MATHEMATICAL CONTENT KNOWLEDGE -
Early number concepts include sorting and classifying, patterns, subitising, counting, place value, and
grouping and renaming.
There are four principles in counting, which include one to one correspondence, stable order rule, grouping and renaming.
order irrelevance rule and the cardinality rule. The one to one correspondence is where each
object is allocated in a number name and only one number name per item. Children may find it
easier to develop this in the beginning by physically touching or moving each object as it is counted.
The stable order rule is the number of names that must be used in a specific order each and every
time a group of objects is counted. The order irrelevance rule is the order in which a group of objects
is counted does not matter. The cardinality rule means the last number used when counting gives the
total number of objects all together.
There are four key counting misconceptions, these are counting teen numbers, bridging to the next
ten or hundred, reversing digits when writing, and writing numbers that were read aloud.
ten or hundred, reversing digits when writing, and writing numbers that were read aloud.
PEDAGOGICAL CONTENT KNOWLEDGE -
When teaching early number sense, enhance students’ interest in mathematics by building on their
real-world experiences with formal and informal examples, to help develop their problem-solving or
reasoning skills. Use hands-on approaches such as counters or objects to help students physically
and visually solve the mathematical problem. Develop their mathematical language skills by ensuring
they use appropriate terms when explaining their thinking processes.
real-world experiences with formal and informal examples, to help develop their problem-solving or
reasoning skills. Use hands-on approaches such as counters or objects to help students physically
and visually solve the mathematical problem. Develop their mathematical language skills by ensuring
they use appropriate terms when explaining their thinking processes.
Reference: (Van et al., 2015)
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Activity - Skip Counting Counters
Year Level - 1
Classroom Context -
For students who have different learning or academic abilities, allow those in the lower mathematical
levels to work with students in higher mathematical levels for collaborative and cooperative learning.
This will increase their social and teamwork skills also.
levels to work with students in higher mathematical levels for collaborative and cooperative learning.
This will increase their social and teamwork skills also.
Content Descriptor -
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)
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)
Learning Objectives -
This activity is a simple and effective learning task that helps students develop fluency in counting
forwards and backwards in multiples. Skip counting is the basis for multiplication and division, which
makes it crucial for students to have confidence in this area. This activity is flexible so it can be easily
adapted when choosing a starting point number.
This activity is a simple and effective learning task that helps students develop fluency in counting
forwards and backwards in multiples. Skip counting is the basis for multiplication and division, which
makes it crucial for students to have confidence in this area. This activity is flexible so it can be easily
adapted when choosing a starting point number.
Resources -
Key Mathematical Language:
Count in, Count on, Skip, Number, Starting from, Ones, Twos, Fives, Tens, One more, Two more,
Five more, Ten more
Five more, Ten more
Hands-on Manipulatives/materials:
Hundreds number charts, clear counters
Hundreds number charts, clear counters
Number charts are effective tools for students to learn with because they can physically see,
visualize and understand the concept. Counters are a great hands-on manipulative that are useful
in early number activities.
visualize and understand the concept. Counters are a great hands-on manipulative that are useful
in early number activities.
Use of video as an ICT tool is an effective way to engage students in a new learning topic. It is
visually entertaining for young children.
visually entertaining for young children.
Prior Knowledge -
Students should recognise small quantities without counting (subitising).
Students should have the ability to recognise all numbers from 0 to 100.
Instructions -
- Play a learning song from Youtube that teaches children how to count by 2’s, 5’s and 10’s.
- Encourage the students to sing along to the catchy song. Play this clip on a TV or a large for the whole class to watch.
- Each student will receive a hundreds chart and clear counters (so they can still see the number underneath when it's placed over the numbers) and begin with a starting number
- Allow the students to count up in ones until they reach their multiple, then place a counter on the multiple, e.g. 10, 20, 30, etc.
- After the students repeat these steps a few more times, they should see a pattern and stop counting in ones to get to the next multiple
- Once students are comfortable with this, allow them to start at a random number such as ‘16’
Questions to ask -
If you are counting in twos, what number will you land on if you start from 4?
What pattern do you see when you count in tens? Twos? Fives?
What pattern do you see when you skip count backwards?
Enabling Prompts - For those struggle with basic counting, allow them to practice normal counting
row by row, then slowly increase the difficulty starting by ‘counting in twos,’ and use counters to assist.
row by row, then slowly increase the difficulty starting by ‘counting in twos,’ and use counters to assist.
Extending Prompts - Have the fast learners skip count backwards on odd numbers for a challenge.
Images -
Play video clip from Youtube: (https://www.youtube.com/watch?v=vq3cDj3Uj3I) on a song about
counting in 2's, 5's and 10's.
counting in 2's, 5's and 10's.
Coloured counters are a good hands-on manipulative for children to work with when counting.
The 100's number chart that students will be using to count. They will be able to count in rows
and see the patterns.
Students will place a counter on every number they land on when they skip-count. This example
is a demonstration of counting in two's.
Reflection -
In week 1, we were introduced to the concept of early number, counting systems and place value
knowledge. As Van et al. (2015) mentioned, teaching mathematics to young children is most effective
when we provide high quality learning activities so they can develop basic numeracy understandings.
My understanding of this is that early number development in young learners is an important part of the
foundation for their future success in academics. These early number concepts include understanding
quantity, counting, subitising, patterns, and value.
knowledge. As Van et al. (2015) mentioned, teaching mathematics to young children is most effective
when we provide high quality learning activities so they can develop basic numeracy understandings.
My understanding of this is that early number development in young learners is an important part of the
foundation for their future success in academics. These early number concepts include understanding
quantity, counting, subitising, patterns, and value.
The activity I have planned for this particular concept links to the curriculum as it focuses on developing
confidence in number sequences to and from 100 from any starting point. The activity focuses on skip-
counting, a skill that is vital for future mathematical concepts to be learnt. I have come to understand that
in my future classroom, it is essential to create activities that are based on hands-on approaches, as this
strategy is most effective for young students when learning about early number concepts such as counting,
patterns or order. Without something hands-on and visual, it would be difficult for children to focus and be
engaged in the learning activity. I believe it is also important to connect these mathematical ideas to real-
world examples to help their learning and skills more applicable to their everyday lives.
References -
Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle school mathematics: teaching developmentally, global edition. Retrieved from https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au
