Mathematics activities with an Asia focus aligned to the Australian Curriculum

YEAR 1 Mathematics Counting Games This activity pack focuses on the Korean number counting game sam yew gew in the Australian Curriculum for Mathematics: ACMNA012. This and other simple counting games are explained in detail along with variations and complementary counting activities. The activities and games will help students develop confidence with naming numbers, counting and counting patterns.

Contents

Curriculum focus About sam yew gew Activities Equipment Activity preparation Associated learning Activity guide Activity worksheets BLM Extension opportunities

© The University of Melbourne -‐ Asia Education Foundation, 2011

2 2 3 3 3 3 4 8 11

YEAR 1 Counting games Curriculum focus Australian Curriculum for Mathematics Year 1

Number and Algebra

Number and place value

Element code ACMNA012

Content description

Elaboration

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero

• using the traditional Korean counting game (sam yew gew) for skip counting.

This collection of activities and number games assists students to develop confidence with whole numbers. The games (and recording the numbers involved) highlight number patterns and relationships between numbers. The games provide a stimulus for discussions about the observed patterns and the testing of simple student conjectures. The games and activities may be adapted for use with older students.

Extension opportunities in the Australian Curriculum for Mathematics Year 2

Year 4

Number and Algebra Number and place value

Element code ACMNA028

Number and Algebra Number and place value

Element code ACMNA073

More information is provided on page 11.

About sam yew gew Sam yew gew / sam-yuk-gu / sam-nyug-gu This game is a Korean childrenʼs counting game popularised through a Korean television program. It is well known to Australian teachers as buzz or whiz, or even buzz-whiz. It involves replacing numbers in counting with a clap of the hands according to a number rule established before play begins.

© The University of Melbourne -‐ Asia Education Foundation, 2011

2

YEAR 1 Counting games Activities Activity 1

Sam yew gew

4

Activity 2

Counting by ones

6

Activity 3

Skip counting

6

Activity 4

Counting frames, abacus and number grids

7

Equipment Activity 1 None Activities 2- 4 BLM 1: 0 to 99 number grid BLM 2: 1 to 100 number grid Counting frames, abacus and plastic counters Optional Enlarge BLM to A3 size Additional equipment for students to record number sequences and patterns using number grids and counting frames

Activity preparation There is little preparation required to do these activities in class. Read the Activity Guide for the possible variations on the games and ways they can be extended. The games can be played by any number of children: a small group or the whole class. The games are easiest to play if the students are in a circle or a line so that they know their physical order and when it is their turn to respond.

Associated learning Playing games like sam yew gew and its variations gives an opportunity to explore, refine and extend the studentsʼ use of mathematical language. • Involving students in counting games and recording the patterns engages students in discussions beyond the immediate focus of the activity. • The teacher can introduce or use new terms such as odd, even, multiples of, factors, groups of, common multiples, etc. • By using counters to record number patterns on number grids students begin to establish a visual sense of number sequences in addition to saying the number word sequences.

© The University of Melbourne -‐ Asia Education Foundation, 2011

3

YEAR 1 Counting games Activity guide Activity 1 - Sam yew gew Getting started Warm up Nominate a student to start from 1 and get each student in turn to say the number names in order. Variation Start at a number such as 30 and count backwards.

Establish the rule In this game a rule is established for certain numbers to be replaced by a clap of the hands. The language to describe the rule might vary according to the mathematical vocabulary of the students. A simple rule for the numbers 3, 6, 9, 12, 15 … might be: • multiples of 3 • numbers having 3 as a factor • numbers we can make into groups of 3 with no remainder Instead of saying these number words, the student whose turn it is claps their hands. Playing the game With the rule established, the counting aloud begins with every third student clapping once rather than saying the number. To maintain the concentration of students while waiting their turn, encourage all students clap on the appropriate numbers.

Any student making a mistake in the count sits down. The winner is the last student left standing. Alternatively when there are only two students left in, play ʻrock-paper-scissorsʼ or toss a coin to determine the winner.

© The University of Melbourne -‐ Asia Education Foundation, 2011

4

YEAR 1 Counting games Alternative start The game rule can be played without having to use the language of factors or multiples: For example Establish the rule: students are not allowed to say a number that contains a two (2). This means 2 and numbers like 12, all the numbers in the twenties (20, 21, 22, 23 … 29) and 32, 42 and so on, are replaced with a clap of the hands.

Variations The number of variations in playing this game is limited only by the imagination of the teacher and students. • The game can be played with younger children who are unfamiliar with terms such as factors / multiples / groups of. In this version the teacher can use number flash cards during the counting sequence for the numbers that require a clap of the hands. At this level the flash cards could replace any numbers in the counting sequence rather than follow a rule, to familiarise students with the game. They could include different representations of numbers such as figurative pictures, dice faces, playing card numbers and so on. Vary the game by counting: • groups of three starting at 30 • groups of three from 30 going backwards • from any starting number: e.g. 8 or 13 • groups of 5, or any other number • odd numbers • even numbers Extension Extend the game by: • nominating two or more numbers in the rule: e.g. 2 and 7 • adding actions: e.g. clap hands on multiples of 3, stamp feet on multiples of 7 • playing any of the above backwards • combining skills: e.g. clap hands on multiples of 3, stamp feet on multiples of 5, say buzz for numbers containing a 7

© The University of Melbourne -‐ Asia Education Foundation, 2011

5

YEAR 1 Counting games Activity 2 Counting by ones Using number cards for 1 to 20 made from BLM 1 to provide the starting number prompt, students count on by ones. The whole class can do this together or students can take turns to say the next number. Variations • Start counting at one, getting students to place an item into a basket as each number is said. At different points the teacher asks the class: How many things are there in the basket now? • Count backwards from a nominated starting number • Combine the above variations, getting students to remove items from the basket as they count backwards

Activity 3 – Skip counting Multiplication games Using number cards for 1 to 20 made from BLM 1, the teacher or a nominated student selects two cards and shows them to the class. The first number selected indicates the number to start counting from. The second card provides the multiple for counting on. For example, first card: 7, second card: 2 7, 9, 11, 13, 15 …

7

2

Extension Attention can be drawn to the patterns that emerge depending on the starting number and the multiple. For example: starting at 7 and counting by twos gives all odd numbers, but starting at 8 and counting by twos gives all even numbers. • • • •

comparing the numbers generated by starting at 7 and counting by twos or counting by threes (all odd, mixture of odd and even) comparing the numbers generated by starting at 7 and 8 and counting by threes identifying the number patterns in skip counting from other specific starting numbers: e.g. skip counting on from 13 by twos predicting what patterns to expect with a particular starting number and skip counting number.

© The University of Melbourne -‐ Asia Education Foundation, 2011

6

YEAR 1 Counting games Activity 4 – Counting frames, abacus and number boards Activities 1 – 3 can be supported by physical representations and actions. Students can use a variety of counting aids in the classroom, taking turns to use the materials and record the patterns. Number grids [BLM 1 and 2] For counting games like sam yew gew students record the numbers replaced by an action or word (clapping hands, saying buzz). They can do this in a range of ways, for example by placing a counter on the numbers on a 1 to 99 (BLM 1 page 9) or 0 to 100 number grid (BLM 2 page 10). Alternatively, the BLM can be used with interactive white board or other technology. This works particularly well for games focused on multiples of x and leads to discussions about the patterns that emerge.

Counting frames In counting-on, counting back and skip counting activities, counting frames are useful to show a physical representation of what is occurring.

Abacus The abacus has a long history as a calculating device. It comes in various shapes and forms. The top section of an abacus like these is called heaven or the upper deck. The Chinese abacus – suanpan The Chinese abacus has two beads in the upper deck and five beads on the lower deck.

The number represented on this suanpan is 643.

© The University of Melbourne -‐ Asia Education Foundation, 2011

7

YEAR 1 Counting games The Japanese abacus – soroban The Japanese abacus has one bead on the top deck and four in the lower deck. Both forms of abacus are used to perform base 10 calculations by moving the beads towards the centre beam. They can be used to represent numbers and are useful aids when discussing number representation and place value. The internet is a rich source of information about different types of abacus, their origins and uses. Enter abacus into the Wikipedia search engine at http://en.wikipedia.org/wiki/Main_Page.

Activity worksheets - BLM The following Black Line Masters (BLM) are provided on pages 9 and 10 for use with the activities: •

BLM 1: 1 to 100 number grid

•

BLM 2: 0 to 99 number grid

The BLM are useful for many other mathematical activities. There are significant benefits in students having their own copies and a bag of counters to keep a personal record of the number patterns they create in class. These can be photographed to create a permanent record of the patterns or contribute to a class project on these themes. The BLM may be used in conjunction with interactive white board and other technology for whole class activities.

© The University of Melbourne -‐ Asia Education Foundation, 2011

8

YEAR 1 Counting games

BLM 1

1

2

1 to 100 number grid

3

4

5

6

7

8

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

© The University of Melbourne -‐ Asia Education Foundation, 2011

9

YEAR 1 Counting games

BLM 2

0

1

2

0 to 99 number grid

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

© The University of Melbourne -‐ Asia Education Foundation, 2011

10

YEAR 1 Counting games Extension opportunities Australian Curriculum for Mathematics Year 2

Number and Algebra

Number and place value

Element code ACMNA028

Content description

Elaboration

Group, partition and rearrange collections up to a thousand in hundreds, tens and ones to facilitate more efficient counting

• using an abacus to model and represent numbers

Students may be familiar with a particular form of abacus, or can be introduced to an abacus as a way of reinforcing and extending their understanding of place value. This may draw on the prior knowledge of some students in the class.

Year 4

Number and Algebra

Number and place value

Element code ACMNA073

Content description

Elaboration

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

• recognizing and demonstrating that the place value pattern is built on the operations of multiplication or division of tens

Providing some history and information about how the abacus is used in many countries today can be interesting and may draw on the prior knowledge of some students in the class. Examples include calculating the combined cost of purchase items, tax or discounts in price or length, size or area of materials. Using the tools in new ways •

• • •

More sophisticated tasks such as comparing how a number is represented on a counting frame, a suanpan and a soroban can be useful to complement understanding of the concepts behind place value. Performing addition, subtraction and multiplication on an abacus can review basic concepts in a new context. Links to other relevant studies can be made, for example languages learning and studies of Chinese, Korean or Japanese culture. Comparisons with tools and methods for counting and calculating from other parts of the world can be investigated.

© The University of Melbourne -‐ Asia Education Foundation, 2011

11