Whole Numbers

Theoretical Background

Core Concepts/Skills/Strategies

Concept: A concept is 'the picture we form in our mind'. When looking at prenumber, the concept refers to knowing different attributes. Attributes are characteristics or properties of something. For example, an attribute of a teddy bear is that it is soft and wooly.

To teach the concept of attributes for prenumber work, in accordance with the language model, using children's language, teachers ask students to describe different attributes senses can have. For example, the teacher might ask students what a strawberry tastes like, or to describe the feel of the carpet they are sitting on. As this is prenumber work, in the lesson sequence this should be taught before skills are introduced.

Skill: Once students are able to identify different attributes from all senses it is now time to develop the skill. The skill related to whole numbers it to be able to group and identify different objects based on an attribute that they share with another. Using children's or student's language, the students are given a set of objects with three boxes to 'put' each object in. The boxes are labelled 'round, sour and long'. The students are told that some objects may fit in more then one box but they need to provide two objects for each box. Here are the objects the students are given.

Strategy- A strategy is being able to obtain an answer. Continuing with prenumber work, a strategy here is to demonstate the students can decide their own objects to fix in each box without having a visual representation in front of them like the previous activity. Students will be given a table to draw their own objects to fit in each box. They will be instructed to draw as many objects as they can. Their table will look like this.

Concept: As the topic whole numbers further develops, students learn about the concept of even and odd numbers. To help emphasise this concept, students are taught that odd numbers do not have a partner and even numbers end in a 0,2,4,6 or 8. They are told that every second number is an even number and shown this hundreds chat to reinforce this concept. The teacher explains that the different colours represent even and odd numbers to 100.

Skill: A skill involved in teaching odd and even numbers involves being able to sort numbers by attributes. To develop this skill, students will be given a random selection of 20 cards, with any numbers between 1 and 100. Individually, students will form two piles, one of odd numbers and one of even numbers. Students will be able to look at their book for assistance if needed. In accordance with the language model, the skill will shift from students language to symbolic language using 'odd' and 'even' and will hopefully transition to a later lesson with symbolic and materials language integrating other mathematical concepts.

Strategy: A strategy that involves odd and even numbers is the 'partner strategy'. This is where students are to decide if numbers will be odd or even. To demonstrate this strategy, students will be given a set of objects which are in pairs. If one is not in a pair it is an odd number. Here is a sample of two groups.

Concept: Another concept involving whole numbers is patterning. To introduce students to this concept using student's language, students will be shown an interactive example of a colour pattern on a white board. Starting with a simple pattern, for example, red, green, red, green, red, green. Students will then be shown other patterns such as, phone, tv, phone, tv. A number example, such as, 1,2,1,2,1,2 will then be shown. This will allow students to have a 'mental picture' of the concept of patterns.

Skill: A skill related to patterning is a student demonstrating that they are able to finish a pattern. Shifting to materials and symbolic language, students will be asked to complete a small set of patterns on a worksheet. This will demonstrate their understanding of the concept by applying the skill. Questions will look like this:

1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, _ , _, _.

1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, _, _, _.

Strategy: A strategy that demonstrates understanding of the concept of patterning can be for students to explain each pattern on the sheet. Questions that will be asked will include materials language and will say 'What is repeating?' and 'What comes next?'. After students can finish patterns and explain the repetition, a following lesson could involve students making their own patterns with different objects, numbers or colours.

Teaching and Learning Resources

1. Click here to view video

This first resource is a clip from the Khan Academy Website. Although not appropriate to intoduce this topic, this video relates to the concept of place value and is used to reinforce the skills and strategies associated with whole numbers and in specific, place value. This clip is a very effective tool to use in the classroom because it not only uses ICT to integrate learning but it is also demonstrates appropriate language from the language model for mathematics. It deconstructs the question stage at a time which makes it very effective to reinforce the process involved. This clip would be most appropriate to be used in the year 3 and 4 classrooms to reinforce the skills and strategies associated with place value. To improve this resource I would add extra music and graphics to help maintain student's attention throughout the clip.

2. Number Card Game

This number game is called the 'Who Am I?' card game. This is used to reinforce and help familiarise students with the the five counting principles. These cards could be used in many different ways through many year groups but for the purpose of this unit, as previously stated, they are a great way to reinforce the skills and strategies associated with counting for prep to year one.

Each student is to be given a card and everyone is to stand up. There will be more then one student with each number. In accordance with the language model, the teacher will give clues as to which number he/she is looking for, such as, 'I am an even number', 'I am less then five' and 'I am one less then 3'. The first student to identify that they are the number is the 'winner'. These questions could become much more complex when used in the higher grades with more use of symbolic and material language. To improve this learning experience incorporation of other resources could also be used in addition to these card. This could include use of an Interactive Whiteboard to write the clues, which could also teach symbolic language over time.

3. The BIG Red Counting Box

The BIG Red Counting Box is a fun resource aimed at reinforcing the skills and strategies associated with counting and showing that students can understand that each number represents an object or value. This resource is most effective to be used in the Prep or year one classroom as students are able to demonstrate the 5 counting principles. To use this resource a 'mystery' number of objects will be put into the box. A student that has a time limit of 15 seconds to feel around the box and decide how many objects there are. If the student is correct they get a red dot on their sheets. This competition could run over a week or a month and the student or students with the most can win a mystery prize.

In accordance to the language model, students will be asked to 'count the objects in the box' and will be asked to give a verbal representation of the number present. Students will be asked to count out loud so the teacher is able to hear their counting and assist if necessary. This resource could improve if there were two boxes and students were asked to 'put together' the amounts or could also emphasise the counting on strategy.

Lesson Plan Year 1- Place Value

Reference List

Bancerek, Grzegorz. (2003) Journal of Formalized Mathematics: Cardinal Numbers: Warsaw: Warsaw University

Jamieson-Proctor, R. (2011). EDX 1280: Wk5. ppt. Retrieved from              
http://usqstudydesk.usq.edu.au/mod/resource/view.php?id=405689

Jamieson-Proctor, R. (2011). EDX 1280: Wk6. ppt  Retrieved from             
http://usqstudydesk.usq.edu.au/mod/resource/view.php?id=405689

Karp K, Bay-Williams J & Van De Walle J. (2010) Elementary & Middle School Mathematics 7th ed. USA: Pearson Education

Lovell K. (1971) The Growth of Understanding in Mathematics: Kindergarten through grade three. New York: Holt, Rinehart and Winston

Nunes, T., & Bryant. P. (2007). Key Understandings in Mathematics Learning: Paper 2: Understanding   Whole Numbers. (Review commissioned by the Nuffield Foundation).  Retrieved from:    http://89.28.209.149/fileLibrary/pdf/P2.pdf