Student Actions

Teacher Actions

• Develop mathematical reasoning by discussing and explaining when to convert between fractions and decimals to make comparisons more efficiently.

• Develop the ability to make conjectures, model, and generalize when utilizing manipulatives such as unifix cubes, empty number lines, and fraction tiles to find equivalent representations of fractions and decimals.

• Develop the ability to communicate mathematically when discussing solutions by using appropriate mathematical vocabulary.

• Develop mathematical reasoning when making sense of a real-world problem by ordering a set of numbers (using number lines, models, and representations) that includes fractions, decimals, and mixed numbers.

• Facilitate meaningful mathematical discourse by urging students to continually evaluate the reasonableness of their results in their work and their peersthrough discussing and explaining their mathematical reasoning.

• Pose purposeful questions which provide students opportunities to illustrate their thinking by discussing their solutions and using appropriate mathematical vocabulary.

• Build procedural fluency from conceptual understanding by providing appropriate physical and/or digital tools to represent, explore and deepen student understanding.

Key Understandings

Misconceptions 

• Compare and order decimals, fractions, and mixed numbers

• Find appropriate increments between whole numbers to locate decimals, fractions, and mixed numbers on a number line

• Use benchmark numbers (0,¼, ⅓, ½, ⅔, ¾, 1) to help them compare and order fractions and mixed numbers

• Understand place value to help them compare and order decimals

• Read a number line segment even if it doesn’t show 0 

• Mixed numbers are larger than fractions greater than one because mixed numbers contain a whole number part and whole numbers are larger than fractions.

• Fractions have to be less than 1.

• Overgeneralize the idea that “the bigger the denominator, the smaller the part” by ignoring numerators when comparing fractions.

• Does not use benchmark numbers like 0, ¼, 1/2, ¾, and 1 to compare fractions because they have restricted their understanding of fractions to part-whole situations and do not think of the fractions as numbers.

• Decimals are bigger than fractions because fractions are really small things.

• Decimals with more digits are smaller because tenths are bigger than hundredths and thousandths

• Students look at the number of decimal digits rather than the value of the digits.

• Use the denominator as the number to the right of the decimal point.

• Apply rules for comparingwhole numbers to comparing decimals so that the more digits to the right of the decimal the greater the value, regardless of the digits used.

• Does not use a zero as a placeholder when ordering numbers or finding numbers

  Knowledge Connections

Prior Knowledge

Leads to 

• Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks. (4.N.3.8)

• Compare and order benchmark fractions (0, ¼, ⅓, ½, ⅔, ¾ 1) and decimals (0, 0.25, 0.50, 0.75, and 1.33) in a variety of representations. (4.N.3.9) 

• Compare and order positive rational numbers, represented in various forms, or integers using the symbol “<”, “>”, and “=”. (6.N.1.2)

• Explain that percent represents “out of 100”, and ratios “to 100”. (6.N.1.3)

• Determine equivalencies among fractions, mixed numbers, decimals, and percents. (6.N.1.4)

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.1.3 Locate Decimal