# Solve contextual problems involving addition and subtraction of fractions referring to the same

### Cluster

Use equivalent fractions as a strategy to add and subtract fractions.

Nigel starts working on his math homework. He does $one sixth$ of the homework in the first $ten$ minutes. Then he does $one fifth$ of the homework in the next $ten$ minutes. The number line shows points $E, F, G,$and $H$. They represent different fractional parts of one whole.

Which point on the number line is closest to the fractional part of Nigel’s homework that he does in the first $twenty$ minutes?

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Solve contextual problems referring to the same whole that involve adding and subtracting fractions with like denominators.  A visual fraction model may or may not be provided. Solve contextual problems referring to the same whole that involve adding fractions and/or mixed numbers with unlike denominators where the denominators are 6 or less and one is not a factor of the other and a visual fraction model is provided. Solve contextual problems referring to the same whole that involve subtracting fractions and/or mixed numbers with unlike denominators where regrouping is not required and the denominators are 6 or less and one is not a factor of the other when a visual fraction model is provided. Solve contextual problems referring to the same whole involving addition and subtraction of fractions with unlike denominators.  A visual fraction model may or may not be provided. Use benchmark fractions and number sense of fractions to estimate the solution to contextual problems involving addition and subtraction of unlike denominators. Assess the reasonableness of answers to contextual problems referring to the same whole involving addition and subtraction of unlike denominators by using benchmark fractions and number sense. Create a story context for adding and/or subtracting fractions referring to the same whole with fractions with unlike denominators.

Instructional Focus Statements

Level 3:

Students should interact with contextual problems that elicit adding and subtracting fractional amounts with increasing rigor over the course of instruction. Contextual problems should be framed in multiple ways. A good resource is the “Common Addition and Subtraction Situations” document embedded in the Tennessee mathematics standards.

Additionally, students should be interacting with situations that require them to elicit number sense in order to estimate solutions using knowledge of benchmark fractions. The ability for a student to employ number sense is an invaluable skill. Students should be expected to develop this skill with fractions in the same rigor as number sense is built with whole numbers in previous grades.

Students should justify the reasonableness of solutions to contextual problems by employing number sense coupled with their understanding of benchmark fractions.

Level 4:

Students should justify the reasonableness of solutions to contextual problems by employing number sense coupled with their understanding of any fractions. Students should engage in conversations where they justify their solutions using mathematical, sound reasoning while employing estimation strategies.