Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding by recalling previous knowledge about unit fractions and decomposing fractions and using this information to develop efficient and generalizable procedures, such as multiplying or dividing to create equivalent fractions, and what operation to use to convert fractional forms.

• Develop the ability to make conjectures, model, and generalize by recording their thinking and strategies for adding and subtracting fractions and decimals using numerical expressions as well as pictures and words.

• Develop mathematical reasoning by estimating fractions using benchmark knowledge to find estimated sums and differences and using their findings to assess the reasonableness of their solutions.

• Develop the ability to communicate mathematically by actively listening and communicating when collaborating with peers to strategize and solve problems involving fractions and decimals.

• Develop a deep and flexible conceptual understanding of addition and subtraction of fractions with like and unlike denominators by modeling these operations using a variety of representations (e.g., fraction strips, fraction circles or bars, number lines, pictures).

• Support productive struggle in learning mathematics by allowing students to figure out their errors that include not having their place values lined up, not finding a common denominator, and subtracting requiring regrouping or conversion to a fraction greater than one.

• Facilitate meaningful mathematical discourse by asking students for generalizations they see in solution strategies. How are these strategies alike/different?  What would be the better approach?

• Pose purposeful questions that provide students with different entry points and the opportunity to have success

• Build procedural fluency from conceptual understanding by creating activities that use representations like fraction strips, fraction circles or bars, number lines, and pictures to record the processes which lead to the use of common algorithmic procedures.

Key Understandings

Misconceptions 

• Find common denominators to add or subtract fractions and mixed numbers of benchmark denominator parts (halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths)

• Recognize equivalent fractions in sums and differences (i.e. 2/4 is equivalent to 1/2). 

• Consider place value when adding decimals up to the thousandth place

• Apply addition and subtraction of fractions and decimals to real-world situations i.e. money, measurement, data, and geometry.

• Think when adding fractions, generalize the procedure for multiplication of fractions by adding the numerators and adding the denominators.

• Think when adding two fractions, adding the numerators and multiplying the denominators.

• Think when subtracting mixed numbers, always subtracting the smaller whole number from the larger whole number and subtracting the smaller fraction from the larger fraction.

• Add or subtract decimals without considering place value.  Student lines numbers up starting at the right side just like whole numbers.

• Believe that zeros placed to the right of the decimal number change the value of the number.

  Knowledge Connections

Prior Knowledge

Leads to 

• Rename equivalent fractions in models (4.N.3.1).

• Decompose fractions into unit fractions (4.N.3.4).

• Compare and order decimals (4.N.3.8).

• Subtract money, up to $20 (4.N.4.2).

• Estimate to solve problems with whole numbers, mixed numbers, fractions and decimals (6.N.4.1).

• Multiply and divide fractions and decimals (6.N.4.3).

• Solve problems involving money, measurement, geometry, and data using fractions, decimals, and mixed numbers (6.N.4.4).

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

• 5.N.3.3 Mixed Numbers