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# 4-N-2-8

last edited by 3 years, 8 months ago

4.N.2.8 Compare benchmark fractions (¼, ⅓, ½, ⅔, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations.

In a Nutshell

Students will compare benchmark fractions and decimals in real-world situations.  The comparisons may be a combination of fractions and decimals in the same situation.

## Teacher Actions

• Develop strategies for problem solving by fluently making the connection between benchmark fractions and decimals (½ and .5 are quickly identified as equivalent, ¾ and .75 are quickly identified as equivalent), facilitating efficient problem solving.

• Develop accurate and appropriate procedural fluency by comparing and ordering benchmark fractions and decimals in a variety of contexts, quickly identifying the relevant form of the benchmark (fraction or decimal), and making the translation from one form to the other as necessary.

• Develop a deep and flexible conceptual understanding of comparing benchmark fractions and decimals by recognizing the comparison is only valid when the fractions and decimals being compared both refer to the same whole.

• Develop mathematical reasoning by applying conceptual understanding of fractions and decimals to comparison situations, and verifying the accuracy of comparison results.

• Develop the ability to communicate mathematically by discussing and explaining comparison strategies and justifying results.

• Use and connect mathematical representations by modeling the comparison of benchmark fractions and decimals in a variety of contexts.

• Implement tasks that promote reasoning and problem solving by introducing real-world scenarios which require students to compare and order benchmark fractions and decimals.

• Facilitate meaningful mathematical discourse by encouraging students to discuss comparison scenarios, explain their reasoning, justify their thinking, and critique the thinking of their peers.

## Misconceptions

• Even though fractions and decimals are not written in the same format, they can be accurately compared and ordered by applying knowledge of benchmark numbers in both formats.
• Fractions must be compared to fractions, and decimals must be compared to decimals.

• When comparing fractions, the fraction with the larger denominator is larger; misapplying whole number understanding to comparing and ordering fractions (for example: ⅛ is larger than ⅙ ).

• Failure to make the connection between a benchmark fraction and its decimal equivalent.

OKMath Framework Introduction