Number and Place Value

Year Level: 1

Title of experience or the focus question: Skip-Counting by twos

Outcomes

Australian Curriculum Content Descriptor

At the completion of this lesson, students will be able to skip count by twos to 100 [ACMNA012] (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2019b)

Achievement Standard

By the end of Year 1 students:

  • Describe number sequences resulting from skip counting by twos.
  • Carry out simple additions and subtractions using counting strategies.
  • Continue simple patterns involving numbers and objects.

(ACARA, 2019a)

Objectives

  • Do
  • Use a skip-counting strategy to count to twenty by twos (using manipulatives for support if required).

Produce

  • Students will use skip-counting strategies to fill in a hundreds chart.
  • Students will use skip-counting strategies to highlight multiples of two on a hundred chart
  • Say
  • Students will be able to identify if counting a set of items by one or two is faster.
  • Hook

Time allocation

4 minutes Introduce and play The Counting by Twos Song by Scratch Garden (2014) on Youtube on smartboard/whiteboard/projector.

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Introduction

Time allocation

10 minutes Display and sing the skip-counting song by Splash Math (n.d.-a) on the smartboard:

“Skip counting can be so much fun,

Jump the same number from the previous one.

A pattern you will see, when you are done!”

“Today we will ·’

be learning to skip-count. Skip counting means counting forwards and backward by a number bigger than one (Voutsina, 2016).

We will be skip-counting by two.

To skip-count by two, we need to keep adding the number two to our previous number over and over.

Skip-counting lets us see patterns in our numbers and count things faster (Asia Education Foundation, n.

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d.).

Explicit Modelling

Display the bottom half of the cover of the picture book Let’s Count to 100! (Sebe, 2014) on the smartboard and ask a student to volunteer to count the number of animals (see Appendix 1).

Provide the student with a pointer so they can point to the animal as they count.

NOTE: ideally student counts each animal individually.

Once the student has completed counting, ask the class if they know a faster way to count things than by ones?

NOTE: ideally students should suggest counting by twos if not, teacher to suggest.

Introduce the concept of counting animals by twos firstly as a group by counting aloud by ones, alternating saying the odd numbers quietly and the even numbers loudly, for example, One (softly), two (loudly), three (softly), four (loudly) (Fernandez, 2008).

Provide students with a print out of this image. Recount the images as a group, this time only counting two images at a time (that is, cross of/circle two animals at a time, counting out loud and only saying the even numbers).

This step will require explicit instruction/modelling and may need to be repeated several times until students are able to skip-count by twos the images on the page.

Lesson sequence

Time allocation

47 minutes

Shared Demonstration

Display a hundreds chart on the smartboard that only has the odd numbers filled out (Appendix 2).

Provide students with manipulatives (what is available e.g.: blocks, unit cubes, counters, snap cubes).

Explain to students, using the manipulatives provided and the strategy that was just used (introduction step 4), as a group they are going to fill in the missing squares.

Advise each student to take two pieces of the same coloured manipulatives and place in front of them, saying the number of manipulative aloud as doing so (i.e.: ‘two’) – as students do so, the teacher will fill out the missing number from the hundreds chart (i.e.: two).

Advise students to take two more manipulatives (of a different colour), place them with their original two pieces and say the total number of manipulatives aloud (i.e.: ‘four’), as they do so, record this number in the hundreds chart on the smartboard (i.e.: four).

Ask students “what number might be next?” (adapted from Tuttle, 2008, p. 26) to ascertain if any students have identified a pattern or are able to skip-count without the manipulatives.

Continue with this pattern until the number twenty is reached

NOTE: students should be encouraged to use different coloured manipulatives each time so that if they lose their place they can count by ones to identify the number they are up to, whilst still being able to identify the skip-counting pattern visually through colour groupings.

Guided Practice

Once the class has reached the number twenty on the hundreds chart, as a group, have students skip-count by two out loud (that is, say the number two through twenty but not write it down).

NOTE: encourage students to do so without the use of manipulatives, however, note that some students may require continued scaffolded practice with manipulatives before being able to skip-count (Ashman, 2019).

Independent Practice

Provide students with a worksheet with a hundreds chart that is missing the even numbers (Appendix 1).

Have students work independently to fill in their own hundreds charts, skip-counting by twos.

NOTE: ensure the group completed hundreds chart is removed from the smartboard so that students are encouraged to use skip-counting strategies rather than copying.

Engagement | Expression | Representation (Ashman, 2019).

Provide some students a hundreds chart that is completely filled (Appendix 3) in and have them circle each multiple of two (instead of having to both skip-count and write the numeral, students will only have to concentrate on skip-counting) [Expression].

Walk around the room, assisting students who require greater explicit instruction – perhaps gather these students together in a group and work through the chart together modelling skip-counting strategy with manipulatives [Engagement].

Pair students up in instances where their knowledge can be further scaffolded by a more experienced peer [Engagement].

Some students may be unable to complete this activity and may require further practice with manipulatives/and or alternate methods of grouping items by two, these students can engage with online activities that reinforce counting by twos [Engagement]:

Splash Math (n.d.-b)- Skip Count by 2’s using Sequences, Objects and Number Charts.

The activity asks ‘which number follows’, but provides options with which students can choose form.

Maths is Fun (2018) – Skip Count by 2:

Simultaneously counts by one and by two, allowing students to see which method counts a set of marbles quicker.

Counts twenty marbles in groups of two, similar to them manually doing it with manipulatives.

If required, students may understand skip-counting better through the visual representation of introduced through a number line [Representation].

Introduce the number line method of skip-counting to these students.

Process, Content, Product Modifications for Enrichment (Maker, as cited in Ashman, 2019)

Students can attempt to skip-count backward from twenty in their maths books [Content Modifications].

For students who have finished, have them find a peer who has finished and ask them to compare their charts [Process and Product Modifications].

In these pairs, provide students with several copies of the hundreds chart and have one partner count how long it takes for the other to complete (ensure their previous charts are taken away so that they do not simply copy their answers) [Process and Product Modifications].

Have students use skip-counting to attempt to fill in the hundreds chart up to forty (and continue up to 100 as required) [Content Modifications].

Online Activities [Content and Process Modifications]:

Scootle (Education Services Australia, 2013) – Number Trains.

Students make a train out of carriages which skip-count by two, students must select which carriage to put next to each other.

ABCya (2019) Number Bubble – Skip Counting.

Students must drop the number bubble in the correct chest: the chests go up by twos and the correct number bubble must be popped over the correct chest.

Maths is Fun (2016) Skip Counting by 2s to 20 – Fill in the missing number (Appendix 5).

Several numbers are missing from the number line, students must accurately select which multiple of two belongs in each box.

Conclusion

Time allocation

9 minutes

Conclusion

Bring students back together and stand in a circle.

Starting at zero, have students skip-count until they go all the way around the circle.

NOTE: May need to divide the class into two smaller groups so that they are not required to go too far above twenty.

Challenge students to see if they can skip-count by two backward from twenty or go beyond twenty.

(Adapted from Mr. Elementary Math, 2019).

Play the Youtube video Count by 2 | Dancing 2’s | Skip Counting by 2 |Count to 100 | Educational Songs | Jack Hartmann (Jack Hartmann Kids Music Channel, 2015) to reinforce learning from the lesson.

Questioning for understanding (Tuttle, 2008), ask students:

Ask for two student volunteers: one student is to count the number of students in the room going up by one (as they did with the animals at the beginning of the lesson), whilst the teacher times them. The second student will count the students – this time using the skip-counting by two strategy – whilst the teacher times them.

Ask students who do they think will count faster?

Once completed, advise students which method was faster, and ask students why they think this method was faster?

Knowing which method of counting is quicker (assuming it was skip-counting), ask students:

Why do they think counting by twos is quicker? (link back to the discussion from the beginning of the lesson).

If they know of any other times in which counting by two’s would be helpful? (Provide examples if necessary e.g.: when lining up to go back into class, counting slices of a pizza, when counting how many people on a sports team, when counting how many of a particular coin they have) and why would counting quicker be better at these times?

Resources

  1. YouTube access (Scratch Garden, 2017; Jack Hartmann Kids Music Channel, 2015)
  2. 30 printed copies of Let’s Count to 100! (Sebe, 2014) image (Appendix 1)

Computer/Tablet access:

Number Trains (Education Services Australia, 2013)

Skip Count by 2’s using Sequences, Objects and Number Charts (Splash Math, n.d.-b)

Skip Count by 2 (Maths is Fun, 2018)

  • Number Bubble – Skip Counting (ABCya, 2019)
  • Skip Counting by 2s to 20 (Maths is Fun, 2016)
  • Soft copy of incomplete hundreds chart
  • 60 printed copies of the incomplete hundreds chart
  • 20 printed copies of the completed hundreds chart
  • Mathematics manipulatives (preferably multi-coloured counters or snap cubes)

Target questions

Can students recognise, represent, and continue the pattern of skip-counting by two? That is, counting by twos will always give you an even number (Remote Schools Curriculum & Assessment Materials, 2009).

Will students identify the visual pattern created on a hundreds chart when skip-counting by two? That is, skip-counting by twos gives you every second number (Russo, 2016).

Will students use manipulatives as a strategy to test and confirm their sequencing of numbers?

Do students understand why skip-counting is quicker?

  • Key language
  • Skip-counting
  • Pattern
  • Count
  • Hundreds Chart
  • Two
  • Add
  • Over and Over
  • Forwards
  • Backward

Strategies for assessment and evidence collected

Introduction Activity & Explicit Instruction

Assessment will involve observations of students as they count aloud and interact with manipulatives.

Guided Practice

Make anecdotal notes for student records (adapted from Tuttle, 2008, p. 34) [Appendix 6] and Individual Education Plan (for a student with Autism Spectrum Disorder).

Independent Practice

  • Collect student work samples (completed hundreds chart).
  • Observe students as they work.
  • Question students about their thinking and feelings about sip-counting whilst walking around.

Expression | Engagement | Representation

Monitor what students in pairs/small groups are saying (allow students to talk amongst each other to determine if they understand or correct if their understanding is incorrect).

Observe students who are working in pairs and/or at the online activities, and record these observations – these are to be reviewed in alignment with continuum to determine where students are at and whether further scaffolding could work or if a greater response to instruction is required (Ashman, 2019).

Make anecdotal notes for student records (Appendix 6) and/or Individual Education Plan.

Enrichment

Collect student work samples of attempts to:

  • Skip-count backward from twenty.
  • Skip-count to forty.
  • Skip-count to a hundred.

Observe students skip-counting backward and make anecdotal notes relevant to whether students can easily adapt skip-counting strategies.

Observe students engaging in online activities and question them about the activities and whether they think it is harder to skip-count when not using manipulatives and why – record these observations.

Assessment indicators Year One Mathematics – Australian Curriculum: Number and Algebra – Number and Place Value

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 (ACARA, 2019b)

Achievement Standard – By the end of Year 1, students describe number sequences resulting from skip-counting by 2s, 5s and 10s (ACARA, 2019a)

What this looks like

Students will be able ounting by twos is faster than counting by one because:

  • It allows you to count more at once
  • You are counting two at once which is twice as fast as counting one by one (or a variation of this)

References

  1. ABCya. (2019). Number Bubble – Skip Counting [Computer Game]. Retrieved from
  2. Ashman, A. F. (Eds.). (2019). Education for inclusion and diversity (6th Edition). Melbourne, Victoria: Pearson Australia
  3. Asia Education Foundation. (n.d.). Mathematics: Counting Games. Retrieved from
  4. Australian Curriculum, Assessment and Reporting Authority (ACARA). (2019a). Mathematics Year One Achievement Standard. Retrieved from
  5. Australian Curriculum, Assessment and Reporting Authority (ACARA). (2019b). Mathematics Year One (ACMNA012). Retrieved from
  6. Education Services Australia Ltd. (2013). Number Trains [Computer Game]. Retrieved from
  7. Fernandez, E. (2008). Taking Advantage of Everyday Activities to Practice math every day. Teaching Children Mathematics, 15(3), 174-177.
  8. Jack Hartmann Kids Music Channel. (2015). Count by 2 | Dancing 2’s | Skip Counting by 2 | Count to 100 | Educational Songs | Jack Hartman [Video file]. Retrieved from
  9. Maths is Fun. (2016). Skip Counting by 2s to 20 [Computer Game]. Retrieved from
  10. Maths is Fun. (2018). Skip Counting. Retrieved from
  11. Mr. Elementary Math. (2019). 6 Strategies for teaching skip counting. Retrieved from
  12. Remote Schools Curriculum & Assessment Materials (RSCAM). (2009). Foundation programs: Mathematics – Number and algebra – patterns and functions. Retrieved from
  13. Russo, J. (2016). Skip-counting battle. Teaching Children Mathematics, 22(8), 512.
  14. Sebe, M. (2014). Let’s Count to 100! Toronto, Canada: Kids Can Press
  15. Scratch Garden. (2014, October 7). The Counting by Twos Song | Counting Songs | Scratch Garden [Video file]. Retrieved from
  16. Splash Math. (n.d.-a). Skip Count – Definition with Examples. Retrieved from
  17. Splash Math. (n.d.-b). Skip Count by 2’s using Sequences, Objects and Number Charts – 2nd Grade Math. Retrieved from
  18. Tuttle, H. G. (2008). Formative assessment: responding to your students. Retrieved from
  19. Voutsina, C. (2016). Oral counting sequences: a theoretical discussion and analysis through the lens of representational redescription. Educational Studies in Mathematics, 93(2), 175-193.

Appendix 1

Let’s Count to 100! (Sebe, 2014)

Appendix 2

HUNDREDS CHART

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

Appendix 3

HUNDREDS CHART

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Cite this page

Number and Place Value. (2019, Dec 02). Retrieved from http://studymoose.com/number-and-place-value-essay

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