Connecting number names, numerals and quantities

This resource has been developed in partnership with the NSW Mathematics Strategy Professional Learning team, Curriculum Early Years and Primary Learners, and Literacy and Numeracy.

Using the resource

This resource is the first section of a six-part resource supporting number knowledge. Use this resource in conjunction with the other resources in this series in order to support a connected network of critical mathematical concepts, skills and understanding.

Supporting tasks

Full instructions on how to use each of these tasks, including materials, related tasks and learning intentions are included in the resource, available for download on this page.

Ordering numbers

Experiences with writing and ordering the number naming sequences can help students to establish the stable-order principle (that counting words are said in the same order every time we count). Students who skip or confuse the order of number words have not yet established the stable-order principle. Since counting is about answering questions about quantities, understanding the stable-order principle is not enough on its own. Providing learners with experiences that connect the number word to the numeral (symbol), quantities, gestures and ideas is important is supporting counting skills.

Task 1: Racing to write

Students match ten-frame cards, either showing 1-10 or 11-20 on a (1-10 or 11-20) game board

  • Variation – match number word cards to numerals

Identifying numerals

Identifying a numeral is a different skill than recognising a numeral and students need opportunities to both identify and name numerals to master both skills.

Compare the thinking needed when a student is shown the numeral ‘5’ and asked to say the number word with asking them to point to a card with the numeral five on it from numerals available. Numeral identification refers to the first question (saying ‘five’) whereas numeral recognition refers to the second (can you point to ‘five’).

Task 2: Take a numeral

Students roll a die and match to a set of Numeral Cards 1-6

  • Variation 1: Keep cards in order to support the development of the number naming sequence or out of order to support the development of numeral identification.

  • Variation 2: Extend the number range of cards and dice.

Representations

It is important not to assume that students have developed conceptual understanding of representations like ten-frames because they say “seven” when they see an arrangement of 7 dots. In order to make meaning from representations, students need opportunities to explore structures, noticing features and regularities. Intentional, thoughtful deconstruction of mathematical representations also allow for students to be provided another opportunity to consider how quantities can be represented.

Students need to be provided with multiple opportunities to link concrete, verbal, visual and symbolic representations with a vast range of resources.

Distinguishing between ‘teen’ and ‘ty’ numbers can be challenging for some students. Confusion may occur as students try to differentiate the difference between the final sounds in fourteen and forty, for example. Not being able to discern, or make meaning from, the differences between ‘ty’ with ‘teen' can hinder number sense. We can support students by helping them hear the differences and make meaning from the suffixes ‘teen’ (ten more than) and ‘ty’ (groups of ten), comparing and contrasting pairs or trios of numbers like 14, 40 and 41

Task 3: Concentration

Students play a game of ‘memory’ to match numeral and representation cards 1-20 in a game

Task 4: Teen number puzzle

Using Teen numbers number puzzle cards, students work to match the puzzles and then order them from smallest to the largest or visa versa.

  • Variation 1: Have students sort the dot patterns into categories (for example, odd numbers and even numbers; smaller than 16, not smaller than 1) and discuss the similarities and differences between them.

  • Variation 2: Discuss with students what happens if we “swap” the numerals around for example, 14 now becomes 41. Ask students, “What does the one represent? Does it still represent ten? Why or why not?

  • Variation 3: Discuss what the “1” in 14 represents and whether it is the same “1” as one item, justifying and demonstrating thinking

  • Variation 4: Lay out a series of number teen puzzle cards along a number line and ask students to identify which numbers are missing. Have students draw or write the missing amounts on a post-it note and add to the number line that has been made

  • Variation 5: Provide students with two completed number puzzle cards and have them discuss and record what makes the numbers the same and what makes them different.

Collections

By providing experiences where students make and count collections we are building their understanding of how numbers work which supports the development of their part-part-whole knowledge. Early experiences with comparing and ordering allow students to develop a sense of relative quantity, showing the important link between measurement and counting for the development of the language of comparison. For example, we can check that we both have ten by placing our towers side by side.

Task 5: Building towers

Students watch the ‘Building towers video’ to learn how to play

  • Variation 1: Build the towers and play in reverse. Taking away blocks each time until there are no blocks left.

  • Variation 2: Change the number of towers you build.

  • Variation 3: Change the number of blocks needed for each tower.

Combining quantities

Knowing numbers that nest inside other numbers (using part-part-whole knowledge) is helpful when solving problems

Task 6: Dotty 6

Students watch the ‘Dotty 6’ video to learn how to play

  • Variation 1: show students a video without audio of the game being played. Can they work out the rules?

  • Variation 2: Change the total. So instead of Dotty 6, make it Dotty 12 or Dotty 21, for example

  • Variation 3: Change the number cards you use. So instead of numbers 1 - 6, you could make cards from 1 - 10, or only use odd numbers, for example

  • Variation 4: Change the grid from 3 x 3 to 4 x 4

Exploring ‘teen’ and ‘ty

In order to explore the difference between ‘teen’ and ‘ty’ numbers we need to explore these quantities side by side considering what is the same and what is different. Looking at collections of 14 and 40 using bundles of ten we can connect them to the numeral and number word, supporting students to see how the value of the digit ‘4’ represents different quantities in 14 compared to 40, for example. Comparing 14, 40 and 41 is also valuable.

Task 7: Go fish - teen/ty

Student play a teen/ty version of ‘go fish’ using “teen” and “ty” cards .

Download part 1 of the number knowledge series

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