ALEX Classroom Resource

Students:

• Reason about the impact of scaling one or both factors on the size of the product before multiplying and justify their thinking.

Example: Which is greater? 3/5 x 13 or 13 x 3/4? 13 x 3/4 is greater than 3/5 x 13 because both expressions contain a factor of 13, but the scale factor of 3/4 will result in a greater product than a scale factor of 3/5 because 3/4 > 3/5.
• Explain the size of the product when multiplying a number by a fraction greater than 1 and when multiplying a number by a fraction less than 1.

Students know:

• How to interpret multiplicative comparisons.
• Strategies to compare products with whole numbers using reasoning and justification.
  Example: Which is greater? 5 x 2 x 13 or 13 x 9? 10 x 13 is greater than 9 x 13 because both expressions contain a factor of 13, but the scale factor of 10 will result in a greater product than a scale factor of 9.
• Fraction meaning and magnitude of fractions less than and greater than 1.

Students are able to:

• Interpret multiplication as scaling.
• Use reasoning to compare products of multiplication expressions.
• Reason and explain when multiplying a given number by a fraction why the product will be greater than or less than the original number.

Students understand that:

• a product reflects the size of its factors.

Learning Objectives:
M.5.13.1: Define scaling.
M.5.13.2: Define principle of fraction equivalence.
M.5.13.3: Multiply a fraction by a whole number.
M.5.13.4: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
M.5.13.5: Recognize that comparisons are valid only when the two fractions refer to the same whole.
M.5.13.6: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
M.5.13.7: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
M.5.13.8: Identify factor and product.
M.5.13.9: Use comparison symbols.
Examples: >, =, or <.