subitizing Archives - Maths 4 All

When children are first shown two groups to combine they often ‘count all.’ If they are not presented with suitable activities ‘counting all’ might become the default strategy for later computational tasks. Being able to subitise supports later mathematical abilities. It is important that children are supported in developing their ability to subitise as not all are able to, especially those children who may suffer from dyscalculia.

Developing Conceptual Subitising

Once children are able to perceptually subitise standard dot configurations to six (those on die) they can be supported to develop the ability to ‘count on’ then subitising two or more groups.

Activities using Standard Dot Cards

Begin with ‘Counting On’ Skills

Provide students with a 2 sets of standard dot cards 1-6.
Use a set of dot cards 1-6 and an extra 1, 2 and 3. The extra cards will be used to practise ‘counting on.’
Begin with two cards, for example a 5 and a 2. Identify the cards with the students using perceptual subitising.
Turn over the larger card and leave the ‘count on’ card face up. Model how to ‘count on.’

“We know that the face down card is showing 5 dots. Let’s count on from 5 to find out how many dots altogether. (Touch the face down card saying) 5 then count on 6, 7. There are 7 dots altogether.”

Repeat the process with two more cards.
Make sure when you check how many that you do not count the dots on the face down card. It should be ‘seen’ by subitising.
Have students work in pairs, one choosing the larger number 4, 5 or 6 and the other the ‘counting on’ card 1, 2 or 3.

What’s the Difference

Begin with two cards. One card is 4, 5 or 6. The other card is 1, 2 or 3.e
Place the largest card face up, while the other card stays face down.
Say the total of the two cards and ask what might be on the hidden card. Encourage students to ‘cont on’ to work out the difference.
Turn the hidden card over and check the answer by ‘counting on.’
With a bit of practise, students could play with a partner.

More or Less

Provide students with cards 1 to 6.
Lay the cards out in front of each child.
Ask, “Which card is one more than ______? Which card is two less than _______?
Lastly, have students generate their own questions.

Activities Using Non-Standard Dot Cards

Here are a few ‘oldies’ to use along with the activities for standard dot cards. If you need the instructions just click on the name of the game as it has a link to a version of the instructions.

Go Fish

Memory

Snap

If you haven’t already discovered Natural Maths, Ann and Johnny Baker have produced two resources, Subitizing: Laying the Foundations and Conceptual Subitizing: Laying the Foundations for Mental Computation. There is a purchase cost for both books but I would highly recommend them. The later focuses on using subitising as a springboard for counting on, doubling and facts to ten knowledge.

Yet, subitising doesn’t only assist addition and subtraction facts. It can also support the ability for student’s to develop visual images of multiplication facts. Graham Fletcher provides an explanation on his blog.

Often, teachers do not fully appreciate the need for students to be able to subitise. Yet, it is a vital component in developing their ability to mentally computate.

Until next time,

Carole

Subitising refers to being instantly and automatically able to recognise small numerosities without having to count (Clements, 1999; Jung et al., 2013; Moeller et al., 2009; Clements & Sarama, 2009).

‘Some suggest that subitising may well be the developmental prerequisite skill necessary to learn counting. If so, we should examine subitising more closely and determine if reinforcing this skill in children will help them learn counting easier’ (Sousa, 2008). There are also ‘strong suggestions that all later mathematics is built on the ability to subitise (Baker, 2015).

Clements (1999) describes two types of subitising: perceptual and conceptual.

Perceptual Subitising

Perceptual subitising involves recognising a number without using other mathematical processes. It assists children to separate collections of objects into single units and connect each unit with only one number word, thus developing the process of counting.

Conceptual Subitising

Conceptual subitising allows one to know the number of a collection be recognising a familiar pattern, such as the spatial arrangement of dots on the faces of dice or on domino tiles. Other patterns may be kinesthetic, such as using finger patterns to figure out addition problems, or rhythmic patterns, such as gesturing out one “beat” with each count.

What Does Research Tell Us?

Subitizing: What Is It? Why Teach It? Douglas H. Clements (1999)

A seminal article which is often referred to!!

Subitizing: A Critical Early Math Skill Subitizing Paula Hartman, Myoungwhon Jung and Greg Conderman, Northern Illinois University (2012)

An easy to read article that contains activities and apps.

Subitizing: A Skill That Leads to Strong Number Sense ThoughtCo (2017)

Again, an easy to read article that contains activities to support children in learning to subitize.

Activities to Support Perceptual Subitising

Dice games – simply playing board games with a 6-sided subitised die will assist children in developing perceptual subitising.

Making Patterns – show a quick image or flash card of a subitised pattern. Children then use counters or coloured glass stones to replicate the pattern. This activity assists children to visualise patterns and embed the image in their minds.

PowerPoint of Quick Images

Display each dot pattern for only 3 seconds. Click ‘enter’ to go to a blue screen then click again to reveal the answer.

Domino: Games with Dots from Lessons Learnt Journal

Printable Dominoes from First-School.ws

Printable Dominoes from Helping With Math

Subitizing with Dot Plates from Mathematics for the Curious Pre-K-K Click on the owl to download

Flower and Flower Pot Match from Lovely Commotion

1-6 Playing Cards for Go Fish and Concentration

Monster Dice Match from The Measured Mom

Ladybug, Ladybug Roll and Cover from Oceans of First Grade Fun

Ice Cream Count and Match from The Measured Mom

Subitizing – Laying the foundations for number sense – yes, there is a cost involved but this book by Ann and Johnny Baker provides activities and games, problematized situations and mental routines. The mental routine includes closed, open and flipped questions, that encourage a deeper level of thinking. great resource!!