Decimals Misconceptions
Decimals – Misconceptions and Strategies
Section 1
Decimals are a part of our everyday life in some way, when we put fuel in our cars to buying meat from the butcher. Mastering this critical mathematical concept is a necessity (Stephanie Welch, 2010). A decimal is a proper fraction, which is a number less than 1. It is a part of a whole number.
Since our numbering system is based on the powers of 10, it is called a decimal system. Decem in Latin means ten (The Maths Page, 2012, Lesson 3). Decimal fractions are represented as the numbers found between two whole numbers. The decimal fraction shows part of a whole number and is written after the decimal place.
Some key understandings in learning about decimals would be-
* …show more content…
A major misconception students have with decimals is the idea that the decimal place separates two different whole numbers. This is demonstrated when students read 29.15 as, “twenty-nine decimal fifteen”. This misconception is compounded by the fact that the first experience of decimals for most students is working with money. Instead of seeing $28.35 as twenty-eight dollars and thirty-five hundredths of a dollar, students are taught that all the numbers to the left of the decimal point represent dollars and everything to the right represents cents. This leads to further difficulties because with money we only ever use 2 decimals places to the right to represent the hundredths of a dollar. When confronted with three decimal places ie. $5.362 students will read this as $5 and 362 cents instead of 362 thousandths of a dollar.
Another misunderstanding is that the number’s length determines its greatness. With whole numbers, the longer the number the bigger its value (247 397 is larger than 45 673). We determine this by assessing the value of the number systematically, beginning with the left hand place column. When comparing decimal numbers, students commonly misunderstand that the longer the number the greater its value ie. When comparing 3.45 and 3.12345 students may rely on their whole number understanding …show more content…
This incorrectly suggests that the number contains 25 ones. | Use the extended place value chart to reinforce placement and value of each digit. | SWBAT order a mixed set of numbers with up to 3 decimal places | Numbers with more digits are larger. | Refer to place value charts to prompt students to always order numbers reading the value from the far left hand column first. | SWBAT plot a number on a number line demonstrating that to the left of the decimal we have ones, tens, hundreds and to the right is tenths, hundredths, thousandths. | The first place to the right of the decimal place is ‘oneths’ | Concrete materials demonstrating that whole number is shared into 10 parts (tenths) or into 100 parts (hundredths). | SWBAT work with money representing dollars and parts of a dollar (cents) after the decimal place. SWBAT calculate money up to 3 decimals places | The decimal place separates two different mediums.Students read $7.125 as $7 and 125 cents or $8.25 | Use play money kits with notes and coins and hundreds boards to allow students to manipulate and record money to two decimal places. Students also need exposure to financial maths problems where the answer contains more than two decimal places, and be guided to consider the reasonableness of the answer.
Section 1
Decimals are a part of our everyday life in some way, when we put fuel in our cars to buying meat from the butcher. Mastering this critical mathematical concept is a necessity (Stephanie Welch, 2010). A decimal is a proper fraction, which is a number less than 1. It is a part of a whole number.
Since our numbering system is based on the powers of 10, it is called a decimal system. Decem in Latin means ten (The Maths Page, 2012, Lesson 3). Decimal fractions are represented as the numbers found between two whole numbers. The decimal fraction shows part of a whole number and is written after the decimal place.
Some key understandings in learning about decimals would be-
* …show more content…
A major misconception students have with decimals is the idea that the decimal place separates two different whole numbers. This is demonstrated when students read 29.15 as, “twenty-nine decimal fifteen”. This misconception is compounded by the fact that the first experience of decimals for most students is working with money. Instead of seeing $28.35 as twenty-eight dollars and thirty-five hundredths of a dollar, students are taught that all the numbers to the left of the decimal point represent dollars and everything to the right represents cents. This leads to further difficulties because with money we only ever use 2 decimals places to the right to represent the hundredths of a dollar. When confronted with three decimal places ie. $5.362 students will read this as $5 and 362 cents instead of 362 thousandths of a dollar.
Another misunderstanding is that the number’s length determines its greatness. With whole numbers, the longer the number the bigger its value (247 397 is larger than 45 673). We determine this by assessing the value of the number systematically, beginning with the left hand place column. When comparing decimal numbers, students commonly misunderstand that the longer the number the greater its value ie. When comparing 3.45 and 3.12345 students may rely on their whole number understanding …show more content…
This incorrectly suggests that the number contains 25 ones. | Use the extended place value chart to reinforce placement and value of each digit. | SWBAT order a mixed set of numbers with up to 3 decimal places | Numbers with more digits are larger. | Refer to place value charts to prompt students to always order numbers reading the value from the far left hand column first. | SWBAT plot a number on a number line demonstrating that to the left of the decimal we have ones, tens, hundreds and to the right is tenths, hundredths, thousandths. | The first place to the right of the decimal place is ‘oneths’ | Concrete materials demonstrating that whole number is shared into 10 parts (tenths) or into 100 parts (hundredths). | SWBAT work with money representing dollars and parts of a dollar (cents) after the decimal place. SWBAT calculate money up to 3 decimals places | The decimal place separates two different mediums.Students read $7.125 as $7 and 125 cents or $8.25 | Use play money kits with notes and coins and hundreds boards to allow students to manipulate and record money to two decimal places. Students also need exposure to financial maths problems where the answer contains more than two decimal places, and be guided to consider the reasonableness of the answer.