Activities to support Pattern and number structure
Where are they now?
Students:
- identify and recognise standard dice patterns (subitise)
- raise their fingers sequentially when asked to show a number from one to ten using their fingers. That is, they tend to count each finger as it is raised
Where to next?
Students:
- recognise instantly a range of dot patterns up to 10 without counting (subitise), developing strong visual images for given numbers
- subitise random collections up to 4 items
- automatically raise the correct number of fingers when asked to show a number from one to ten
- know that numbers can be separated and combined in a variety of ways (i.e. numbers are flexible - they can be represented, partitioned and combined in many ways)
Outcomes
The following activities provide opportunities for students to demonstrate progress towards the following outcomes. A student:
MAe-1WM describes mathematical situations using everyday language, actions, materials and informal recordings
MAe-2WM uses objects, actions, technology and/or trial and error to explore mathematical problems
MAe-3WM uses concrete materials and/or pictorial representations to support conclusions
MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0-20
MAe-5NA combines, separates and compares collections of objects, describes using everyday language, and records using informal methods
How?
Rabbit ears
Ask students to put their hands above their head. Then ask them to show various numbers by raising the correct number of fingers. This is best done in random order, first in the range one to five and then six to ten.
For example, “Show me the number four,... two,...five,...three.” The aim is for the students to raise their fingers simultaneously rather than sequentially. Students may verify their count by bringing their hands down and counting their fingers.
Examine the various ways students made the given number and write them down. E.g. Ali made 6 by having 4 fingers on one hand and 2 fingers on the other hand. Sarah made 6 by having 5 fingers on one hand and 1 finger on the other hand.
Why?
When demonstrating numbers in the range six to ten using their fingers children are developing concepts of partitioning or part-whole number relationships.
Continued practice with part-whole number relationships provides a basis for learning more efficient strategies to solve number problems.
Variation
• Display a finger pattern for a nominated number to the students. Have the students copy the finger pattern. Encourage instant demonstration rather than students raising their fingers sequentially. If necessary, the students may lower their hands to count and confirm that they have raised the correct number of fingers. The students then find a dot card or numeral word card corresponding with the number. Students may check that they have the correct card by matching their raised fingers with the dots on the card
Speedy dominoes
Distribute domino pieces to the players. This activity is played in the same way as regular dominoes, except that there is no turn taking. As soon as a player see an opportunity to place a domino in the game, they may do so. The first player to correctly place all dominoes is the winner.
Teaching Point
Dot pattern activities
Dot cards can be made using a range of materials – cardboard, paper plates, interactive whiteboard, photos of finger patterns and post-it notes as well as using resources readily available such as a variety of dice, dominos and ten frames. Students should be regularly exposed to a variety of dot patterns to support their subitising skills, including standard and random patterns. It is important to note however, that students’ abilities to subitise random amounts is generally within the range of 0-4 items.
1. Make my pattern
Provide the students with counters and paper plates to build their patterns on (alternatively, use mini whiteboards). Using an interactive whiteboard, briefly display a small number of dots before screening the collection. Ask students to replicate the same pattern as shown on the board. Ask the students to make statements about the patterns they saw, drawing out the combinations of parts for the pattern. For example, for a pattern of five dots the student may see the combination “two and three”, or, “four and one”. Check the patterns students created by revealing the original pattern and using reasoning and/or counting to check. Repeat.
- Provide each pair of students with dot cards, mini whiteboards and a marker. Have one student flash a pattern card to their partner. The second student looks carefully at the card for 1-2 seconds and then draws what he or she saw and labels the collection. The second student then describes what he or she has recorded to his/her partner. Together, the students use counting to check. Students swap roles
- Students could record their working by taking photos using a tablet device which they present back to the class
Teaching point
Expose students to a variety of dot patterns for each number so they do not come to associate only one pattern with a given amount.
Why?
Students need to develop instant recognition of small groups of items and associate a number word with the group. This will eliminate the need to count each group from one, leading to more efficient strategies.
2. Matching patterns
Using an interactive whiteboard, briefly display a dot pattern then screen the pattern. Provide the students with dominos and ask them to find, and show, a corresponding number of dots. Ask students to explain why they made their selections. Reveal the original pattern to check. Repeat activity varying the dots in the patterns from 0 -10.
- Construct two sets of dot pattern cards in the range of 0-10. Place one set of cards in a pile and display the other set in a row. Have the students take turns to select a card from the pile and then find a dot pattern card from the row which has the same number of dots as the card chosen. Students take matching cards and the player with the most cards wins. Alternatively, play as a version of snap or concentration
- Increase the number range to include teen numbers and beyond
3. Name and identify my pattern
Flash a dot pattern plate (or card, image or ten frame) for a few seconds to the students. Ask the students to draw and label the pattern they saw on their mini whiteboards before sharing with a partner. Have students describe the pattern they drew and share their thinking. The teacher should model how to check representations by counting and reasoning based upon the combinations found within the pattern. For example,“I know It’s a number larger than 5 because I saw a full row and a few more counters”.
4. The pattern before or after
Make 1-10 dot pattern cards for students (BLM - Flash Cards). Provide pairs of students with a set of the dot pattern cards, a special dice labelled with “+0”, “-1”, “+1”, “the number before”, “the number after”, “is the same as” and a mini whiteboard and markers. The first student rolls the dice to work out what their partner has to do to the pattern they will see. The student then flips over a pattern card and briefly shows it to their partner.
The second student draws or makes the pattern as indicated. Once complete, the first student unveils the original card and the students check. Students swap roles.
This could be turned into a game by gaining a counter for each correct pattern drawn or made. The person who has the greatest number of counters at the end is declared the winner. Students could record their work by taking photos of each round using a tablet device, recording their explanations.
Why?
When students are able to instantly recognise a set of objects (such as a pattern of dots) and are able to associate a number word with the set, the need for the student to count all of the objects from one is eliminated.
5. Combining dot patterns
Provide the students with two sets of dot plates (or cards) with dot patterns. Ask the students to find a pair of plates which combine to have the same number of dots as another plate (e.g. dot patterns that combine to make 5). Extend this activity by asking the students to attach a corresponding numeral card to each paper plate as well as labelling the sum.
Provide students with a large set of dot pattern cards (ten frame cards or dominos could be used as an alternative) and a 0-9 dot dice. Students deal out the cards. Students take turns to roll the dice to form a target number. Both students try to form a pair of dot cards that combine to make the given total. If they are able to form a match, students must prove why their thinking is accurate and place their two cards to the side. Students play until one player has used all of their cards or no one else can play. Students could then be asked to record the moves made in the game by taking a photo of the pairs they created and annotating it, writing the total those cards combined create.
Why?
Frequent practice with dot patterns, combining groups to form patterns and partitioning collections, leads to visualisation of numbers. Strong visualisation of numbers enables students to solve problems without relying on concrete materials.
6. Missing dots
Provide students with a pile of dot cards (or ten frame cards, dominos, playing cards, etc.) Show a dot pattern to the students for 1-2 seconds. Ask students to name the number of dots they saw. Cover some of the dots before showing students the same card again. Ask the students to find a dot card that corresponds to the missing number of dots. Ask students to explain their thinking. Students could replicate this activity in pairs, recording their thinking. E.g.
