Fractions
Fractions have always presented a challenge for students, even those that are going into middle level courses. Typically, fraction knowledge develops in the third grade, and emphasizes unit fractions (fractions with a numerator of one). Concepts associated with fractions are typically covered between grades 3-7, focusing on topics such as equivalence, operations, and proportional reasoning. Here are some big ideas to consider upon fractional teaching:
1. For students who really understand fractions, they must experience fractions across many constructs, including part of a whole, ratios, and division.
2. Three categories of models exist for working with fractions-area (like 1/3 of a garden), length (like 3/4 of an inch), and set or quantity (like 1/2 of the class).
3. Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerators and denominators.
4. Students need many experiences estimating with fractions.
5. Understanding equivalent fractions is critical. Two equivalent fractions are two ways of describing the same amount by using different-sized fractional parts.
1. For students who really understand fractions, they must experience fractions across many constructs, including part of a whole, ratios, and division.
2. Three categories of models exist for working with fractions-area (like 1/3 of a garden), length (like 3/4 of an inch), and set or quantity (like 1/2 of the class).
3. Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerators and denominators.
4. Students need many experiences estimating with fractions.
5. Understanding equivalent fractions is critical. Two equivalent fractions are two ways of describing the same amount by using different-sized fractional parts.
Decimals & Percents
Decimals and Percents are used in many individuals everyday lifestyle. For example, we use them for metric measures, calculating distances, interpreting output on a calculator, or understanding sports statistics such as those at the Olympics, where winners and losers are separated by hundredths of a second. Decimals are used for nurses, pharmacists, and workers building airplanes, for example. Students AND teachers have demonstrated lack of understanding and knowledge in both decimals and percents, conceptually their connections to fractions. Therefore, comprehension must be taken into careful consideration, and carefully developed. Here are some big ideas to think about in decimal and percentage teachings:
1. The base-ten place-value system extends infinitely in two directions: to tiny values as well as to large values. Between any two place values, the 10-to-1 ratio remains the same.
2. The decimal point is a convention that has been developed to indicate the units position. The position to the left of the decimal point is the unit that is being counted as singles or ones.
3. Decimal fractions are simply another way of writing fractions. Both notations have value. maximum flexibility is gained by understanding how the two symbol systems are related.
4. Percents are hundredths and as such are a third way of writing both fractions and decimals.
5. Addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values- a simple extension from the whole numbers.
6. Multiplication and division will produce the same digits, regardless of the positions of the decimal point. As a result, the computations can be performed as whole numbers with the decimal placed by way of estimation.
1. The base-ten place-value system extends infinitely in two directions: to tiny values as well as to large values. Between any two place values, the 10-to-1 ratio remains the same.
2. The decimal point is a convention that has been developed to indicate the units position. The position to the left of the decimal point is the unit that is being counted as singles or ones.
3. Decimal fractions are simply another way of writing fractions. Both notations have value. maximum flexibility is gained by understanding how the two symbol systems are related.
4. Percents are hundredths and as such are a third way of writing both fractions and decimals.
5. Addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values- a simple extension from the whole numbers.
6. Multiplication and division will produce the same digits, regardless of the positions of the decimal point. As a result, the computations can be performed as whole numbers with the decimal placed by way of estimation.
Activities
Extra Resources
If you are on a one-to-one classroom or students have access to computers/laptops, utilize the following link. It is a website with online manipulatives, and supports students grades 2-4th that are learning decimals, fractions and percentages!