EARLY NUMBER DEVELOPMENT
Mathematical content knowledge
This is a brief summary of what mathematical content knowledge that teachers need to have.
Early number concepts include:
(Reference: Van de Walle, Karp & Bay-WIlliams, 2014)
Early number concepts include:
- sorting and classifying – sorting for size, colour, shape
- skip counting – counting in 2s, 3s, 5s, 10s
- comparing and sequencing
- subitising – ability to know number without counting
- patterns
- counting on and counting back
- benchmark to 5 and to 10
- more than, less than and equal to
- numeral writing and recognition
- one to one correspondence - each object being counted is allocated a number name and only one number name per item. Children may find it easier to develop this skill in the beginning by physically touching or moving each object as it is counted.
- stable order rule - the number names must be used in a specific order each and every time a group of objects is counted.
- order irrelevance rule - the order in which a group of objects is counted does not matter.
- cardinality rule - the last number name used when counting gives the total number of objects altogether
(Reference: Van de Walle, Karp & Bay-WIlliams, 2014)
Common student misconceptions |
KEY MATHEMATICAL LANGUAGE |
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RESOURCES
(Further resources can be found in the activities below)
CURRICULUM MAP
Foundation
Establish understanding of the language and processes of country by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)
Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
Subitise small collections of objects (ACMNA003)
Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
Year 1
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 (ACMNA012)
Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
Count collects to 100 by partitioning numbers using place value (ACMNA014)
Year 2
Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026)
Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
Year 3
Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
Year 4
Investigate and use the properties of odd and even numbers (ACMNA071)
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
Establish understanding of the language and processes of country by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)
Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
Subitise small collections of objects (ACMNA003)
Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
Year 1
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 (ACMNA012)
Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
Count collects to 100 by partitioning numbers using place value (ACMNA014)
Year 2
Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026)
Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
Year 3
Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
Year 4
Investigate and use the properties of odd and even numbers (ACMNA071)
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
ACTIVITY - BIRTH to 5 years
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NUMBER MATCHING
Outcome: This activity is designed as an independent pair or small group activity to consolidate student understanding of numeral and quantity and one-to-one correspondence. This particular example includes number to 6 but it can be adapted to include numbers up to 10 and beyond depending on the skill level of the child. Curriculum Link: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) Resources: Plates with numerals, pegs (large and/or small), teddies Activity: Each student will select a plate (or have a set of plates each). They will be required to place the correct number of pegs on the edge of the plate. They will also be asked to place the correct number of teddies on each plate. Finally, students will have the opportunity to place the numbers is sequence, starting from one. If students require further extension, they could be asked to go from biggest to smallest starting from 6 or 10. Assessment opportunities: The teacher will have opportunity to assess the students' numeral recognition, one-to-one correspondence through observation and questioning. It will be clear from observation whether or not the student has developed the ability to count. To clarify however, the teacher could point to a particular plate and ask questions - "How many teddies are on this plate?" "Can you count them for me" The student should be able to recall the number name and demonstrate one-to-one correspondence. |
ACTIVITY - PREP (Foundation)
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NUMBER BINGO
Outcome: This activity is designed as an independent pair or small group activity to consolidate student understanding that connects number names, numerals and quantities. This particular example includes number to 6 but it can be adapted to include numbers up to 10 and beyond as per the curriculum. Curriculum Link: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) Resources: Bingo cards, bottle tops as counters, dice (can either be tradition dice with dots or a dice with numerals) Activity: Each student will take turns to roll the dice and have the opportunity to place a counter on the numeral, number name or picture relating to that number. If the student does not have the correct number, play passes to the next player. Turns will continue until a student has a full card and calls "BINGO". Assessment opportunities: The teacher will have opportunity to assess the students' numeral and name recognition, subitising ability through observation and questioning. For example, student rolls a 4 on the die "How do you know that was four?" The teacher can observe the child physically pointing to the dots on the die or whether they just "know" there is four. Additional information: This activity also supports students social development as it requires them to take turns and wait for the other players. There is also opportunity for support and encouragement to be shown if a student is having difficulty. |
ACTIVITY - YEAR 3
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MY NUMBER IS...
Outcome: This activity is designed as a whole class activity or it can be played in small groups. The aim of the activity is for students to build the "biggest", "smallest" or "closest to" four digit number depending on the numerals they turn over. Curriculum Link: Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) Resources: "My number is..." game cards (place value charts - thousands, hundreds, tens, ones), numeral cards (0-9) (Each student will have a game card and a set of numeral cards between 2 students), counters or blocks for scoring. Activity: Each student will have a game card and a set of numeral cards between 2. The teacher will write the object of the game on the board - "highest number wins", "lowest number wins", "number closest to ? wins". The numeral cards are laid face down in front of the students. All players will select a number and decide whether it will represent the thousands, hundreds, tens or ones. Students will need to think strategically For example: if the object of the game is to have the highest number, and the student draws a 9, it would be best if they consider placing this number in the thousands column or if they draw a 2, they would place this in the ones column. Each player would then select a second digit and so on until their game board is full and forms a four digit number. . Students compare their numbers to see who has the highest number. The winner takes a counter. Repeat, changing the rule if desired. Play five rounds. Assessment opportunities: The teacher will have opportunity to assess the students ability to read four digit numbers and understanding of place value through observation and questioning. As a further step to the activity, the students can then "build" their number using MAB blocks. This can help struggling students to visualise the number and see whose is the biggest/smallest number. Additional information: This activity would also be suitable for assessing place value knowledge and understanding. This activity could be adapted to suit all year levels ie tens and ones for lower grades or hundreds of thousands or decimals for grades 5 and up. (Adapted from http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.2.pdf) |
REAL WORLD CONTEXTUAL WORD PROBLEMS
How many lollies are in the cookie jar? How many children in the class? How many legs does the cat have? How many toes do you have?
(Questions such as these can help develop the students ability to estimate and count. It helps them develop a real-world understanding of number and how many.)
(Questions such as these can help develop the students ability to estimate and count. It helps them develop a real-world understanding of number and how many.)
REFERENCES
Catholic Education Diocese of Cairns. (nd).Numbers to 10000. Retrieved from http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.2.pdf
Van De Walle, J.A., Karp, K. S. & Bay-Williams, J. M. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England:
Pearson Education Limited.
Van De Walle, J.A., Karp, K. S. & Bay-Williams, J. M. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England:
Pearson Education Limited.