Math Mates Group 1

1. Math Mates Group 1 Week 3 Contribution Place value and Numeration

2. Objective One Explain what place value is and why it is essential for developing number sense and numeracy skills. Place value is the value of a digit as determined by its position in a number, the location of a digit in a number or the name of the place (Education.com, Inc, 2011). The ability to understand place values is an important mathematics skill. More specifically, students should be able to identify place values in integers to the hundreds place to achieve this skill. For example, a student who sees the number 123 and can correctly identify that the 1 refers to the hundreds place, the 2 refers to the tens place, and the 3 refers to the ones place has succeeded in understanding place values. Students need to understand the concept of place value as it is essential for developing number sense and numeracy skills. Without an understanding for place value, students’ abilities in basic mathematical functions like addition, subtraction, multiplication and division may suffer. Students may incorrectly read and or write numbers in their numerical, written or symbol form. An insufficient or incorrect understanding of place value may also keep students from learning to round numbers, use scientific notation, regroup and rename numbers and read numbers off a calculator correctly (Reys, Lindquist, Lambdin & Smith, 2009). All of these mathematical tasks are link to students’ number sense, numeracy skills and understanding of place value.

3. Objective Two Give examples of common problems and misconceptions children have with place value and give examples of appropriate activities to support children’s ‘correct’ learning. Common problems and misconceptions children have with place value vary from child to child. Some students have difficulty placing the value of digits in numbers like 11, 12 and 13 (Booker, Bond, Sparrow & Swan, 2010). Transposing digits in the number eleven is not evident as the same number is in each place, but some children do not understand the concept of why each 1 is where it is. Twelve presents difficulties as its spoken form does not resemble the symbols assigned to each digit. Thirteen, and other teen numbers, present problems to some students as they are read differently than other numbers. If teen numbers follow the predictable place value patterns of numbers 20-99, then they would be read ‘onety-three, onety-four, onety-five’ and so on. This deviation from the norm confuses some children and makes it harder for them to retain knowledge of the place value of teen numbers. Appropriate activities to support children’s ‘correct’ learning of place value for teen numbers are suggested by Booker, Bond, Sparrow and Swan (2010) and Reys, Lindquist, Lambdin & Smith (2009). Booker, et. al (2010), suggest for children having difficulty with teen number place values, games like ‘Concentration’ or ‘Fish’ – using cards with numbers that students have problems or misconceptions with. An entire game, of both suggested, can be held with only teen numbered cards to concentrate on problem areas. Reys, et. al (2009) highly recommends activities using calculators – this will establish the order of digits in teen numbers in another fashion for students having difficulties. “Seeing each value displayed on the calculator helps students develop important insight into what digits are changing and when” (Reys, et. al, 2009, p. 172).

4. Objective Three: Explain patterns and relationships in the place value system. Place value provides an organised structure for counting (Reys et al., 2009, p.161) Children recognise when counting by 10’s to one hundred, then 100’s to 1000, that each takes the same amount of turns. It is important for children to recognise and understand this as it will lead to a better understanding of place value (Reys et al., 2009, p.172) Children recognise when counting by 10’s to one hundred, then 100’s to 1000, that each takes the same amount of turns. It is important for children to recognise and understand this as it will lead to a better understanding of place value (Reys et al., 2009, p.172). Patterns underline many of the thinking strategies needed to learn basic facts and bring them to the point of automatic responses. (Booker, et al., 2010, p. 19) Counting backwards provides students with a new perspective on the patterns in place value. They learn to recognise that place value patterns form in positive and negative integers (Reys et al., 2009, p.173). Children recognise when counting by 10’s to one hundred, then 100’s to 1000, that each takes the same amount of turns. It is important for children to recognise and understand this as it will lead to a better understanding of place value (Reys et al., 2009, p.172). (Place value Rods [image] (n.d.)) Students who are given the opportunity to count in larger numbers will be able to recognise when counting by 100’s that after 10 counts the 1000 unit will change. Students need to recognise this pattern in order to develop place value properties sense (Reys et al., 2009, p.173). Number patterns allow the extension of the place value ideas readily shown with materials to provide a means of recording large numbers, decimal fractions, small numbers and infinite numbers (Booker, et al., 2010, p.18) Children recognise when counting by 10’s to one hundred, then 100’s to 1000, that each takes the same amount of turns. It is important for children to recognise and understand this as it will lead to a better understanding of place value (Reys et al., 2009, p.172).

5. Objective Four: Give examples of learning activities to develop ‘trading’ or ‘renaming’ concepts and skills and explain why these understandings are essential for children’s number learning Once students understand numbers and the place system they are able to increase number value to move places. They start with ones or whole numbers and move through ten, hundreds, thousands and further. Working with concrete models gives students a clearer picture of when numbers become larger and the patterns that occur. They are able to see that 10 objects form a new unit. That is 10 ones = 1 ten. This happens in our base 10 system. When we have ten of a particular place we start using the next place value. Regrouping happens whenever bridging occurs. Good understanding develops when children experience bridging with physical models and practice trading and regrouping 1 Hundreds 4 Tens = 143 3 Ones 1 Hundreds 0 Tens = 143 43 Ones 0 Hundreds 14 Tens = 143 3 Ones In this example we have 143 icy pole sticks. It can be shown in the three ways as pictured, all equal to the same value.

6. Objective Six

7. Objective SevenIdentify important principles for teaching place value ideas. • Students need to understand the mathematical conventions, algorithms and concepts concerning place value to learn it effectively (Garlikov, 2000). • Base of tens – having students grouping items into tens forms the basis of understanding for place value (Reys et al., 2009). • Students need to first be able to use and understand proportional models for representing place value, such as base-ten blocks or bean sticks before then being introduced to non-proportional models, such as currency (Reys et al., 2009). Exposure to both proportional and non-proportional models is essential. • Children need to learn that the same numbers written in a different order represent different numbers (Reys et al., 2009). • Having students recognising patterns, such as those found on hundreds charts, or skip counting using a calculator, can help develop number sense with regards to place value (Reys et al., 2009). • Trading is an important principle in place value ideas. Students will need to understand regrouping numbers and bridging the decades. The use of models can provide experiences for conceptual understanding, later developed to more abstract representations (Reys et al., 2009).

8. Objective EightOutline important learning in place value for children to develop.

9. Reference List Booker, G., Bond, D., Sparrow, L., and Swan, P. (2010). Teaching Primary Mathematics. (4th Edition). French Forest: Pearson Australia. Department of Education and Early Childhood Development, (2011). Retrieved from: http://www.education.vic.gov.au/ Education.com, Inc. (2011). Place Value | Definition. Retrieved from http://www.education.com/definition/place-value/ Garlikov, R. (2000). The concept and teaching of place value. Retrieved from http://www.garlikov.com/PlaceValue.html Place Value Rods [Image]. (n.d.) Retrieved from www.learningresources.com/product/teachers/shop+by+category/manipulatives/math/base+ten+-+place+value/place+value+rods+activity+set.do Reys, R. E., Lindquist, M. M., Lambdin, D. V., and Smith, N. L. (2009). Helping Children Learn Mathematics. (9th Edition). Hoboken, New Jersey: John Wiley & Sons, Inc.