Teaching numeration and place value, types of numbers:
The big ideas:
Extending on last weeks learning, we discussed how to create a teaching sequence for place value concepts, and how to include the language model within the teaching. We discussed the need for the number 0 within a place value system, and noted that the Roman system did not include 0. Something new I learnt is that the symmetry of the number system revolves around the ones.
The use of numeration or place value numbers >9 is to:
- help form a picture when solving problems
- help to calculate logical placement of digit
- help to estimate
- help to learn new number places
Pascals triangle
Student language
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Material Language
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Mathematical language
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Symbolic Language
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Language
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Ones, tens, places, how many, place holder
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Ones, tens, places, how many, place holder
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Place value, base
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Materials
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Familiar objects
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Sticks, MAB blocks, place value charts
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Sticks, MAB blocks, place value charts
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Non-word symbols
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Recording
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Drawings
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Drawings
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Write the words "place value, place holder"
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Write symbols
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Personal reflection:
Learning about exponents this week has been a good refresher for me, as this was a concept I struggled with in primary school.
Concept, skills and strategies:
Source: unknown
An exponent refers to the number of times a number is multiplied by itself. To teach this concept, I would rely on MAB blocks or counters to assist students in the visualisation. As stated by Reys et al. (2020) seeing the numbers visually as a quantity will emphasise the physical difference between two numbers.
A possible misconception:
A common misconception is students misinterpreting exponents in equations. The student may multiply or double the number instead of squaring to find the answer. Using the LMM I would return to the materials language stage and work with the student using MAB blocks to demonstrate visually.
ACARA:
Place value: Year one / Number and algebra / Number and place value / ACMNA014
Elaboration:
- Understand partitioning of numbers and the importance of grouping in tens
- Understanding two-digit numbers as comprised of tens and ones/units
Scootle resource: Scale matters: simple units http://www.scootle.edu.au/ec/viewing/L2002/index.html this interactive game allows students to explore number lines, and units of ones, tens and hundreds.
Resources:
The base 10 blocks app gives students hands-on practice using MAB blocks on a place value mat https://apps.apple.com/au/app/base-ten-blocks-math/id878351349
Source: base 10 blocks
Word Count: 299