Grade 6

Number and Operations: Develop an understanding of and fluency with multiplication and division of fractions and decimals in a context that promotes problem solving, reasoning, communication, making connections, and designing and analyzing representations.

Big Idea: Fractions and decimals can be multiplied and divided in a meaningful and useful way.

1. Develop, analyze, and apply strategies and procedures to multiply and divide decimals, including powers of 10.

Concept:	Skills:
Strategies Procedures Multiply Divide Powers of 10	Develop · Analyze Apply Multiply Divide

Topic	Lesson Number	Lesson	Objective	Assessment
Multiply and Divide Decimals Ch 2	2.6	Multiply Decimals McGraw 58-61 Connections Pg 62-63	Multiply decimals by whole numbers and by decimals.
	2.7 ** **	Properties of Multiplication McGraw pg 62-65	Use the properties of multiplication and mental math strategies to multiply whole numbers and decimals.	Students distinguish multiplicative comparisons from additive comparisons. Students use the commutative, associative, and distributive properties to show that two expressions are equivalent. They also illustrate properties of operations by showing that two expressions are equivalent (e.g., determining the area in two different ways for a rectangle whose dimensions are x + 3 by 5).
	2.9	Divide Decimals by Whole Numbers McGraw 72-75	Divide decimals by whole numbers.
	2.12	Div Mult of 10 McGraw pg 80-81	Multiply and divide decimals and whoile numbers by multiples of 10.
	2.13	Divide Decimals by Decimals McGraw pg 82-85	Divide decimals by decimals and whole numbers by decimals.
Multiply and Divide Fractions	6.1	Fractions of Whole Numbers	Find fractions of whole numers using mental math.
	6.2	Multiply Fractions	Multiply fractions by fractions
	6.3	Multiply Mixed Numbers	Multiply mixed numbers
	6.4	Estimate Products	Estimate products of mixed numbers
	6.5	Problem Solving Choose the Operation	Decide what operation is needed to solve a problem.
	6.6 **	Properties of Multiplication	Use properties of multiplication of numbers.
	6.8 **	Explore Dividing Fractions	Divide by fractions.
	6.9 **	Divide Fractions and Mixed Numbers	Divide by fractions and mixed numbers.
	6.10 A	Problem Solving Decision Making	Apply multiplying fractions to making decisions.
	6.10 B	Problem Solving Math and Science	Apply dividing fractions to investigate science concepts.

2. Use the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and explain why they work.

Concept:	Skills:
Inverse Multiplication Division Procedures Fractions	Use Make sense of procedures Explain

Topic

Lesson Number

Lesson

Objective

Assessment

3. Apply the commutative, associative and identity properties of addition and multiplication and the distributive property to simplify calculations.

Concept:	Skills:
Commutative Associative Identity Properties of Addition Properties of Multiplication Distributive property Calculations	Apply Simplify

Topic	Lesson Number	Lesson	Objective	Assessment
Add and Subtract Decimals Ch 1	1.8	Properties of Addition McGraw 24-27	Review using properties of addition of whole numbers and decimals.
Multiply and Divide Decimals Ch 2	2.7	Properties of Multiplication McGraw pg 62-65	Use the properties of multiplication and mental math strategies to multiply whole numbers and decimals.
Add and Subtract Fractions	5.5	Properties of Addition	Use properties of addition of numbers
Multiply and Divide Fractions	6.6	Properties of Multiplication	Use properties of multiplication of numbers.

4. Develop, analyze, and apply strategies and procedures to multiply and divide fractions, including mixed numbers.

Concept:	Skills:
Strategies Procedures Fractions Mixed Numbers	Develop Analyze Apply Multiply fractions including mixed numbers Divide Fractions including mixed numbers

Topic	Lesson Number	Lesson	Objective	Assessment
Multiply and Divide Decimals Ch 2	2.2	Mult 2 digit McGraw 48-49
	2.6	Mult Dec McGraw 58-61	Multiply decimals by whole numbers and by decimals.
	2.7	Properties of Multiplication McGraw pg 62-65	Use the properties of multiplication and mental math strategies to multiply whole numbers and decimals.
	2.8	Divide Whole numbers McGraw pg 68-71	Divide whole numbers by whole numbers.
	2.9	Divide Decimals by Whole Numbers McGraw 72-75	Divide decimals by whole numbers.
	2.12	Divide by Multiples of 10 McGraw pg 80-81	Multiply and divide decimals and whole numbers by 10; 100; 1000; and 10000.
	2.13	Divide Decimals by Decimals McGraw pg 82-85	Divide decimals by decimals and whole numbers by decimals.
Number Theory and Fraction Concepts Ch 4	4.1	Divisibility McGraw 162-165	Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
	4.2	Explore Prime and Composite Numbers McGraw 166-167	Review determining whether a number is prime or composite and expressing a composite number as a product of primes.
	4.3	Greatest Common Factors and Least Common Multiples McGraw pg 168-171	Review finding common factors, greatest common factors, common multiples and least common multiple.
	4.4	Understanding Fractions McGraw pg 172-175 Practice, Reteach, Enrich Math Traveler Mount Frost 4.5 Extra or Missing information Problem Solving McGraw 176-177 Practice, Reteach, Enrich	Review writing fractions to represent situations and finding equivalent fractions.
	4.6	Simplify Fractions McGraw pg 178-179 Practice, Reteach, Enrich Math Traveler Blip’s Satellite Service, Mount Frost 4.7 Making a Table Problem Solving McGraw pg 182-183	Review writing fractions in simplest form.
	4.8	Compare and Order Fractions McGraw pg 184-185 Practice, Reteach, Enrich Math Traveler Mount Frost	Review finding the least common denominator of two or more fractions, and comparing and ordering fractions with unlike denominators.
	4.9	Mixed numbers McGraw pg 186-187 Practice, Reteach, Enrich Math Traveler Blip’s Satellite Service, Mount Frost	Review writing a mixed number as an improper fraction and writing an improper fraction as mixed numbers or as a whole number.
Multiply and Divide Fractions	6.1	Fractions of Whole Numbers	Find fractions of whole numbers using mental math.
	6.2	Multiply Fractions	Multiply fractions by fractions
	6.3	Multiply Mixed Numbers	Multiply mixed numbers
	6.4	Estimate Products	Estimate products of mixed numbers
	6.5	Problem Solving Choose the Operation	Decide what operation is needed to solve a problem.
	6.6	Properties of Multiplication	Use properties of multiplication of numbers.
	6.8	Explore Dividing Fractions	Divide by fractions.
	6.9	Divide Fractions and Mixed Numbers	Divide by fractions and mixed numbers.
	6.10 A	Problem Solving Decision Making	Apply multiplying fractions to making decisions.
	6.10 B	Problem Solving Math and Science	Apply dividing fractions to investigate science concepts.

5. Use the relationship between decimals and fractions to solve problems, including measurement.

Concept:	Skills:
Relationship Decimals Fractions Problems Measurement	Use Solve problems including measurement

Topic	Lesson Number	Lesson	Objective	Assessment
Add and Subtract Decimals Ch 1	1.1	Decimal place value McGraw pg 2-5	Review place value of whole numbers and decimals and equivalent decimals.
Number Theory and Fraction Concepts Ch 4	4.4	Understanding Fractions McGraw pg 172-175	Review writing fractions to represent situations and finding equivalent fractions.
	4.10	Relate Fractions and Decimals McGraw pg 188-191	Review changing decimals to fractions and mixed numbers, and changing fractions and mixed numbers to decimals.
	4.11	Compare and Order fractions and Mixed numbers McGraw pg 192-193	Compare and order fractions, mixed numbers, whole numbers, and decimals.
Perimeter, Area, and Volume **	11.2	Area of Rectangles and Parallelograms	Find the area of rectangles, squares, and parallelograms.
	11.3