## Mathematics Support Materials

### Mathematics snapshot: Problem solving using fractions

Mathematics/Number and Algebra/Fractions and decimals

Content Description Relevant aspects of the Achievement Standards

Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)

Students solve problems involving all four operations with whole numbers.

Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions

### Purpose of the assessment

To assess students’ ability to formulate and solve problems using fractions

### Stage in the teaching sequence

End of a teaching cycle

The teacher allocated students to groups based on her observations of students’ responses to previous activities in the teaching cycle. Each group was given two problems to solve: a routine problem and a non-routine problem. The problems were different for each group and were selected so they were challenging relative to the group’s ability.

### Teacher observation

When observing a group attempt the routine problem, the teacher looked for evidence that the students could:

• understand the fractional quantities involved and what was required
• explain the problem in their own words
• identify the appropriate operation required
• represent the problem using a number sentence
• complete the algorithm correctly
• recall basic number facts
• check the reasonableness of the answer obtained.

When observing a group attempt the non-routine problem, the teacher looked for evidence that the students could:

• explain the problem in their own words
• identify relevant information within the problem
• come up with a strategy for beginning the task
• make use of available materials
• persevere
• explain the strategy used and the solution.

### Using the information

Based on her observations the teacher identified that she needed to give students more practice at basic number facts and that she also needed to revise strategies for solving non-routine problems.