These 100 lessons accompany and are based on Go Math textbook (5th Grade), with rich content and higher level questions. The lessons can stand on their own even if the instructor does not use Go Math, where alternative practice exercises can be utilized.
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Students will explore multiplication and division by focusing on the relationship that one operation is the inverse of the other. They look for and make use of structure when they find patterns that connect the operations. Consider the following:
40 x 8 = 320 320 ÷ 40 = 8
8 x 40 = 320 320 ÷ 8 = 40
This relationship is an extension of the related facts students learned in previous grades.
Understanding different meanings of division helps students make sense of problems and persevere in solving them. Such understanding gives students strategies to make sense of situations. This, in turn, helps them persevere in finding solutions.
Students add and subtract decimals using several models. Of particular importance is the place-value model represented with base-ten blocks. As students solve addition problems with base-ten blocks where the flat is equal to one, the long is equal to one-tenth and the small cube is equal to one-hundredth, they are led to see that when adding decimals, the hundredths can be combined with hundredths, the tenths with tenths, and so on. They see that similar reasoning can be applied to subtraction. These experiences help students to look for and make use of structure as they make sense of place-value algorithms for adding and subtracting decimals.
These lessons, aligned to the Common Core Standard, provide a comprehensive approach to teach multiplying decimals for fifth grade students. Components include the AIM (or Essential Question), objective, common core standard, motivation, model/teach, guided practice, independent practice and summary.
These lesson plans are recommended for January or February of the school year, to 5th Grade level and are aligned to the Common Core Standards. They cover dividing with decimals and are written utilizing the workshop model and problem-based model.
**This unit covers dividing decimals to provide students with opportunities to make sense of problems and persevere in solving them. Students make sense of problems when they model decimal division. The modeling helps them develop procedures for determining quotients. Eventually, students solve multistep problems involving decimal division. When they encounter difficult problems, they can use models to help them.
**Modeling operations helps students make sense of the procedures. Students make sense of procedures for dividing decimals by estimating the quotient using compatible numbers. This estimate can help the student place the decimal point after dividing. Exploring division with models and contexts and making sense of the placement of the decimal point after dividing will help students to understand how the decimal division algorithms work.
Decimal models can be used to show how to divide decimals by decimals.
These lessons guide students to use models to multiply fractions, including numbers and then fractions and fractions, including mixed numbers. Students will be asked to use the area model to make sense of the algorithm for multiplying fractions. Students use appropriate tools strategically when they decide if it makes more sense to use an area model or the algorithm to determine the product.
In this unit students will learn about dividing fractions by whole numbers and dividing whole numbers by fractions, they look for and make use of structure. They do this when they develop connections between whole-number division and fraction division, as well as between division expressions and related multiplication expressions. This builds a foundation for developing the fraction division algorithm.
In this unit, students will graph number pairs on a coordinate grid. They will analyze patterns and then model those relationships using graphs. These experiences provide meaningful opportunities for students to model with mathematics. Early explorations, such as these, will lead students to make sense of more formal explorations in algebra in later grades like determining the slope of a line.
Converting units of measure within the customary or the metric system provides students an opportunity to attend to precision. As they make conversions, they need to check the reasonableness of their results. Students who can apply the techniques on this page will be able to evaluate the reasonableness of their results.
The study of geometry and volume offers many opportunities for students to interact with other students and listen to their arguments and justifications. This may occur when students examine defining attributes and properties of a figure. As students create definitions based on properties of figures and discuss with their classmates whether or not certain figures have the properties to meet specific definitions, they have ample opportunities to construct viable arguments and critique the reasoning of others.
Table of Contents
Lesson 1.1 Investigate ● Place Value and Patterns
Lesson 1.2 Place Value of Whole Numbers
Lesson 1.3 Algebra ● Properties
Lesson 1.4 Algebra ● Powers of 10 and Exponents
Lesson 1.5 Algebra ● Multiplication Pattern
Lesson 1.6 Multiply by 1-Digit Numbers
Lesson 1.7 Multiply by 2-Digit Numbers
Lesson 1.8 Relate Multiplication to Division
Lesson 1.9 Problem Solving ● Multiplication and Division
Lesson 1.10 Algebra ● Numerical Expression
Lesson 1.11 Algebra ● Evaluate Numerical Expressions
Lesson 1.12 Algebra ● Grouping Symbols
Lesson 2.1 Place the First Digit
Lesson 2.2 Divide by 1-Digit Divisors
Lesson 2.3 Investigate ● Division with 2-Digit Divisors
Lesson 2.4 Partial Quotients
Lesson 2.5 Estimate with 2-Digit Divisors
Lesson 2.6 Divide by 2-digit Divisors
Lesson 2.7 Interpret the Remainder
Lesson 2.8 Adjust Quotients
Lesson 2.9 Problem Solving ● Division
Lesson 3.1 Investigate ● Thousandths
Lesson 3.2 Place Value of Decimals
Lesson 3.3 Compare and Order Decimals
Lesson 3.4 Round Decimals
Lesson 3.5 Investigate ● Decimal Addition
Lesson 3.6 Investigate ● Decimal Subtraction
Lesson 3.7 Estimate Decimal Sums and Differences
Lesson 3.8 Add Decimals
Lesson 3.9 Subtract Decimals
Lesson 3.10 Algebra ● Patterns with Decimals
Lesson 3.11 Problem Solving ● Add and Subtract Money
Lesson 3.12 Choose a Method
Lesson 4.1 Multiplication Patterns with Decimals
Lesson 4.2 Multiply Decimals and Whole Numbers
Lesson 4.3 Multiplication with Decimals and Whole Numbers
Lesson 4.4 Multiplying Using Expanded Form
Lesson 4.5 Problem Solving Multiply Money
Lesson 4.6 Investigate Decimal Multiplication
Lesson 4.7 Multiply Decimals
Lesson 4.8 Zeros in the Product
Lesson 5.1 Algebra, Division Patterns with Decimals
Lesson 5.2 Investigate, Divide Decimals by Whole Numbers
Lesson 5.3 Estimate Quotients
Lesson 5.4 Division of Decimals by Whole Numbers
Lesson 5.5 Investigate, Decimal Division
Lesson 5.6 Divide Decimal
Lesson 5.7 Write Zeros in the Dividend
Lesson 5.8 Problem Solving; Decimal Operations
Lesson 6.1 Investigate – Addition with Unlike Denominators
Lesson 6.2 Investigate – Subtraction with Unlike Denominators
Lesson 6.3 Estimate Fraction Sums and Differences
Lesson 6.4 Common Denominators and Equivalent Fractions
Lesson 6.5 Add and Subtract Fractions
Lesson 6.6 Add and Subtract Mixed Numbers
Lesson 6.7 Subtraction with Renaming
Lesson 6.8 Algebra – Patterns with Fractions
Lesson 6.9 Problem Solving – Practice Addition and Subtraction
Lesson 6.10 Algebra – Use Properties of Addition
Lesson 7.1 Find Part of a Group
Lesson 7.2 Investigate; Multiply Fractions and Whole Numbers
Lesson 7.3 Fraction and Whole Number Multiplication
Lesson 7.4 Investigate – Multiply Fractions
Lesson 7.5 Compare Fraction Factors and Products
Lesson 7.6 Fraction Multiplication
Lesson 7.7 Investigate; Area and Mixed Numbers
Lesson 7.8 Compare Mixed Number Factors and Products
Lesson 7.9 Multiply Mixed Numbers
Lesson 7.10 Problem Solving; Find Unknown Lengths
Lesson 8.1 Investigate – Divide Fractions and Whole Numbers
Lesson 8.2 Problem Solving; Use Multiplication
Lesson 8.3 Connect Fractions to Division
Lesson 8.4 Fraction and Whole-Number Division
Lesson 8.5 Interpret Division with Fractions
Lesson 9.1 Line Plots
Lesson 9.2 Ordered Pairs
Lesson 9.3 Investigate, Graph Data
Lesson 9.4 Line Graphs
Lesson 9.5 Numerical Patterns
Lesson 9.6 Problem Solving | Find a Rule
Lesson 9.7 Graph and Analyze Relationships
Lesson 10.1 Customary Length
Lesson 10.2 Customary Capacity
Lesson 10.3 Weight
Lesson 10.4 Multistep Measurement Problems
Lesson 10.5 Metric Measures
Lesson 10.6 Problem Solving ⚫ Customary and Metric Conversions
Lesson 10.7 Elapsed Time
Lesson 11.1 Polygons
Lesson 11.2 Triangles
Lesson 11.3 Quadrilaterals
Lesson 11.4 Properties of Two Dimensional Figures
Lesson 11.5 Three-Dimensional Figures
Lesson 11.6 Investigate ⠂Unit Cubes and Solid Figures
Lesson 11.7 Investigate ⠂Understand Volume
Lesson 11.8 Investigate ⠂Estimate Volume
Lesson 11.9 Volume of Rectangular Prism
Lesson 11.10 Apply Volume Formula
Lesson 11.11 Compare Volumes
Lesson 11.12 Find Volume of Composed Figures