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Essential Mathematics Concepts (Book 2)

This master may only be reproduced by the original purchaser for use with their class(es). The publisher prohibits the loaning or onselling of this master for the purposes of reproduction.

Published by Prim-Ed Publishing 1997 Revised and reprinted by Prim-Ed Publishing 2012 CopyrightÂŠ Michelle Markham 1997 ISBN 978-1-84654-542-9 PRâ€“0019

Copyright Notice Blackline masters or copy masters are published and sold with a limited copyright. This copyright allows publishers to provide teachers and schools with a wide range of learning activities without copyright being breached. This limited copyright allows the purchaser to make sufficient copies for use within their own education institution. The copyright is not transferable, nor can it be onsold. Following these instructions is not essential but will ensure that you, as the purchaser, have evidence of legal ownership to the copyright if inspection occurs.

Titles in this series:

Essential Mathematics Concepts (Book 1) Essential Mathematics Concepts (Book 2) Essential Mathematics Concepts (Book 3)

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In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class teacher checks all URLs before allowing pupils to access them.

View all pages online

Website: www.prim-ed.com

Foreword Essential Mathematics Concepts is designed to assist teachers in assessing and recording individual mastery of mathematical concepts that have been taught in the classroom. The children play a part in assessing their work; encouraging reflection upon their individual skills and a sense of ‘ownership’. The package brings together teacher and pupil assessment, providing parents with an ongoing awareness of their child’s progress throughout the year.

Number

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Number Rolling/Butterflies.......................................2 How Many?/Finish the Box........................................3 The Star/Flower Power..............................................4 Trees, Trees, Trees........................................................5 My Stars.........................................................................6 How Many More?........................................................7 Fly the Kite...................................................................8 Flowers in Order.........................................................9 Patterns.......................................................................10 Odd and Even/Missing Numbers...........................11 One-to-One/One-to-Many.....................................12 Fractions......................................................................13 Sharing Out.................................................................14 Fishy Facts...................................................................15 Balloon Counting.......................................................16 Spaceman Number Facts.........................................17 Sharing Out.................................................................18 How Many Groups?..................................................19 What’s Left Over?.....................................................20 Number Rolling.........................................................21 Breakfast Time............................................................22 What Do You Think?.................................................23 Coins and Values........................................................24 Giving Change............................................................25 Essential Mathematics Concepts

Share the Money........................................................26 Coin Counting...........................................................27

Shape, Space and Measure

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Teachers Notes............................................................ ii Overview...................................................................... iii Pupil Record................................................................ iv A Note to Parents...................................................... v

Contents

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Essential Mathematics Concepts provides teachers with a ready-made assessment programme for mathematics in the lower primary years.

3-D Shapes..................................................................28 2-D Shapes/Open and Closed Shapes..................29 Symmetrical Shapes..................................................30 Changing Shapes........................................................31 How Long?..................................................................32 Snail Trails....................................................................33 Hands and Pencils......................................................34 10-cm Rods.................................................................35 Tracing/Read and Draw............................................36 Comparing Area........................................................37 Blocks and Areas.......................................................38 Cups of Water............................................................39 Build it Up!..................................................................40 Heavier and Lighter..................................................41 Seesaw.........................................................................42 How Many Times?.....................................................43 Reading a Calendar...................................................44 Seasons........................................................................45 Clocks..........................................................................46

Prim-Ed Publishing - i -

Teacher Notes The Teacher • Uses the assessment boxes, both as a method of recording the child’s current level of concept understanding as well as a tool for communication between the school and home. • Plans future activities based on outcomes. • Sends the activities home as part of the child’s work sample file or portfolio.

Objective Number - Addition: Combining more than two numbers. This indicates the activity is a number activity in sorting and classifying; arranging and ordering.

Using the Activities

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• Ensure the concept has already been covered in class and have ready resources. • Go through the activity with the children to ensure correct understanding of what is required of them. • Encourage the children to work independently. • Remind the class that upon completion they can complete and colour the face. • Remind the class that the boxes are for you to fill in—which can simply and quickly be done while the activity is in progress!

The Child • Completes the activity. • Completes the ‘face’ to express their perception of their understanding of the activity.

The Parent • Notes the assessment of their child’s understanding of each mathematical concept.

Assessment

Concept: Combining more than two numbers together to find the total. Reinforcing the concept and for quick reference when looking at the assessment boxes.

Is able to combine more than two numbers together to find the total.

❑ Is still learning to combine more than two numbers together to find the total.

OR Is able to combine more than two numbers together to find the total. ❑ Is still learning to combine more than two numbers together to find the total. OR ❑ Is able to combine more than two numbers together to find the total. Is still learning to combine more than two numbers together to find the total. - ii - Prim-Ed Publishing

Indicates concept mastery.

Indicates good–fair understanding. Indicates little understanding at this time – more work needed.

Essential Mathematics Concepts

Overview Page

Title

Objective

2

Number Rolling/Butterflies

=

3

How Many?/Finish the Box

=

Addition: Combining more than two numbers (each less than 10).

4

The Star/Flower Power

=

Addition: Separating a set into subsets to investigate addition facts.

5

Trees, Trees, Trees

=

Addition: Making a set of a given number by building onto a given set of objects.

6

My Stars

=

Subtraction: Separating a set of objects to investigate basic subtraction facts.

7

How Many More?

=

Subtraction: Comparing sets of objects to find the differences between the number in each set.

8

Fly the Kite

=

Addition and Subtraction: Solving number sentences using addition and subtraction.

9

Flowers in Order

=

Place Value: Using ordinals to 20 based on pattern, position and order.

10

Patterns

=

Place Value: Identifying and completing patterns.

11

Odd and Even/Missing Numbers

=

Place Value: Constructing patterns according to odd and even numbers.

12

One-to-One/One-to-Many

=

Place Value: Investigating number correspondence.

13

Fractions

=

Fractions: Investigating parts of a whole.

14

Sharing Out

=

Multiplication and Division: Sorting and arranging amounts.

15

Fishy Facts

=

Multiplication and Division: Combining equivalent sets to investigate basic number facts in multiplication.

16

Balloon Counting

=

Multiplication and Division: Investigating basic number facts in multiplication.

17

Spaceman Number Facts

=

Multiplication and Division: Investigating basic facts in multiplication.

18

Sharing Out

=

Multiplication and Division: Investigating sharing of objects.

19

How Many Groups?

=

Multiplication and Division: Separating a set of objects into subsets.

20

What’s Left Over?

=

Multiplication and Division: Separating sets of objects into subsets with a remainder.

21

Number Rolling

=

Statistics and Chance Processes: Investigating the frequency of chance events.

22

Breakfast Time

=

Statistics and Chance Processes: Collecting and recording data using a tally.

23

What Do You Think?

=

Statistics and Chance Processes: Exploring activities that have a chance outcome.

24

Coins and Values

=

Money: Recognising coins to £1; Using coins in shopping activities to 20p.

25

Giving Change

=

Money: Giving change from 20p.

26

Share the Money

=

Money: Sharing coins to £1.

27

Coin Counting

=

Money: Counting coins to £1.

28

3-D Shapes

·

Exploring and describing three-dimensional shapes.

29

·

Exploring and describing two-dimensional shapes: Exploring and recognising closed and open shapes.

30

2-D Shapes/Open and Closed Shapes Symmetrical Shapes

·

Exploring and describing symmetrical shapes.

31

Changing Shapes

·

Transforming and moving shapes to investigate changes in position.

32

How Long?

=

Length: Comparing and seriating lengths of objects.

33

Snail Trails

=

Length: Comparing and seriating distance.

34

Hands and Pencils

=

Length: Measuring distances using non-standard units.

35

10-cm Rods

=

Length: Using the 10-cm rod as a measuring device.

36

Tracing/Read and Draw

=

Area: Investigating and comparing the size of area.

37

Comparing Area

=

Area: Investigating and comparing the area of objects (by direct comparison).

38

Blocks and Areas

=

Area: Measuring and seriating surfaces according to size of area, using non-standard units.

39

Cups of Water

=

Volume and Capacity: Comparing the capacity of containers.

40

Build it Up!

=

Volume and Capacity: Using non-standard units to measure and compare volume of blocks.

41

Heavier and Lighter

=

Mass: Using non-standard units to compare mass.

42

Seesaw

=

Mass: Using a seesaw to investigate balance.

43

How Many Times?

=

Measuring time using non-standard units.

44

Reading a Calendar

=

Time: Reading a calendar.

45

Seasons

=

Time: Sequencing the seasons.

46

Clocks

=

Time: Using a clock to read and show times on the hour.

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Addition: Combining a set of objects to investigate basic addition facts (up to 9 + 9 = 18).

Essential Mathematics Concepts

Prim-Ed Publishing - iii -

objective

Pupil Record

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pupil name

- iv - Prim-Ed Publishing

Essential Mathematics Concepts

A Note to Parents Dear Parents, Your child has attempted to complete the mathematics sheets independently. These sheets consolidate and reinforce concepts taught in mathematics throughout each term. As your child brings the worksheets home you will notice a gradual progression of conceptual development. The purpose of these sheets is threefold. • To consolidate in your child a mathematical concept. • To assess your child’s understanding of the concept at that time. • To give you the opportunity to observe your child’s ongoing work. Each sheet shows the concept and my assessment. Below is an example. Number – Addition: Combining more than two numbers (each less than 10).

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This indicates the mathematics activity is a number activity in sorting and classifying, arranging and ordering. Concept: Combining more than two numbers together to find the total.

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Reinforcing the concept and for quick reference when looking at the assessment boxes. Is able to combine more than two numbers together to find the total.

Indicates concept mastery.

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Is still learning to combine more than two numbers together to find the total.

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OR

Is able to combine more than two numbers together to find the total. Is still learning to combine more than two numbers together to find the total.

Indicates good–fair understanding.

OR Is able to combine more than two numbers together to find the total. Is still learning to combine more than two numbers together to find the total.

Indicates little understanding at this time – more work needed.

A face on each sheet is completed by your child at the end of each activity to indicate how he/she felt about their ability to complete the worksheet. I then tick the appropriate assessment box, referring back to previous observations as well as the current worksheet. By referring to these worksheets, you will be able to observe on an ongoing basis the understanding your child has of mathematical concepts being covered in the classroom. Come report time you will know what to expect! Should you have any queries, please don’t hesitate to make an appointment to discuss them with me. Yours sincerely,

Classroom teacher Essential Mathematics Concepts

Prim-Ed Publishing - v -

Number Rolling Number – Addition: Combining more than two numbers (each less than 10).

❖ Make your own number sequences by rolling your 3 dice.

1 1 3 5 e.g. + + = +

+

=

+

+

=

+

+

=

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+ + = Can you make six more number sentences on the back of this page?

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Concept: Combining more than two numbers to find the total.

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❑ Is able to combine more than two numbers to find the total. ❑ Is still learning to combine more than two numbers to find the total.

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Butterflies

❖ Add the numbers in each butterfly to find the total. If the total matches that of a number in a cocoon, colour both the cocoon and that butterfly the same colour.

2

5

3

1

3

2

11

4

5 2

2

5

9

5

5

3

5

8

1

14

7 Concept: Combining more than two numbers to find the total.

❑ Is able to combine more than two numbers to find the total. ❑ Is still learning to combine more than two numbers to find the total. - 2 - Prim-Ed Publishing

Essential Mathematics Concepts

How Many? Number – Addition: Combining a set of objects to investigate basic addition facts (up to 9 + 9 = 18).

❖ How many little rockets? How many big rockets? How many rockets altogether? How many bees? How many wasps?

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How many insects altogether? How many straight flowers?

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How many drooping flowers?

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How many flowers altogether?

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Concept: Combining a set of objects to investigate basic addition facts.

❑ Is able to combine a set of objects to investigate basic addition facts. ❑ Is still learning to combine a set of objects to investigate basic addition facts.

Finish the Box

❖ Finish this box by adding the numbers together.

+

9

8

17

7

6

4

10

6 2 Concept: Combining a set of objects to investigate basic addition facts.

❑ Is able to combine a set of objects to investigate basic addition facts. ❑ Is still learning to combine a set of objects to investigate basic addition facts. Essential Mathematics Concepts

Prim-Ed Publishing - 3 -

The Star Number –Addition: Separating a set into subsets to investigate addition facts.

❖ Collect 15 blocks or counters. Use them to make 7 different ways to make the number 15.

0 7

+

1

15

+

+

2

+

3

+ 4

+

+

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6

+ 15

Concept: Separating a set into subsets to investigate addition facts.

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❑ Is able to separate a set into subsets to investigate addition facts. ❑ Is still learning to separate a set into subsets to investigate addition facts.

Flower Power

❖ Use two colours to shade all of the petals on each flower. Record those numbers as a sum.

+

= 14

+

= 14

+

= 14

Concept: Separating a set into subsets to investigate addition facts.

❑ Is able to separate a set into subsets to investigate addition facts. ❑ Is still learning to separate a set into subsets to investigate addition facts. - 4 - Prim-Ed Publishing

Essential Mathematics Concepts

Trees‚ Trees‚ Trees Number – Addition: Making a set of a given number by building onto a given set of objects.

❖ Add on to each picture to make the number shown.

= 9

8 +

= 15

= 13

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7 +

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6 +

= 12

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3 +

4 +

= 6 2 +

= 8

Concept: Making a set of a given number by building onto a given set of objects.

❑ Is able to make a set of a given number by building onto a given set of objects. ❑ Is still learning to make a set of a given number by building onto a given set of objects. Essential Mathematics Concepts

Prim-Ed Publishing - 5 -

My Stars Number – Subtraction: Separating a set of objects to investigate basic subtraction facts.

❖ In each box, colour the stars you should take away, then count what is left. Write down your answers.

12 – 4 = 8

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14 – 6 =

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17 – 5 = 9–4=

10 – 8 = 13 – 6 = 11 – 3 =

Concept: Separating a set of objects to investigate basic subtraction facts.

❑ Is able to separate a set of objects to investigate basic subtraction facts. ❑ Is still learning to separate a set of objects to investigate basic subtraction facts. - 6 - Prim-Ed Publishing

Essential Mathematics Concepts

How Many More? Number – Subtraction: Comparing sets of objects to find the differences between the number in each set.

❖ Compare the sets of objects in each box.

How many more flowers are there than ladybirds?

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How many more stars are there than moons?

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How many more lilypads are there than frogs?

How many more squares are there than triangles?

How many more apples are there than strawberries?

Concept: Comparing sets of objects to find the difference between the number in each set.

❑ Is able to compare sets of objects to find the difference between the number in each set. ❑ Is still learning to compare sets of objects to find the difference between the number in each set. Essential Mathematics Concepts

Prim-Ed Publishing - 7 -

Fly the Kite Number – Addition and Subtraction: Solving number sentences using addition and subtraction.

❖ Solve the problems along the string of the kite.

=

e

3 – 17

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12 + 3 =

=

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6 5+

6=

6–

7–

1=

4+9

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9–7=

=

6=

14 + 3

– 15

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16 – 8 =

+6 12

=

Concept: Solving number sentences using addition and subtraction.

❑ Is able to solve number sentences using addition and subtraction. ❑ Is still learning to solve number sentences using addition and subtraction. - 8 - Prim-Ed Publishing

Essential Mathematics Concepts

Flowers in Order Number – Place Value: Using ordinals to 20 based on pattern, position and order. Teacher Instructions: Colour the 1st flower red. Make the 20th flower blue and red striped. Colour the 3rd flower blue. Make the 18th flower pink and white spotted. Colour the 5th flower yellow. Make the 14th flower pink and blue spotted. Colour the 7th flower green. Make the 12th flower blue and yellow striped. Colour the 9th flower purple. Make the 16th flower blue and white striped. Colour the 11th flower black. Make the 8th flower blue and purple striped. Colour the 13th flower orange. Make the 2nd flower pink and black spotted. Colour the 15th flower pink. Make the 6th flower pink and green spotted. Colour the 17th flower brown. Make the 10th flower pink and yellow spotted. Colour the 19th flower white. Make the 4th flower blue and black striped.

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❖ Listen to your teacher as you are told what to do. Finish the instructions.

flower is black

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flower is red

flower is blue and purple striped

flower is blue

flower is orange

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flower is blue and red striped

flower is pink and white spotted

flower is pink and black spotted

flower is yellow

flower is pink

flower is pink and blue spotted

flower is pink and green spotted

flower is green

flower is brown

flower is blue and yellow striped

flower is pink and yellow spotted

flower is purple

flower is white

flower is blue and white striped

flower is blue and black striped

Concept: Using ordinals to 20.

❑ Is able to use ordinals to 20. ❑ Is still learning to use ordinals to 20. Essential Mathematics Concepts

Prim-Ed Publishing - 9 -

Patterns Number – Place Value: Identifying and completing patterns.

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❖ Complete each pattern.

Concept: Identifying and completing patterns according to shape.

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❖ Complete each pattern.

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❑ Is able to identify and complete patterns according to shape. ❑ Is still learning to identify and complete patterns according to shape.

1 2 3 4 5 6 7

20

1 2 3 4 5

20

1 2 3 4 5

20

Concept: Identifying and completing patterns according to number.

❑ Is able to identify and complete patterns according to number. ❑ Is still learning to identify and complete patterns according to number. - 10 - Prim-Ed Publishing

Essential Mathematics Concepts

Odd and Even Number – Place Value: Constructing patterns according to odd and even numbers. Materials: Container and counters.

1

2

3

4

5

6

7

8

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❖ You will need a container with 20 counters in it. Take a handful of counters from the container, count them and record the number using the graph. (For example, if I took 17 counters from my container, I would put an ‘X’ above 17.) Do that ten times. Then colour the odd numbers red and the even numbers blue.

9 10 11 12 13 14 15 16 17 18 19 20

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Concept: Constructing patterns according to odd and even numbers.

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❑ Is able to construct patterns according to odd and even numbers. ❑ Is still learning to construct patterns according to odd and even numbers.

Missing Numbers

❖ What number comes next on the caterpillars?

5 10 15 20 25 2 4 6

35 40

50 55 60

10 12 14

1 6 11 16 21 26

18 20 36 41 46 51

Concept: Constructing patterns according to odd and even numbers.

❑ Is able to construct patterns according to odd and even numbers. ❑ Is still learning to construct patterns according to odd and even numbers. Essential Mathematics Concepts

Prim-Ed Publishing - 11 -

One-to-One Number – Place Value: Investigating number correspondence.

❖ Draw one bee on each flower. How many bees did you draw?

❖ Draw one face on each moon. How many faces did you draw?

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❖ Draw one bow on each kite. How many bows did you draw?

Concept: Investigating one-to-one correspondence.

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One-to-Many

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❑ Is able to investigate one-to-one correspondence. ❑ Is still learning to investigate one-to-one correspondence.

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❖ Draw 2 legs on each Humpty Dumpty. How many sets of legs have you drawn?

How many legs altogether?

❖ Draw 4 legs on each dog. How many sets of legs have you drawn?

How many legs altogether?

Concept: Investigating one-to-many correspondence.

❑ Is able to investigate one-to-many correspondence. ❑ Is still learning to investigate one-to-many correspondence. - 12 - Prim-Ed Publishing

Essential Mathematics Concepts

Fractions Number – Fractions: Investigating parts of a whole.

❖ Circle the pie showing half (1/2).

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❖ Circle the pie showing one-quarter (1/4).

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❖ Circle the pie showing one-third (1/3).

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❖ Circle the pie showing two-thirds (2/3).

❖ Circle the pie showing two-quarters (2/4).

Concept: Investigating parts of a whole—1/2, 1/3 and 1/4.

❑ Is able to investigate parts of a whole—1/2, 1/3 and 1/4. ❑ Is still learning to investigate parts of a whole—1/2, 1/3 and 1/4. Essential Mathematics Concepts

Prim-Ed Publishing - 13 -

Sharing Out Number – Multiplication and Division: Sorting and arranging amounts.

❖ Share 10 counters equally.

+

= 10

+

+

+

= 10

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❖ Share 12 counters equally.

+

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❖ Share 10 counters equally.

+

+

= 12

❖ Share 15 counters equally.

+

+

+

+

= 15

Concept: Sorting and arranging amounts.

❑ Is able to sort and arrange amounts. ❑ Is still learning to sort and arrange amounts. - 14 - Prim-Ed Publishing

Essential Mathematics Concepts

Fishy Facts Number – Multiplication and Division: Combining equivalent sets to investigate basic number facts in multiplication.

❖ Count the bubbles and complete these number sentences.

3 x 4 = 12 4 +

4 + 4 = 12 =

+

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+

=

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+

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x

+

+

+

+

+

+

+

x

=

x

=

=

=

Concept: Combining equivalent sets to investigate basic number facts in multiplication.

❑ Is able to combine equivalent sets to investigate basic number facts in multiplication. ❑ Is still learning to combine equivalent sets to investigate basic number facts in multiplication. Essential Mathematics Concepts

Prim-Ed Publishing - 15 -

Balloon Counting Number – Multiplication and Division: Investigating basic number facts in multiplication.

❖ Count by 2s.

x

=

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❖ Count by 3s.

=

x

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❖ Count by 4s.

x

=

❖ Count by 5s.

x

=

Concept: Investigating basic number facts in multiplication.

❑ Is able to investigate basic number facts in multiplication. ❑ Is still learning to investigate basic number facts in multiplication. - 16 - Prim-Ed Publishing

Essential Mathematics Concepts

Spaceman Number Facts Number – Multiplication and Division: Investigating basic facts in multiplication.

❖ Complete these number sentences.

4

x2

x2 = 2

=

e

6x2=

x2

5

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x3

x3

4

=

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=

3x3=

x3

4

x4

x4 =

3x4=

2

x4

=

5

x5

x5 = 2x5=

4

x5

=

Concept: Investigating basic facts in multiplication.

❑ Is able to investigate basic facts in multiplication. ❑ Is still learning to investigate basic facts in multiplication. Essential Mathematics Concepts

Prim-Ed Publishing - 17 -

Sharing Out Number – Multiplication and Division: Investigating sharing of objects.

❖ Share 14 sweets into seven sweet bags.

14 = 7 x ❖ Share 18 frogs onto six lily pads.

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❖ Share 9 apples into three lunch boxes.

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18 = 6 x

9=3x

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❖ Share 20 leaves onto four flowers.

20 = 4 x

❖ Share 16 bows onto four kites.

16 = 4 x ❖ Share 12 apples onto six trees.

12 = 6 x Concept: Investigating the sharing of objects.

❑ Is able to investigate the sharing of objects. ❑ Is still learning to investigate the sharing of objects. - 18 - Prim-Ed Publishing

Essential Mathematics Concepts

How Many Groups? Number – Multiplication and Division: Separating a set of objects into subsets.

❖ How many groups of two can you make from these sets?

groups of 2

groups of 2

x 2 = 12

x 2 = 16

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❖ How many groups of three can you make from these sets?

groups of 3

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x 3 = 15

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groups of 3

x 3 = 18

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❖ How many groups of four can you make from these sets?

groups of 4

groups of 4

x 4 = 16

x 4 = 12

❖ How many groups of five can you make from these sets?

groups of 5

groups of 5

x 5 = 20

x 5 = 15

Concept: Separating a set of objects into subsets.

❑ Is able to separate a set of objects into subsets. ❑ Is still learning to separate a set of objects into subsets. Essential Mathematics Concepts

Prim-Ed Publishing - 19 -

What’s Left Over? Number – Multiplication and Division: Separating sets of objects into subsets with a remainder.

❖ Share the bones into groups of two.

How many groups did you make?

How many bones left over?

How many bones left over?

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How many groups did you make?

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❖ Share the bones into groups of three.

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❖ Share the bones into groups of four.

How many groups did you make?

How many bones left over?

❖ Share the bones into groups of five.

How many groups did you make?

How many bones left over?

Concept: Separating sets of objects into subsets with remainders.

❑ Is able to separate sets of objects into subsets with remainders. ❑ Is still learning to separate sets of objects into subsets with remainders. - 20 - Prim-Ed Publishing

Essential Mathematics Concepts

Number Rolling Number – Statistics and Chance Processes: Investigating the frequency of chance events. Materials: Die.

❖ Roll a die 20 times. Use a stroke to record each number you roll. Before you begin, what number do you think you will roll: the least times?

the most times?

Strokes

Total

e

1

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2

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3

5 6

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4

What number did you roll the most times? What number did you roll the least times? Did you roll some numbers the same amount of times?

Yes

No

If your answer was yes, what numbers were they? Concept: Investigating the frequency of chance events.

❑ Is able to investigate the frequency of chance events. ❑ Is still learning to investigate the frequency of chance events. Essential Mathematics Concepts

Prim-Ed Publishing - 21 -

Breakfast Time Number – Statistics and Chance Processes: Collecting and recording data using a tally.

❖ As a class, collect the relevant information on breakfast. How many children in your class eat breakfast? How many children in your class don’t eat breakfast? ❖ Record the information below.

BREAKFAST

How many children…

Tally

Total

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had fruit at breakfast?

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had cereal at breakfast?

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had milk at breakfast?

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had porridge at breakfast?

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had toast at breakfast?

had eggs at breakfast?

What did most children have for breakfast?

What did the least number of children have for breakfast? Was there something that no-one ate at breakfast time? Concept: Collecting and recording data using a tally.

❑ Is able to collect and record data using a tally. ❑ Is still learning to collect and record data using a tally. - 22 - Prim-Ed Publishing

Essential Mathematics Concepts

What Do You Think? Number – Statistics and Chance Processes: Exploring activities that have a chance outcome.

❖ Decide your answers to the questions below by ticking one box only.

Do you think …

Yes

No

No way!

it will rain today?

e

you will meet a dinosaur today?

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you will get growled at today?

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you will eat some food today?

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you will find the end of a rainbow today? you will play today?

you will meet someone new today? the teacher will smile today? you will learn something new today? you will get a cuddle today?

Concept: Exploring activities that have a chance outcome.

❑ Is able to explore activities that have a chance outcome. ❑ Is still learning to explore activities that have a chance outcome. Essential Mathematics Concepts

Prim-Ed Publishing - 23 -

Coins and Values Number – Money: Recognising coins to £1; Using coins in shopping activities to 20p.

❖ Match the coins to the values and put them in order from the least value to the greatest value (1-6). Values

5p

50p

2p

£1

20p

10p

Coins

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Numbers 1 – 6

❑ Is able to recognise coins to £1. ❑ Is still learning to recognise coins to £1.

sa

Concept: Recognising coins to £1.

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❖ Use 5p, 10p or 20p coins to buy these items. Remember you can use the same coin more than once.

Use 3 coins to buy this.

Use 1 coin to buy this. Use 4 coins to buy this.

20p 20p

15p

Use 2 coins to buy this.

10p

Use 2 coins to buy this.

20p

Use 1 coin to buy this.

10p

Concept: Using coins in shopping activities to 20p.

❑ Is able to use coins in shopping activities to 20p. ❑ Is still learning to use coins in shopping activities to 20p. - 24 - Prim-Ed Publishing

Essential Mathematics Concepts

Giving Change Number – Money: Giving change from 20p.

❖ For each item you purchase at the school canteen you use a 20p coin. Colour the coin or coins you will receive as your change.

10p

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15p

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20p

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5p

15p

10p

Concept: Giving change from 20p.

❑ Is able to give change from 20p. ❑ Is still learning to give change from 20p. Essential Mathematics Concepts

Prim-Ed Publishing - 25 -

Share the Money! Number – Money: Sharing coins to £1.

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❖ Colour the amounts which have been shared fairly. Remember – each person’s purse must hold the same amount.

Concept: Sharing coins of up to £1 in value.

❑ Is able to share coins of up to £1 in value. ❑ Is still learning to share coins of up to £1 in value. - 26 - Prim-Ed Publishing

Essential Mathematics Concepts

Coin Counting Number – Money: Counting coins to £1.

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❖ Count the money in each purse and write the total.

Concept: Counting coins to £1.

❑ Is able to count coins to £1. ❑ Is still learning to count coins to £1. Essential Mathematics Concepts

Prim-Ed Publishing - 27 -

3-D Shapes Space – Exploring and describing three-dimensional shapes. Materials: Magazines, catalogues, newspapers, etc.

❖ Find pictures of objects to match these. Write how many faces each one has.

object triangular prism

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cylinder

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cube

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sa

rectangular prism

cone

sphere

Concept: Describing three-dimensional shapes.

❑ Is able to describe three-dimensional shapes. ❑ Is still learning to describe three-dimensional shapes. - 28 - Prim-Ed Publishing

Essential Mathematics Concepts

2-D Shapes Space – Exploring and describing two-dimensional shapes: Exploring and recognising closed and open shapes.

❖ Sort the letters of the alphabet. a b c d e f g h i j k l m n o p q r s t u v w x y z Letters with curves…

Letters with tails…

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Letters with closed shapes...

Concept: Describing two-dimensional shapes.

sa

❑ Is able to describe two-dimensional shapes. ❑ Is still learning to describe two-dimensional shapes.

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Open and Closed Shapes

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❖ Colour all the closed shapes.

Concept: Recognising closed and open shapes.

❑ Is able to recognise closed and open shapes. ❑ Is still learning to recognise closed and open shapes. Essential Mathematics Concepts

Prim-Ed Publishing - 29 -

Symmetrical Shapes Space – Exploring and describing symmetrical shapes.

Colour the shapes that are symmetrical.

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Colour the shapes that are not symmetrical.

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Make the other half look the same.

Colour the symmetrical patterns.

Concept: Recognising symmetrical shapes.

❑ Is able to recognise symmetrical shapes. ❑ Is still learning to recognise symmetrical shapes. - 30 - Prim-Ed Publishing

Essential Mathematics Concepts

Changing Shapes Space – Transforming and moving shapes to investigate changes in position.

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✤ Colour the shapes in the right-hand side box that are the same as the ones in the left-hand side box. They have been moved so be careful, don’t get tricked.

Concept: Investigating changes in position.

❑ Is able to investigate changes in position. ❑ Is still learning to investigate changes in position. Essential Mathematics Concepts

Prim-Ed Publishing - 31 -

How Long? Measurement – Length: Comparing and seriating lengths of objects. Materials: Paperclips, dusters, tins, pencils, books and rulers.

❖ Use paperclips to record the lengths of these objects. Graph the objects, according to the number of paperclips. Order from smallest to largest. 14 13 12 11 10

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8 7

sa

6 5 4

g

Number of Paperclips

9

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3 2 1

duster

tin

pencil

The duster is

paperclips long. The tin is

The pencil is

paperclips long. The book is

The ruler is

book

ruler

paperclips long. paperclips long.

paperclips long.

Concept: Comparing and seriating lengths of objects.

❑ Is able to compare and seriate lengths of objects. ❑ Is still learning to compare and seriate lengths of objects. - 32 - Prim-Ed Publishing

Essential Mathematics Concepts

Snail Trails Measurement – Length: Comparing and seriating distance. Materials: Wool.

❖ Use wool to measure the length of each snail trail.

Hecto

r

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Horace

Ho

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Horatio

me

r

old Har Which snail has crawled the longest distance? Which snail has crawled the shortest distance? Concept: Comparing and seriating distances.

❑ Is able to compare and seriate distances. ❑ Is still learning to compare and seriate distances. Essential Mathematics Concepts

Prim-Ed Publishing - 33 -

Hands and Pencils Measurement – Length: Measuring distances using non-standard units. Materials: Card, scissors, pencils, desks, rulers, chairs and door.

❖ Trace your hand onto card. Use your cut out hand shape and a pencil to measure the length of these objects. Guess: Hand

Measurement: Hand

Guess: Pencil

Measurement: Pencil

The length of your teacher’s desk.

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The length of the whiteboard ruler.

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The length of your chair.

g

sa

The length of your desk.

The width of the door.

What have you noticed?

Concept: Measuring distances using non-standard units.

❑ Is able to measure distances using non-standard units. ❑ Is still learning to measure distances using non-standard units. - 34 - Prim-Ed Publishing

Essential Mathematics Concepts

10-cm Rods Measurement – Length: Using the 10-cm rod as a measuring device. Materials: 10-cm rods.

sa

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✤ Find or make a 10-cm rod. Colour the rectangles that are the same size as the rod.

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✤ Use a 10-cm rod to measure the following (you will need to work with a partner).

My Guess

My Measurement

The length of my arm The length of my leg My height

The length of my desk The length of my foot Concept: Using the 10-cm rod as a measuring device.

❑ Is able to use the 10-cm rod as a measuring device. ❑ Is still learning to use the 10-cm rod as a measuring device. Essential Mathematics Concepts

Prim-Ed Publishing - 35 -

Tracing Measurement – Area: Investigating and comparing the size of area.

❖ Trace your hand in the space.

g

How can you tell?

sa

Whose hand has the bigger area?

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Trace your partner’s hand over yours using a different colour.

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Read and Draw

❖ Draw a square smaller than this one.

❖ Draw a triangle smaller than this one.

❖ Draw a circle smaller than this one. Concept: Comparing area sizes.

❑ Is able to compare area sizes. ❑ Is still learning to compare area sizes. - 36 - Prim-Ed Publishing

Essential Mathematics Concepts

Comparing Area Measurement – Area: Investigating and comparing the area of objects (by direct comparison).

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❖ Cut out the shapes at the bottom of the page. (Look at the colour written in each star.) Match the cut out shapes to the shapes below. If the shapes fit perfectly, colour that shape using the same colour as the stars.

Concept: Comparing sizes of areas by direct comparison.

❑ Is able to compare sizes of areas by direct comparison. ❑ Is still learning to compare sizes of area by direct comparison.

w yello

Essential Mathematics Concepts

red blue

Prim-Ed Publishing - 37 -

Blocks and Areas Measurement – Area: Measuring and seriating surfaces according to size of area, using non-standard units. Materials: 2-cm cubes.

❖ Using 2-cm cubes, measure and record the areas of these shapes. Number these in order from the smallest to the largest.

Number

e

Number

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My Guess: My Answer:

My Answer:

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My Guess:

Number

My Guess: My Answer:

My Guess: Number

My Answer:

Concept: Measuring and seriating according to size of area, using non-standard units.

❑ Is able to measure and seriate according to size of area, using non-standard units. ❑ Is still learning to measure and seriate according to size of area, using non-standard units. - 38 - Prim-Ed Publishing

Essential Mathematics Concepts

Cups of Water Measurement – Volume and Capacity: Comparing the capacity of containers. Materials: Water, cups, jugs, ice-cream containers, vases and buckets.

❖ You will need a cup, a jug, an ice-cream container, a vase and a bucket. ❖ Colour the container you think will hold the most water.

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❖ Measure the capacity of each container using the cup.

My Guess

cups

cups

cups

cups

cups

cups

cups

cups

My Measure

Which container held the most water? Which container held the least water? Concept: Comparing the capacity of containers.

❑ Is able to compare the capacity of containers. ❑ Is still learning to compare the capacity of containers. Essential Mathematics Concepts

Prim-Ed Publishing - 39 -

Build it Up! Measurement – Volume and Capacity: Using non-standard units to measure and compare volume of blocks. Materials: 2-cm cubes.

❖ Use 2-cm cubes to build a model three cubes long and four cubes wide. How many cubes have you used altogether? ❖ Add another layer to your model. How many cubes are in your new layer? How many cubes in your model altogether?

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❖ Add another layer to your model. How many cubes are in your new layer?

sa

How many cubes are in your model altogether?

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❖ Count the number of blocks in each model and record. ❖ Colour the sets of blocks that have the same volume.

Concept: Using non-standard units to measure and compare volume.

❑ Is able to use non-standard units to measure and compare volume. ❑ Is still learning to use non-standard units to measure and compare volume. - 40 - Prim-Ed Publishing

Essential Mathematics Concepts

Heavier and Lighter Measurement – Mass: Using non-standard units to compare mass. Materials: Balance scales, books, dusters, pencils, tins, cups and vases.

❖ Compare the mass of each object. Find how many blocks it takes to balance each object. The heavier object is The

. Its mass is blocks.

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’s mass is

blocks.

The heavier object is The

. Its mass is blocks.

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’s mass is

blocks.

The heavier object is The

’s mass is

. Its mass is

blocks.

blocks.

Concept: Comparing mass using non-standard units.

❑ Is able to compare mass using non-standard units. ❑ Is still learning to compare mass using non-standard units. Essential Mathematics Concepts

Prim-Ed Publishing - 41 -

Seesaw Measurement – Mass: Using a seesaw to investigate balance.

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❖ Make sentences for these pictures.

Concept: Using a seesaw to investigate balance.

❑ Is able to use a seesaw to investigate balance. ❑ Is still learning to use a seesaw to investigate balance. - 42 - Prim-Ed Publishing

Essential Mathematics Concepts

How Many Times? Time – Measuring time using non-standard units. Materials: Beanbags.

❖ In the time it takes your teacher to clap 20 times, how many times can you… name? w r i te your

nd down? j u mp up a

guess:

guess:

actual:

actual:

nbag? c a t c h a bea

guess:

e

nd touch your toes? (be

actual:

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guess:

sa

actual:

your knees)

g

❖ Using an egg timer, how many times can you…

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name? w r i te your

nd down? j u mp up a

guess:

guess:

actual:

actual:

nbag? c a t c h a bea

guess:

nd your knees)

touch your toes? (be

actual:

guess:

actual:

Concept: Measuring time using non-standard units.

❑ Is able to measure time using non-standard units. ❑ Is still learning to measure time using arbitrary units. Essential Mathematics Concepts

Prim-Ed Publishing - 43 -

Reading a Calendar Measurement – Time: Reading a calendar.

❖ Make a calendar for this month. Month: ay nd

ay d s e

Tu

ay

sd ne

d We

y da s r u

Th

ay

y da i r F

rd atu

S

y da

n Su

g

sa

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e

Mo

Year:

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How many days in this month?

How many days are you at school this month? How many days are you not at school this month? How many Mondays are there this month? How many Saturdays are there this month? Colour the days you have sport red. Colour the days you have assembly blue. Colour the days children in your class have birthdays yellow. Concept: Reading a calendar.

❑ Is able to read a calendar. ❑ Is still learning to read a calendar. - 44 - Prim-Ed Publishing

Essential Mathematics Concepts

Seasons Measurement – Time: Sequencing the seasons.

❖ As a class, find and record how many birthdays are in your class for each season. Summer

Autumn

Winter

Spring

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❖ In the chart below,draw how you would dress for each season.

Concept: Sequencing the seasons.

❑ Is able to sequence the seasons. ❑ Is still learning to sequence the seasons. Essential Mathematics Concepts

Prim-Ed Publishing - 45 -

Clocks Measurement – Time: Using a clock to read and show times on the hour.

❖ Complete these clocks or the times. wake up

11 12 1 2

10 9

4

8 7

school

5

6

11 12 1 2

10 9

3

lunch time

5

6

11 12 1

10

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7

2

3

9

sa

8

7

home time

e

4

8

6

12 noon

4

5

g

11 12 1

2

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3

9

4

8

7

tea time

7 o'clock

3

5

6

11 12 1 2

10 9

3

6 o'clock

4

8 7

6

5

11 12 1

bed time

2

10

3

9

4

8 7

6

5

Concept: Using a clock to read and show times on the hour.

❑ Is able to use a clock to read and show times on the hour. ❑ Is still learning to use a clock to read and show times on the hour. - 46 - Prim-Ed Publishing

Essential Mathematics Concepts

Other titles for this age range include:

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0018 - Essential Mathematics Concepts Book 1 0020 - Essential Mathematics Concepts Book 3

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6565 - Developing Maths Concepts in the Early Years

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Early Years series: 0607 - Number 0608 - Addition 0609 - Subtraction

View

every page of every book

online at

www.prim-ed.com