Numeracy in the 3/4 Neighbourhood

Mathematics Investigation

The mathematics investigation has been based on the question ”What mathematics do you use in your life”  and “How is the mathematics used in our lives” In looking at this the children have focused mostly on measurement, money and the symbols in mathematics. Some conceptual knowledge is present however interest in the number system itself has been a conspicuous absence in the neighbourhoods. We want to build student understanding of the base ten system, its connections to everyday life and the mathematical concepts that they have explored. We need to do this because children haven’t had the number system explained to them so that they have a clear connection to why place value is so important. This understanding will likely move children from a position of knowing how to ‘do’ to a position of understanding why. We want to communicate to the children what an amazing invention the number system is and how connected it is to societal needs. It is with this where the link to the inquiry can be developed. The inquiry question of looking at the conditions and motivations for change link in to examining the different number systems and the reasons for the variations based on the needs of the people using them.

We will be completing our initial Investigation this week and moving on to a new question. We would like students to begin thinking about our number system by investigating our base‐10 number system and how we use it. Children will begin an investigation where they explain through a presentation, how we use the base‐10 number system. They can do this by writing an instruction manual, a documentary, a presentation or another expression that they can negotiate with their teachers.

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During the week the children have been introduced to the concept behind the base‐10 system.

Teachers have explained the meaning of the term “number system” We use a number system to describe a number. Every number system has a base. The base tells you how many symbols you use in the system. In Australia, we mostly use the base-­‐10 system. The base‐10 system uses 10 symbols or digits. The digits we use for the base‐10 system are 0,1,2,3,4,5,6,7,8,9. We use these to describe every number.

Using just one of these digits will describe any number from 0-­‐9. If we want to describe a number more than 9, then we have to position the digit in the right place. We sometimes call this PLACE‐VALUE because the place the digit is in describes the value (or the amount).

Before number systems, we recorded numbers through tallies. A shepherd would count his sheep by cutting a notch on his stick for each sheep. He would know how many sheep he has got by the amount of notches he has on his stick. The problem is, he has to count it to check.

A prisoner would scratch a line for every day he spends in his cell. This is fine for small numbers like five or ten. But it is useless when we want to describe big numbers like a hundred or a million. The great thing about the base‐10 place value system is that you can describe a really big number like one hundred with just three symbols (or digits).  A one and two 0s. They are placed in columns that describe their value. 100 has 1 in the hundreds column, none in the tens column and none in the units (or the ones) column. Even a bigger number like nine hundred and ninety-­‐nine still only use three symbols (three 9s). 9 in the hundreds column because there are nine one hundreds. 9 in the tens column because there are nine tens, and 9 in the ones column because there are nine ones. Imagine what the shepherd’s stick would look like if he wanted to describe nine hundred and ninety‐nine with notches! It’s much easier to show nine hundred and ninety‐nine with three symbols. The order and position is very important. To describe two different numbers like nineteen and ninety‐one, you would use the same two symbols 1 and 9. Depending on how we position the two symbols, we describe a different value (or amount). There is a huge difference between 19 and 91. It would be very annoying if you have to pay $91 for something that should cost $19 and so the way we position the digits is very important!

Targeted number learning

As students begin to further investigate the base-10 number system, some students will look into how we describe numbers smaller than 1 through the use of decimal fractions and numbers that are ‘between’ whole numbers. They will begin by visualising what tenths are through use of materials and then consolidate this understanding through ordering of decimal fraction numbers.