Brush up on your multiplication, division, and factoring skills with this interactive multiplication chart. Three levels and timed or untimed options are available.

This unit is an EQuIP Exemplar for adult education (http://achieve.org/equip). Students will connect their prior, real-world knowledge to the concept of order in mathematics. They will go through a discovery process with content that will build a deep, conceptual understanding of the properties of operations to explain why we perform operations in a certain order when we see just the naked numbers.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

The class reviews the properties of operations. The use of “ask myself” questions to make sense of problems and persevere is modeled. Students review things to do when they feel stuck on a problem. Finally, students use the properties of operations to evaluate expressions.Key ConceptsStudents use the properties of operations to justify whether two expressions are equivalent.Goals and Learning ObjectivesTo start to work on a problem, make sense of the problem by using “ask myself” questions.Persevere in solving a problem even when feeling stuck.Use the properties of operations to evaluate expressions.

Students discuss as a class the important ways that listeners contribute to mathematical discussions during Ways of Thinking presentations. Students then use the properties of operations to find the value of each fruit used in equations.Key ConceptsStudents use the properties of operations to find the value of each fruit used in different equations. By considering several equations, students can match each of the 10 fruits to the whole numbers 0 through 9. This work helps students see why representing unknown numbers with letters is useful.Goals and Learning ObjectivesContribute as listeners during the Ways of Thinking discussion.Identify the whole numbers that make an equation true.Use the properties of operations, when appropriate, to justify which whole numbers represent unknown values.