Week 8: Numeration and Place Value

Big ideas

Place Value (PV) was further explored this week, with a large focus being put on the teaching sequence for PV concepts. PV for numbers above 9 is useful for many mathematical purposes, including helping us form a picture when we’re solving problems, and helping us use estimation. As a teacher, I need to ensure I am providing students with opportunities to picture large numbers in and outside the classroom, as it is just as important for older students in primary school to understand the concept of large numbers as it is for young learners to understand the concept of numbers less than 10.

Concept, Skill or Strategy

As we learnt in week 7, PV is actually made up of 8 concepts. This week, we learnt about a sequence of 8 steps to teach PV:


The first step is particularly important as there may be confusion around trading e.g. 10 ones for 1 ten. This week I found it really interesting when one of our own teachers reflected on her teaching of mathematics, when she once told a student “this is ten” while showing him a tens MAB to which he responded, “no it’s one” as he was telling her it is only one block of wood (Jamieson-Proctor, 2021). This is a misconception I had never thought about, and really highlights the importance of modelling place value in many different ways to form a picture in children’s minds. Reys et al. (2020) gives some examples of ways to bridge the understanding from ones to tens in the table below:

(Reys et al., 2020)

Misconception

Common misconceptions are often found surrounding certain 2-digit numbers, particularly in the ‘teens’ due to the lack of pattern in the numbers (11, 12, 13, 15), as well as numbers with internal zeros (Jamieson-proctor, 2021). Reys et al. (2020), suggests that for students having trouble with the teen numbers, it is recommended to skip to the twenty and thirty decades where the pattern is consistent with the larger numbers, and return to the teens at a later stage.

ACARA

Numeration is first seen in the Australian curriculum in year 1 (ACMNA013)

Strand: number and algebra/ patterns and algebra
Sub-strand: number and place value

(ACARA, 2021)

Scootle

This resource is the same game which was briefly explored in week 1. From level 3, the train carriages include written numbers, symbols, and MAB blocks to represent numbers, where students must sort them into numerical order. This makes it more suitable for older children, and those who are moving from the materials stage of the language model to the mathematics stage. 



(Education Services Australia, 2016)


Personally sourced

This short video can be used as an introduction or refresher in numbers 11-19. The teacher can pause the video when the character asks questions, to get responses from the children so they can show their current understanding. 


(Maths & Learning Videos 4 Kids, 2015)

References

ACARA. (2021). Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Education Services Australia (2016). Number trains. https://www.scootle.edu.au/ec/viewing/L2317/index.html

Jamieson-Proctor, R. (2021). Week 8 learning activities: Part 1a lecture. Australian Catholic University. https://vimeo.com/user36828324/review/200614369/0a699008ad

Maths & Learning Videos 4 Kids. (2015). Teenage numbers - ten and ones [Video]. https://www.youtube.com/watch?v=m1JOSkkpIPM&ab_channel=Math%26LearningVideos4KidsMath%26LearningVideos4Kids
 
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons.







Comments

Post a Comment

Popular posts from this blog

Week 1: What is Mathematics?

Image
Big Ideas Mathematics is a universal language that is not just used inside the classroom. It is used in facets of everyday life whether an individual is aware or not. When helping children to understand the language of mathematics, teachers can use the four levels of the mathematics language model, which allows them to assist children to go from a material, to a symbolic understanding of mathematics. Concept, Skill, or Strategy: The Language Model The framework of the language model is useful for educators as it can aid in the planning and implementation of mathematics activities, that help children progress through the four levels of the framework. It is important to us materials and language that match the developmental stage a child is up to, as they need to progress through each stage in order so they move through familiar and concrete material first, and then progress towards abstract materials (Jamieson-Proctor & Larkin,). This is because to completely understand a mathematic...
Read more

Week 11: Measurement

Image
Big ideas This week was all about the concept of measurement. Measurement is of important significance in our everyday lives, with Reys et a. (2020), identifying measurement as the concept from the primary mathematics curriculum that is used the most directly in students’ lives. We use measurement for areas such as time, temperature and money, and other real-life situations, like finding the number of tiles needed to cover a bathroom. The concept of any measurement is counting units. Teaching sequence for measurement: 1. Identify the concept and make sure students understand the attribute they are measuring e.g. area, length 2. Choose an appropriate unit of measurement for the attribute being measured 3. Measure object using chosen unit 4. Record the number of units Concept A focus on length: This concept, like any other measurement concept, needs to be taught using the 4-step teaching sequence mentioned above. An appropriate unit of measurement should be chosen based on the stage of t...
Read more

Week 7: Number and Place Value

Image
Big Ideas This week in lectures and tutorials, we covered a large array of content. We firstly looked at number sense, numeration and mental computation. Numeration and mental computation was linked back to our content from weeks 2-5, and we were reminded of the big 7 thinking strategies across addition, subtraction, multiplication and division.  We then moved on to place value, which I found to be a much larger concept than I expected. This week I learnt that there is not just the ‘ones, tens, hundreds, thousands’ or the base 10 system. I found it really interesting to learn about other bases such as base 5 and base 3, and to see them modelled for me, as I was only ever taught the base 10 system at school. As a teacher, I will need to ensure I emphasise the importance of place value to my students and incorporate it into every area of mathematics. This is because place value is “one of the cornerstones of our number system” and is part of all work with whole numbers, the metric sy...
Read more