MAFS.4.NF.3.5 – SMathSmarts

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

[divider] [/divider]Students are able to…

Convert tenths to hundredths and when applicable hundredths to tenths using models and pictures.
Find patterns and make generalizations about equivalent fractions that are tenths and hundredths.
Add and subtract tenths with hundredths using models, pictures, words and numbers to explain their thinking.

[divider] [/divider]Students are able to…because teachers…

Provide opportunities for students to find equivalent fractions for tenths and hundredths.
Provide activities and facilitate discussion on finding equivalent fractions of tenths and hundredths using models, including base-then blocks and hundreds grids, which later can be connected to students’ work with decimals.
Provide opportunities for students to add and subtract tenths and hundredths using models, pictures, words, and numbers.

[divider] [/divider]Questions to ask students:

Is 1/10 equivalent to 1/100? Use a model to prove your answer.
- Sample answer that indicates understanding: No, 1/10 is greater than 1/100. (model shown below)

How do 1/10 and 10/100 compare?
- Sample answer that indicates understanding: 1/10 is equivalent to 10/100 because if I shade in 1/10 of a whole and 10/100 of a whole they cover the same amount of space.

What if you combined the 1/10 and 1/100 what would be the new value?
- Sample answer that indicates understanding: Student demonstrates the understanding that 1/10 must be converted to hundredths then added. (model shown below)

Sample answer that indicates an incomplete understanding or a misconception: Student does not convert tenths to hundredths, adds the values and find a sum 2/100 or 2/10.

[divider] [/divider]FSA Notes

Cognitive Complexity Level: 1: Recall

Achievement Level Descriptors:

2-expresses a fraction with denominator 10 as an equivalent fraction with denominator 100 by using a model

3-adds two fractions with respective denominators 10 and 100 by first finding equivalent fractions with like denominators

4-solves missing addend problems with respective denominators 10 and 100 by first finding equivalent fractions with like denominators

5-[intentionally left blank]

Assessment Limits:

Denominators must be either 10 or 100.

Decimal notation may not be assessed at this standard.

[divider] [/divider]Additional Resources:

Additional in depth content knowledge