranging the angles of a triangle to create a straight line. What does this tell us? Model using the angle sum to calcualte missing angles. Stduents can then move on to caclualting missing angles independently.

Can students calculate the missing angle in a triangle?

Can students use properties of a special triangles

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For example: Calculate the missing angles a, b, c, d.

Extend to questions which use properties of ‘special triangles’ for example 2 angles the same in an isosceles triangle.

Teach over 2 days

to calculate the missing angle in a triangle?

Can students investigate given statements?

Can students calculate the missing angle in a quadrilateral?

Can students investigate the properties of quadrilaterals?

Can students use the properties to name a quadrilateral?

Investigate properties of different triangles

Present students with the following statements: 1. Triangles can have more than one

obtuse angle2. A right angled triangle can also be an

isosceles triangle3. A triangle with a 60° angle is an

equilateral triangle. 4. There are two triangles in all 4 sided

shapesAre these always, sometimes or never true?Ensure that students understand each statement and discuss possible ways to start investigating them.

Students work in pairs, finding examples to help explain and justify their decisions.

http://nrich.maths.org/1052 this link may help some students to take statement 4 further.

Allow time for a longer plenary to discuss and present findings.

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http://nrich.maths.org/1052



Calculate the missing angle in a quadrilateral

Model using the angles of a quadrilateral to make a circle. What does this tell us?

Model how to calculate a missing angle in a quadrilateral.

Calculate the missing angle in a range of quadrilaterals.

Identify the properties of quadrilaterals

Model using paper shapes to investigate the properties of quadrilaterals.

Use this investigation to create a table showing the properties of quadrilaterals.

Investigate the properties of different quadrilaterals

Investigate: How many different quadrilaterals can you make on a 3 x 3 pin board?a) Names? b) Side properties? c) Angle properties?d) Symmetry?

Discuss shapes found on 3 x 3 pin board. Use to review:- names;- angle properties;- side properties;- symmetry properties.

Identify the types of quadrilateral using a sorting table

Model using one shape how to add the shapes to the decision tree showing the properties of quadrilaterals. Identify shape names. Students complete with other shapes in pairs, discussing the properties.

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Students could then go on to play the game described here – need to print cards in advance – students must try and collect 4 cards which have a picture of a shape, name of a shape and properties of a shape. See the link for more detailed instructions.


Unit 4: Area 75aMM01

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Use a formula to find the area of a rectangle

Ask students to record details for the rectangles in a table. At this stage they will need to count the squares to find the area. Ask students to look at the pairs and discuss anything they notice. It may be necessary to add another rectangle to the table.

Calculate the area of a range of rectangles and squares, using a range of side lengths, including decimals to develop mental and written methods of multiplication further.

In the plenary draw students’ attention to the area of a square

area of square = s2

where s is the side of the square

Explain the relationship between the formulas for the areas of rectangles and squares.

Can students use a formula to calculate the area of a rectangle?

Can students calculate a missing length when given the area?

Can students calculate the area of compound shapes?

Can students develop

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Length Width Area3 4 122 6 12




Develop the formula:

area of rectangle = lb

where l is the length and b is the breadth of the rectangleModel substituting values into the formula to find the area of different rectangles and squares.

formulae?

Can students calculate the area of a triangle?

Can students calculate the area of a parallelogram?

Use the formula for area of a rectangle to calculate missing lengths

Problem: A rectangle has an area of 104 cm2 and one of its sides has width 8 cm

Discuss with students how we can solve this problem.

Look at the formula and substitute the known values.

A = lb

104 = l x 8

Recap on the work from algebra how to rearrange the equation so

l = 104 ÷ 8 = 13.

Model with a range of examples.

Calculate missing side lengths when given the area and one side length.

Complete a table such as:

Rectangle L B Area

3cm

6cm

5cm

15cm2

Solve worded problems in a range of contexts.

Calculate the area of compound shapes

Find the area of this shape: Model how to find the area of a compound shape, splitting it into two rectangles.

Solve problems involving a range of compound shapes made from rectangles and squares. For example:

What is the area of the shaded part of this flag?

Develop and use Ask students to calculate the area of the Use the formula to calculate the area

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the formula for the area of a triangle

first triangle by counting squares and discuss using the diagram to help, how the area of a triangle is half the length x width.

Show students the second triangle and repeat the process. Use this to help explain that they must use the perpendicular height of the triangle.

Complete the table below (diagrams are not drawn to scale):

of a range of triangles.

Solve word problems in a range of contexts.

Complete a table such as the one below, which also involves calculating missing lengths, by rearranging the formula.

Investigate and Show students a picture of a parallelogram Use the formula to find area of a

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develop formulas to find the areas of parallelograms.

and ask them to create one using triangles and rectangles – provide plastic shapes. Working in pairs students should develop a formula for finding the area. AS a class review their ideas and use the following diagram to help illustrate.

range of parallelograms.

Find the area of compound shapes.

Teach using a range of contexts over 2 days, developing the complexity of the shapes and problem solving.

Refer to diagram on the following page for problem below: Ursula is going to paint the front of the house for her parents.a) Find the area that needs to be painted.b) Ursula gets 50 toea for every 1 m2 that

she paints. How much money does she get?

Find the area of a range of compound shapes and use to solve problems. Include examples such as:

Find the shaded area

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Unit 5: Transformation

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Reflect a point in a mirror line

The line joining two points P and P’ is perpendicular to the line of symmetry. Is this always, sometimes or never true? Can you add anything to the statement?

Check that students understand the statement, particularly P and P’. Model how to test a point.

Students reflect a range of points and shapes in a mirror line and check to see if the line is perpendicular.

Guide students towards the idea that the line is also bisected by the mirror line.

Can students reflect points in a mirror line? Can students investigate the co-ordinates of shapes reflected in the x-axis?

Can students rotate a shape around a point?

Can students find the inverse of a rotation?

Can students perform a range



Investigate the co-ordinates of points reflected in ones of the axes

Investigate and describe the relationship between the coordinates of P and P’ following a reflection in the x- or y-axis.

Model reflecting points in one of the axes. Record in a table.

Students work in pairs, record results in a table. Describe what happens. Use to predict and then reflect the point and check.

NB: Students should discover: if is reflected in the x-axis, has the same x-coordinate, and its y-coordinate has the same magnitude but opposite sign.

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of transformations?

Can students identify the transformation which has been made?

Can students investigate the effect when transformations are combined?

Rotate a shape around a point of reflection

Think Pair share.

What is the same about these rotations? What is different?

Discuss where the point of rotation is, discuss the amount of turn.

Rotate shapes about a point.

Identify the point of rotation and the amount of turn.

Find the inverse of a rotation

Problem: How can we find the inverse of a rotation? Discuss with students their ideas.

The inverse of any rotation is either: a. an equal rotation about the same point in the opposite direction, or b. a rotation about the same point in the same direction, such that the two rotations have a sum of 360°

Find the rotation needed to return the image of a shape to its original position. Can students find both ways?

Perform a range of transformations

The points (–5, –3), (–1, 2) and (3, –1) are the vertices of a triangle.

Identify where the vertices lie after:a. translation of 3 units parallel to the x-axis;b. reflection in the x-axis;c. rotation of 180° about the origin.

Perform a range of transformations on different shapes.

Identify the different transformation which has been made.

Investigate symmetry

Introduce students to the following Students investigate the two problems, working with a partner.

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problems:

Combine these shapes to make a shape with reflection symmetry.

How many different solutions are there? (Five)

Combine the shapes to make a single shape with rotational symmetry of order 2.

Can they solve other similar problems?

For example: Identify the lines of symmetry in this pattern

Identify the transformations


transformation game – moving a triangle to different images.

NB the game and transformation cards need to be downloaded. Model playing the game with the class.

Students play the game in pairs, identifying the transformation their partner has made, checking it matches the card their partner has used.

Investigate the effect of performing more than one transformation

http://nrich.maths.org/5332 Does changing the order always/sometimes/never produce the same transformation?

Use the prompt sheet from nrich website to help guide through the investigation.

Unit 6: Chance 55aSC01

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Identify the probability of an event

A set of snooker balls consists of 15 red balls and one each of the following: yellow, green, brown, blue, pink, black and white.

If one ball is picked at random, what is the probability of it being:

Investigate a range of questions involving the probability of different events – packs of cards, containers of coloured balls etc.

Can students identify the probability of different events?

Can students

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5TM 01 a. red?b. not red?c. black?d. not black?e. black or white?

design a spinner to meet conditions?

Can students solve problems involving probability?

Can students compare experimental and theoretical probabilities?

Create a spinner to meet given conditions

Design a spinner, given the relationships between the likelihood of each outcome, e.g. design a spinner with three colours, red, white and blue, so that red is twice as likely to occur as blue, and blue is three times more likely to occur than white

Solve similar problems OR find alternative solutions to the opening problem.

Solve problems involving probability

Problem: http://nrich.maths.org/10144

A square is divided into eight congruent triangles, as shown.

Two of these triangles are selected at random and shaded black.

What is the probability that the resulting figure has at least one axis of symmetry?

Introduce the problem to students and discuss ways to approach solving it.

Solve the problem working in pairs. Move on to solving other problems such as:



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Compare experimental and theoretical probabilities

Yasmin bought a combination padlock for her school locker. The code has four digits, each from 0 to 9. Yasmin forgot the last digit of the code. What is the theoretical probability that she will choose the correct digit first time

Design and carry out an experiment to estimate the experimental probability.Compare the outcome with the theoretical probability.

Compare experimental and theoretical probabilities

Michael said: ‘I bet if I drop this piece of toast, it will land jam side down!’

What is the theoretical probability of this outcome?Devise an experiment to test Michael’s prediction e.g. simulate the toast with a playing card – the jam is represented by the side with spots

Carry out the experiment.Compare the experimental and theoretical probabilities.

Unit 7: Data 55aSD01

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Interpret frequency histograms

What questions could be asked about this graph?

Students interpret a range of histograms and answer a range of questions

Can students interpret frequency histograms?

Can students construct frequency histograms?

Can students find the mean of a set of data?

Can students find the median of a set of data?

Can students find the mode of a set of data?

Construct frequency polygons

Give students a set of data relating to a class of students – for example height or weight. This can be fictional.

Model discussing suitable class sizes for the data, how to group it, construct a frequency table and then draw a graph.

Construct the frequency histogram and then polygon.

Find the mode of a set of data

Problem: Find the modal class for London marathon times for the top 100 women

Solve problems such as:

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times and record the results in a table.

Graph a dot plot of the data. Work out the mode of the data.

Can students find the range of a set of data?

Can students solve problems involving mean, median, mode and range?

Find the median and mean of data

Find the median and mean of: 2, 5, 8, 3, 1, 7, 6.Find the median of the time taken to run the London marathon.Find the median and mean of marks in a test taken by Grade 7 students.

Solve a range of problems finding the median and mean of different data.

Solve problems involving the mean, mode, median and range

Use a stem-and-leaf diagram to help find the median, range and mode e.g. hours of sunshine

Solve problems such as: John has three darts scores with a mean of 30 and a range of 20.His first dart scored 26. What were his other two scores?

Ian and Nina play three games. Their scores have the same mean. The range of Ian’s scores is twice the range of Nina’s scores. Write the missing scores in the table below:

Ian’s score 40Nina’s score 35 40 45

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