#### MAT-03.NF.03

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size:  a) Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b) Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.c) Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.d) Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

## Student Learning Targets:

### Knowledge Targets

• I can recognize when simple fractions are equivalent (equal).
• I can explain why simple fractions are equivalent.

### Reasoning Targets

• I can compare two fractions with the same numerator or the same denominator using the >,<, and = symbols.
• I can understand two fractions are equivalent if they are the same size or the same point on a number line.

### Skills (Performance) Targets

• I can show examples of simple equivalent fractions using a visual model.
• I can use a number line to compare, order, and show equivalent fractions.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced Criteria is Under Development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 Student is able to represent equivalent fractions, explain equivalencies, order fractions, and compare fractions with same numerators or denominators using >,<,= symbols with minimal error. I can compare and order fractions on a number line. I can use >,<,= symbols to compare fractions. I can show equivalent fractions using a visual model and explain why fractions are equivalent. Model and Explain Equivalencies Use Symbols to Compare Fractions Compare and Order Simple Fractions on a Number Line 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to demonstrate understanding of fraction equivalency concepts, but has multiple errors or misconceptions in any one area. I can compare and order fractions on a number line, but I may have mistakes. I can use >,<,= symbols to compare fractions. I can show equivalent fractions using a visual model and explain why fractions are equivalent. Model and Explain Equivalencies Use Symbols to Compare Fractions Compare and Order Simple Fractions on a Number Line 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to demonstrate beginning understanding of fraction equivalency concepts, but has multiple errors or misconceptions in all areas. I can compare and order fractions on a number line, but I have mistakes. I can use >,<,= symbols to compare fractions, but I have mistakes. I can show some equivalent fractions using a visual model and explain why fractions are equivalent, but I have mistakes. Model and Explain Equivalencies Use Symbols to Compare Fractions Compare and Order Simple Fractions on a Number Line 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• fraction
• equal parts
• equivalent
• numerator
• denominator
• compare
• model
• >, greater than
• <, less than
• =, equal to
• justify
• order
• number line
• equal distance
• halves
• thirds
• fourths
• sixths
• eighths