Number:
Whole number
This is not a total teaching program, it provides an overview of the continuum of learning for Whole number
Stage / Outcome/key ideas / Teaching/learning/working mathematically / Resources / Planned assessment / Links to other strandsEarly Stage 1 / NES1.1 Counts to 30, and orders, reads and represents numbers in the range 0-20
Key Ideas
Count forwards to 30 from a given number
Count backwards from a given number, in the range 0-20
Compare, order, read and represent numbers to at least 20
Read and use the ordinal names to at least ‘tenth’
Use the language of money / Everyday counting
Count the number of students in the class each day
Count objects around the room.
Matching dots with numbers
Match dots on number cards and state total
(p. 83 Developing Efficient Numeracy Strategies Stage 1)
Forward number word sequence and backward number work sequence
Count forwards to 20 from a given number and backwards from 20 from a given number using a vertical number line.
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19
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2
1
0
Hundreds chart
Count forwards and backwards by ones on a hundred chart e.g. start at 11 and count forwards to 21, start at 19 and count backwards to 9.
Numeral flip strip
Construct a numeral flip strip and conceal a number line between the flaps of the flip strip. Direct students to determine the missing numerals, before, after, or between nominated numbers on the flop strip, by lifting the strips. Then answers can be verified.
(p. 39 and p. 93 Developing Efficient Numeracy Strategies Stage 1)
Washing line
Count Me In Too learning object - Game 14
Peg counting
Students match, with the corresponding number of pegs, number cards 1-10, attached to wire coat hangers. Order coat hangers from 1 to10 when complete. Compare size of groups.
Extend activity with number cards 11-20. Match number cards with counters, place cards in order, complete number before/number after activities.
Ten frames
Make a set of ten frame cards from
0 to 10. Begin by flashing the ten and asking the students to explain how they know there were ten dots. Continue with the other cards, ensuring students explain how they know the number of dots and ask the students to replicate the numbers with fingers. Continue the activity by flashing the cards to encourage instant recognition of numbers.
Provide each student with a ten frame and ten counters. Students take turns to roll a die displaying dot patterns, count the dots and place the corresponding number of counters onto the ten frame. The exact number needed to complete the ten frame must be rolled to finish.
Number in line
When students are standing in line, practise ordinal counting to ‘tenth’.
Before and after numbers
Computer task – Numeral track
Count Me In Too learning object - Game 2
(p.87 Developing Efficient Numeracy Strategies Stage 1)
/ Mathematics K-6 Syllabus p. 41
Mathematics K-6 Sample Units of Work pp.
12-15
Developing Efficient Numeracy Strategies (DENS) Stage 1
Emergent activities pp. 23-47
Perceptual activities pp. 79-115
Talking about Patterns and Algebra – ES1 activities / Count Me In Too : SENA 1
Select activities to identify where students are on the CMIT framework in number for early arithmetical strategies
For example:
- Forwards and backwards oral counting
Start counting from _____. I’ll tell you when to stop.
- Matching number words to objects
Please get me ___ counters from the pile
- Before and after numbers
Count backwards from 10.
Count backwards from 23.
What number comes before 5, 9, 16, 20, ___, ___, ___?
- Numeral identification
What is this number?
5, 8, 20, 12, 15, 0.
Matching Teddies
Provide students with a selection of matching objects e.g. 2 blue teddies, 3 red teddies, 4 yellow teddies and 5 green teddies. Provide a set of numeral cards. Students sort, count and place groups of objects onto the corresponding numeral cards.
Ten Frames
Punch ten holes in the top of a shoe box to represent a ten-frame. Provide students with a set of numeral cards from 1-10 and golf tees. Students turn over a card and use the corresponding number of golf tees.
Count Me In Too : SENA 1
Use selected tasks from SENA 1 as continual assessment. Record student achievement of SENA 1 tasks.
Class Shop
Use the class shop and other play situations to informally assess students’ use of the language of money. / Patterns and algebra-
continue simple number patterns that increase and decrease
Stage 1 / NS1.1 – Unit 1 (two-digit numbers) Counts, orders, reads and represents two- and three- digit numbers
Key Ideas
Counts forwards and backwards by ones, twos and fives
Counts forwards and backwards by tens, on and off the decade
Read, order and represent two-digit numbers
Read and use the ordinal names to at least ‘thirty-first’
Sort, order and count money using face value / Bingo
Students construct a bingo card (3 x 3 grid) and write two- digit numbers in a specified range in each box, eg from 20 to 40. The teacher describes a number e.g. two tens and 3 ones, the number one more than 22, two less than 25. The student who has 23 covers the number with a counter. Three in a row, column or diagonal is the winner.
23 / 31 / 24
29 / 39 / 28
35 / 26 / 37
Celebrity head
Display a number line showing numbers from 1 to 100 and place movable marker tabs at either end of the strip. One student wears a headpiece to which a numeral card is attached, ensuring the student does not see the number on the card. Ask the student to have the class help to identify the “secret number”. The class, however, can respond only with a yes or no reply to each question. In response to the answers, the selected student then moves the tabs along the number line to indicate the range within which the “secret number” lies. Continue the process until the student is able to identify the number.
(p. 221 Developing Efficient Numeracy Strategies Stage 1)
Hundreds chart
Find patterns and count by fives, tens and ones on a hundreds chart.
Practise counting by tens on and off the decade, forwards and backwards, using a hundreds chart. e.g. 7, 17, 27 …
Provide opportunities for students to continue over 100. e.g. 87, 97, 107, 117.
(p. 161 Developing Efficient Numeracy Strategies Stage 1)
Hundred chart windows
Count Me In Too learning object - Game 14
Click here to access Hundred chart windows
Click here to access the teacher support material.
(p. 76 Developing Efficient Numeracy Strategies Stage 2)
Calculators
Students enter a two- digit (or three digit) number on a calculator. In groups of 5, students read their number and then stand in numerical order. Students use materials e.g. MAB to represent their number.
Provide the students with at least one calculator for each pair of students.
Instruct the students to:
• enter a given number on the calculator
• enter on the calculator the number which is one before or one after a given number
• use the constant function on a calculator to add on from a givennumber.
Provide the students with a hundred chart on which they can record the
number patterns.
(p. 179 Developing Efficient Numeracy Strategies Stage 1) / Mathematics K-6 Syllabus p. 42
DENS
Stage 1
Perceptual activities pp. 79-115
Figurative activities pp. 149-179
Counting On activities
pp. 221-229
Talking about Patterns and Algebra – Stage 1 activities / Count Me In Too : SENA 1, SENA 2
Select activities to identify where students are on the CMIT framework in number for early arithmetical strategies and place value
For example:
- Forwards and backwards oral counting
Start counting from 87. I’ll tell you when to stop.
- Before and after numbers
What number comes before 30, 47, 81, 123, 420, 761, 900?
- Numeral identification
What is this number?
23, 44, 100, 66, 59, 101, 400, 607, 310.
- Counting by 10s and 100s on and off the decade
Start from 7 and count on by 10s.
Start from 924 and count down by 100 each time.
Start from 367 and count on by 10s.
Students have a selection of coins: six 5c pieces, five 10c pieces, four 20c pieces and two 50c pieces. Students record the different ways that the coins can be used to make $1.00 / Patterns and algebra
- create, represent and continue a variety of number patterns and supply missing elements
- make generalisations about number relationships
Stage 1 / NS1.1 –Unit 2 (three-digit numbers) Counts, orders, reads and represents two- and three- digit numbers
Key Ideas
Read, order and represent three-digit numbers
Sort, order and count money using face value / The price is right
Display a vertical numeral strip to the students. Ask one student to think of a number on the numeral strip. The remainder of the class take turns to guess the number. After each guess, allow the student to point to the nominated number on the number line. The student then states if the guess is higher or lower than the number being thought of. Encourage the students to use the responses from previous guesses when making the next guess.
309
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Empty number line
Use an empty number line to record numbers and practise counting forwards and backwards by twos, fives, tens, and hundreds both on and off the decade
Ordinal numbers
Organise students in a circle. Have number cards from 1st - ? Select one student to be first. Students have to work out their order and select the correct ordinal card.
Wipe out
Provide each student with a calculator. Ask the students to enter a specificthree-digit number into their calculators.Choose one of the digits from the number entered and ask the students to use an arithmetical method to change the nominated digit to zero. For example, have the students enter the numeral 268 in their calculator. Follow this by asking, “Howcan you change the 6 to 0?”
Investigations:
How many different numbers can you make using 3, 7, and 4
What numbers less than 100 have a 5 in them? less than 200?
What can you find out about the number 199?
How many numbers between 1 and 100 contain a ones digit that is higher than the tens digit?
Adapted from Peter Sullivan’s work on good questions. / Mathematics K-6 Syllabus pp. 42, 43
DENS
Stage 1
Figurative activities pp. 149-179
Counting On activities
pp. 221-229
DENS
Stage 2
Counting by ones pp. 20-46, pp. 62-68
Talking about Patterns and Algebra
Stage 1 activities / Students have a three-digit place card e.g.
Roll a 0-9 die three times and place numbers in boxes to make a) the largest number, b) the smallest number,
c) the number closest to a given number. Students read, compare and order numbers.
Money Tasks
Use a canteen price list for students to create money problems e.g. Jo bought a salad roll and an orange juice. She paid with a $2 note. How many different ways could she be paid her change? Students exchange tasks for others to solve. / Patterns and algebra
- create, represent and continue a variety of number patterns and supply missing elements
- make generalisations about number relationships
Stage 2 / NS2.1 Counts, orders, reads and records numbers up to four digits
Key Ideas
Use place value to read, represent and order numbers up to four digits
Count forwards and backwards by tens or hundreds, on and off the decade / Mental calculation.
Begin with a number. Ask students to calculate a series of tasks in their head e.g. begin with 15, add 10, add 10, add 100, subtract 10, add 100, what is the number?
Finger counting
Begin with a number e.g. 321. Students add mentally, watching the teacher’s finger strategies: 10 fingers (palms up) means to add 10, a clap means to add 100.
Maths Tipping
Students stand around the room. Make a set ofthree-digit number cards. Ask questions such as: how many tens altogether in 500? What number is 100 more than 602? The student who answers correctly may take one step towards another student. If that student is tipped they sit down.
Largest number wins
Organise the students into small groups and provide them with an“operation die” (A cube marked with “+1”, “-1”, “+10”, “ 10”, “+100”, “-100”.) Each player starts with a score of 500. The die is rolled and each player adds or subtracts the number rolled to his or her score. In turns,players then have four rolls of the “operation die”. After each roll the player calculates and records his or her tally. The winner is the playerwith the largest number.
(p. 181 Developing Efficient Numeracy Strategies Stage 2)
Bingo
Students make up a bingo card (3 x 3) and fill it with three-digit numbers e.g. using the digits 6, 3, 2, 5 and 0. The teacher reads a clue, e.g. the number 100 more than 256. If the student has that number, they cross it out. First to three in a row, column or diagonal is the winner.
Arrow card game
Count Me In Too learning object - Game 6
Click here to access Arrow card game
Wishball
The wishball learning object encourages thinking about place value and provides opportunities for mental addition and subtraction.
Investigations:
-A number is rounded off to 1500. What could the number be?
-How many numbers can you write using the digits 3, 8, 1, 6 once only?
-How many different ways can you write the number 5783? e.g. how many tens altogether?
Adapted from Peter Sullivan’s work on good questions. / Mathematics K-6 Syllabus p. 44
Mathematics K-6 Units of work pp. 84-86
DENS
Stage 2
Counting by ones pp.70-90
Forming groups
pp. 174-196
Talking about Patterns and Algebra
Stage 2 activities / Count Me In Too : SENA 2
Select activities to identify where students are on the CMIT framework in number for place value
For example:
- Numeral identification
What is this number?
607, 310, 1000, 4237, 3060, 8838, 9909.
- Counting by 10s and 100s on and off the decade
Start from 1089 and count on by 10s.
Start from 3224 and count down by 100 each time.
Start from 6779 and count on by 100 each time.
Four digit numbers
(Assessment CD) Students construct a four-digit numeral by taking turns to draw a digit card from a pile and place it in a column on a place value mat. Once placed, the digit cards cannot be changed. Students take turns to read and order their four-digit numbers. (Movie).
Four digit numbers in order
Students enter a four digit number on a calculator. In a group of five, students take turns to read their number and order themselves according to their number. (Assessment focus: uses place value to read, represent and order numbers up to four digits).
Ordered numbers
Provide students with 4 numeral cards, one card must be a zero. Using all four cards make the:
- largest number you can
- second largest number you can
- smallest number you can
Record all the numbers that can be made using the four numeral cards. Oder the numbers from smallest to largest and explain how you worked out the order. / Patterns and algebra
- generate, describe and record number patterns using a variety of strategies
Stage 3 / NS3.1 Orders, reads and writes numbers of any size
Key Ideas
Reads, write and order numbers of any size using place value
Record numbers in expanded notation
Recognise the location of negative numbers in relation to zero
Identify differences between Roman and Hindu-Arabic counting systems / Hundreds chart
Use activities from the chapter on Hundreds Chart (p. 69 Counting On) to review understanding of place value concepts
Number people
Make number cards with the digits 0-9. Hand out, for example, five cards to students. Without speaking, the students are asked to make the largest number, smallest number, the smallest odd number etc. Extend range of numbers to 6, 7, 8 digits.
Investigating numbers
Students predict the total, then investigate: How many four -digit numbers can be made using the digits 8, 2, 0, 3, each once only? Extend to combining more digits.
Calculators
Students work in pairs. One student uses a calculator to count back by tens from 30. The partner uses a number line. Students compare the number they reach after 5 terms – discuss negative numbers in relation to zero.
Roman numerals
Students investigate writing a number in many forms, including expanded notation and Roman Numerals. Include examples such as the year they were born and the year the school opened.
Number Stories
Students create number stories for a partner to solve e.g. my four-digit number is even, the tens digit is larger than the hundreds, the ones digit is larger than the tens. What could my number be? / Mathematics K-6 Syllabus p. 45
Counting On teaching activities pp. 15 - 89 Place Value
Talking about Patterns and Algebra / Counting On:
Select activities to identify where students are on the place value framework.
For example:
Show four cards with digits, 4, 5, 8, 1.
Can you use these cards to make the largest possible number? Read it to me. How do you know it is the largest number?
Now, can you change the cardsto make the next highest number?
Show the number 1 593 on a card.
What is this number?
What is the number which is 10 more than this number?
Show the number 621 on a card.
If you had 621 counters, how many groups of 10 could you make?
Provide each student with a frame which has seven boxes e.g.
Students take turns to spin a spinner (or roll a 0-9 die). Each student records the numeral in one of the boxes, until all boxes are full. Students read their number to the group and numbers are placed in order from lowest to highest.
Individually, students roll a 0-9 die to make the largest number they can read to the teacher. They write the number in expanded notation and write two numbers higher and two numbers lower than their number. / Links to other strands
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