Unit 2

Arithmetic Operations Including Division by a Fraction

 

Grade 6

Math

Description:

 

In Unit 2, students divide whole numbers by fractions and fractions by fractions to solve word problems. Students add, subtract, multiply, and divide multi-digit decimals. The use of estimation strategies supports student understanding of decimal operations.

 

Students find the greatest common factor of two whole numbers less than or equal to 100, they understand that the greatest common factor of two prime numbers will be 1, they use the greatest common factor and the distributive property to find the sum of two whole numbers, and students use the least common multiple of two whole numbers less than or equal to twelve.

 

Louisiana Student Standards for Mathematics (LSSM)

RP Ratios and Proportional Relationships

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.A.1

 

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 3/4- cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

NS- The Number System

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.B.2

 

Fluently divide multi-digit numbers using the standard algorithm.

6.NS.B.3

 

 

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.B.4

 

 

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

 

Enduring Understandings:

 

         Operations of decimals and whole numbers are based upon place value relationships.

         When we divide one number by another, we may get a quotient that is bigger than the original number, smaller than the original number, or equal to the original number.

         Least common multiple and greatest common factor are helpful when solving real-world problems.

         Multiplication and division are inverse operations.

 

Essential Questions:

 

         What role does place value play in multi-digit operations?

         How can the distributive property help me with computation?

         When I divide one number by another number, do I always get a quotient smaller than my original number?

         Which strategies are helpful when performing operations on multi-digit decimals?

         What kind of models can I use to show solutions to word problems involving fractions?

         How can I check a division problem?