Theory |
Common Student Misconceptions |
Place-value is based on the Hindu-Arabic system that has a base of ten. The placement of the digit in a number determines its value including zero which is used as a placeholder.
Place-value is based on the understanding that ten is equivalent to a group of ten ones, a hundred is a group of ten tens, and a thousand is a group of ten hundreds and it continues upwards. Understanding this concept and the base-ten language will assist with mental computation. It is important that counting by one is achieved in order to move on to base-ten (Van de Walle, Karp, & Bay-Williams, 2014). It is important to provide multiple concrete representations when teaching place-value. Place-value can be modelled with grouped objects such as sticks and ungrouped objects such as MAB blocks. MAB blocks are also considered a proportional modelling tool as the ten is the same size as ten ones. An example of an unproportional tool is money. Notes and coins are not in proportion to there value. When working with two-digit number names start by using the "base-ten language" (Van de Walle et al., 2014, p. 212) of tens and ones then move on to numerals. Practicing grouping and renaming numbers or composing and decomposing is important to learning. Composing requires students to bridge to the next 10 or 100. Students can also decompose a number by grouping with “fewer than the maximum number of tens” (Van de Walle et al., 2014). Use of a hundreds chart will assist students to visualise patterns in numbers. The ability to to visualise patterns in numbers helps students with partitioning numbers for mental computation (Van de Walle et al., 2014). |
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Mathematics Language for Place-value Concepts
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Early years
Base of ten Caterpillars Students make collections of ten. The Early Years Learning Frameworks (EYLF) key numeracy concept (Outcome 5, p. 6) that is met is: student has the ability to count and order numbers; recognise and write numerals; and compare quantities such as 'more than' and 'less than'. Objective: Students develop foundational knowledge of base-ten. (Adapted from Bleakley, 2012)
Year 3 Find the... Students will use their knowledge of numbers and place value to manipulate digit cards to create numbers that meet a specific criteria. ACMNA052 Recognise, model, represent and order numbers to at least 10 000 Objective: For students to understand how place value affects the value of a number up to 10 000. (Adapted from Kawas, n.d.)
Year 4 Partitioning for place-value Students will use their knowledge of place-value to represent specified numbers on a place-value mat, along with representing number through numerical and word forms. ACMNA073 Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems Objective: students to partition numbers up to at least tens of thousand and reproduce in words, as well as numerical form. (Adapted from Pearson Australia, n.d.)
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Eva has 40 pencils and Danny has 23 pencils. How many pencils do they have altogether?
Year 2 and 3 students are visiting the zoo. Year 2 has 30 students and Year 3 has 32 students. How many students altogether will visit the zoo? |
Resources
Curriculum Map
The key numeracy concepts for place-value is located under Outcome 5, page 6 of the Early Years Learning Framework (EYLF). Student will display their ability to count and order numbers, recognise and write numerals, and compare quantities such as ‘more than’ and ‘less than’.
(Charles Sturt Universtity Early Years Learning Framework Consortium, 2009)
Place-value is aligned with the Australian Curriculum from Foundation through to Year 4.
FOUNDATION
YEAR 1
YEAR 2
YEAR 3
YEAR 4
(Charles Sturt Universtity Early Years Learning Framework Consortium, 2009)
Place-value is aligned with the Australian Curriculum from Foundation through to Year 4.
FOUNDATION
- Students should develop understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point. (ACMNA001)
- Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
- Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
YEAR 1
- 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 (ACMNA012)
- Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
- Count collections to 100 by partitioning numbers using place value (ACMNA014)
YEAR 2
- Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026)
- Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
- Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
YEAR 3
- Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
- Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)
YEAR 4
- Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
- Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
References
Bleakley, T. (2012). The very hungry caterpillar: Two pre-school lesson plans. Retrieved from
http://www.brighthubeducation.com/preschool-lesson-plans/37032-the-very-hungry-caterpillar-two-lesson-plan-ideas/
Charles Sturt Universtity Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective
communicators. Retrieved from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?
layout=3#page=3
Kawas, T. (n.d.) More place value activities. Retrieved from http://mathwire.com/numbersense/morepv.html
Lawton, F. & Hansen, A. (2011). Numbers and the number system. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 20-
46). Exeter, England: Learning Matters.
Pearson Australia. (n.d.). Reading and writing thousands. Retrieved from http://pearson.com.au/media/570883/envisionmaths_4ab.pdf
Van De Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
http://www.brighthubeducation.com/preschool-lesson-plans/37032-the-very-hungry-caterpillar-two-lesson-plan-ideas/
Charles Sturt Universtity Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective
communicators. Retrieved from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?
layout=3#page=3
Kawas, T. (n.d.) More place value activities. Retrieved from http://mathwire.com/numbersense/morepv.html
Lawton, F. & Hansen, A. (2011). Numbers and the number system. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 20-
46). Exeter, England: Learning Matters.
Pearson Australia. (n.d.). Reading and writing thousands. Retrieved from http://pearson.com.au/media/570883/envisionmaths_4ab.pdf
Van De Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.