Students should see a fraction as the numerator times the unit fraction with the same denominator. Example: (Progressions CCSS Writing Team, August 2011, page 8) for the CCSSM, Number and Operation Fractions, – This standard extended the idea of multiplication as repeated addition. For example, 3 x (2/5) = 2/5 + 2/5 + 2/5 = Understand a multiple of a/b as a 6/5 = 6 x (1/5). Students are expected to use and create visual fraction models to multiply a whole number by a multiple of 1/b, and use this understanding to multiply a fraction fraction. by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) The same thinking, based on the analogy between fractions and whole numbers, allows students to give meaning to the product of whole number and a fraction. Example: (Progressions CCSS Writing Team, August 2011, page 8) for the CCSSM, Number and Operation Fractions, – When introducing this standard make sure student use visual fraction models to word problems related to Solve word problems involving multiplying a whole number by a fraction. multiplication of a fraction by a Example: whole number, e.g., by using visual In a relay race, each runner runs ½ of a lap. If there are 4 team members how long is the race? fraction models and equations to represent the problem. For example, if each person at a will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between
Students should see a fraction as the numerator times the unit fraction with the same denominator. Example: (Progressions for the CCSSM, Number and Operation – Fractions, CCSS Writing Team, August 2011, page 8) Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) This standard extended the idea of multiplication as repeated addition. For example, 3 x (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 6 x (1/5). Students are expected to use and create visual fraction models to multiply a whole number by a fraction. The same thinking, based on the analogy between fractions and whole numbers, allows students to give meaning to the product of whole number and a fraction. Example: (Progressions for the CCSSM, Number and Operation – Fractions, CCSS Writing Team, August 2011, page 8) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between When introducing this standard make sure student use visual fraction models to word problems related to multiplying a whole number by a fraction. Example: In a relay race, each runner runs ½ of a lap. If there are 4 team members how long is the race?