Math Misconceptions

4.NF.5-7

Look closely at errors in students’ work (formative assessment) to help you reflect

and make instructional decisions to suit all students’ needs.

When generating equivalent decimal fractions, students may make errors that incorrectly represent the intended value. For example, they may understand that they are working to create decimal fractions with denominators of 100, but not understand how or why the numerator is involved. Provide multiple experiences for constructing more than one visual representation of a decimal fraction. The visual models will reinforce the equivalency, which is the focus of this standard. Once the equivalencies are understood, then students can use this technique to add the two decimal fractions together. MISCONCEPTION:

WHAT TO DO:

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When students use decimal notation for fractions (to create decimal fractions or base-ten fractions) they often make errors because they are applying whole number thinking to these different values. For example, given the value of 8/100, students see 8 and think of it in the context of the single digit 8 as they have seen it in context before. Therefore, they place it on the page along with a decimal, not attending to the place value notation. Once again, multiple experiences with different visual models will help build stronger understanding. Also, it is very important for students to attend to precision when naming a decimal fraction. When a decimal fraction is read correctly, the name reinforces the place value of each digit, such as “eight hundredths”. Prevent students from using language such as “point zero eight”. MISCONCEPTION:

WHAT TO DO:

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Comparing decimal values can bring out student misconceptions that may have formulated some time ago while comparing whole numbers. For whole number comparisons, students may have concluded that numbers are larger or smaller based on the number of digits in the entire number. So when working with decimals, students may see .38 as greater than .5 because it has more digits and 38 is greater than 5 when in the context of whole numbers. An emphasis in reinforcing place value is extremely important here. A digit of 5 has different values depending on its location in a number. MISCONCEPTION:

WHAT TO DO:

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