Day 61: Use Patterns to Write and Solve Equations

Students in Math 6 and Math 6+ today worked with Lesson 4.9: Use Patterns to Write and Solve Equations. During this lesson,  students were asked to analyze simple patterns in tables and write rules and equations to describe the relationship between the dependent and independent variables similar to the example below.

Lesson Objectives: The student will be able to...

• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• write equations to represent the relationships between variables.

Day 60: Dependent and Independent Variables

Students in Math 6 today continued their work with Lesson 4.8: Understand Dependent and Independent Variables. To help with our overall understanding, students created illustrations that modeled the difference between independent and dependent variables.

• CLICK HERE to practice more dependent and independent variables.
• CLICK HERE to play with some independent variables that affect the dependent variable.

In Math 6+, students reviewed last night's evening practice dealing with independent and dependent variables. Mr. Giomini then had them work in pairs to review solving multi-step inequalities using story problems.

Lesson Objectives: The student will be able to...

• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• analyze the relationship between the dependent and independent variables.

Day 59: Dependent and Independent Variables

Students in Math 6 and Math 6+ today worked with Lesson 4.8: Understand Dependent and Independent Variables. The lesson provides a nice connection to science for later on in the year.

We connect these two variables to mathematics by looking at prices, speeds, distances traveled and determine how they relate with other factors. Variables can be used to represent quantities that change in relationships to one another. The dependent variable changes in response to the independent variables.

Lesson Objectives: The student will be able to...

• use variables to represent two quantities in a real-world problem that change in relationship to one another.
• analyze the relationship between the dependent and independent variables.

Day 58: Solve and Graph Inequalities

Students in Math 6 today reviewed Lesson 4.6: Writing and Understanding Inequalities by checking over their homework from last night and completing a Quizzizz that dealt with the skill. Lesson 4.7: Solve Inequalities was then introduced and modeled.

The focus of this lesson was how to read and graph inequalities on number lines. Graphs were both read and created to help build an understanding for the concept. Mr. Giomini recommended this skill on Khan Academy for all students to complete.

During Math 6+, students worked with solving one and two-step inequalities that were both in written form in and word problem format.

Lesson Objectives: The student will be able to...

• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• recognize that inequalities of the form x > c or x < c have infinitely many solutions.
• represent solutions of such on number line diagrams.

Day 57: Understand and Write Inequalities

Students in Math 6 and Math 6+ worked with inequalities. Mr. Giomini modeled how to appropriately use the symbols that are pictured below to write accurate mathematical statements.

Lesson Objectives: The student will be able to...

• write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
• recognize that inequalities of the form x > c or x < c have infinitely many solutions.
• represent solutions of such on number line diagrams.

Day 56: Topic Four Midpoint

All classes completed the Topic Four Midpoint today in class.

Remember that today is Veteran's Day. The purpose of today is for us to remember and pay respect to those men and women who have served in the Armed Forces. These individuals have made sacrifices to help keep us safe and free.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• interpret and compute quotients of fractions.

Day 55: Gallery Walk

Students in all of Mr. Giomini's classes participated in a Gallery Walk to help prepare for tomorrow's Topic Four Midpoint.

Gallery Walk Math 6
Gallery Walk Math 6+

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• interpret and compute quotients of fractions.

Day 54: Review

Students in Math 6, continued their work with Lesson 4.5: Write and Solve Equations with Rational Numbers. Opportunities for practice and guidance were offered during class as students worked to complete pages 206 and 207 in their enVision workbook.

In Math 6+, students reviewed solving equations with rational numbers and the distributive property.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• interpret and compute quotients of fractions.

Day 53: Write and Solve Equations with Rational Numbers

Students in Math 6, Mr. Giomini spent time reviewing how to add and subtract fractions and mixed numbers to help improve students success with Lesson 4.5: Write and Solve Equations with Rational Numbers.

This lesson requires that students are fluent with adding, subtracting, multiplying, and dividing whole numbers, decimals, fractions, and mixed numbers. In this lesson, we extend our work with solving one-step equations with whole numbers and use that foundational understanding to work with different rational numbers.

In Math 6+, students continued their work with solving for a variable with literal equations. Mr. Giomini began to model how to graph equations to determine if they are linear.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
• interpret and compute quotients of fractions.

Day 52: Two-Step Equations / Solving Literal Equations

Students in Math 6, continued their work with Lesson 4.4: Write and Solve Equations with Multiplication and Division. The focus was on extending our work with one-step equations to solving two-step equations.

In Math 6+, students worked with solving a formula for an variable.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non negative rational numbers.

Day 51: One Step Equations with Multiplication and Division

Students in Math 6, worked with Lesson 4.4: Write and Solve Equations with Multiplication and Division. In the lesson, students learned the inverse relationship that multiplication and division have with each other. Multiplication can undo division and division can undo multiplication.

In Math 6+, students continued their work with writing algebraic equations from real-world scenarios. Students worked with their partners from yesterday to complete the fourteen story problems assigned from Thursday's class period.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non negative rational numbers.

Day 50: Writing Equations

Students in Math 6, reviewed solving equations using addition and subtraction properties of equality. Mr. Giomini modeled how to write equations from story problems. In pairs, students practiced this skill and ended the class by completing a Kahoot on solving one-step equations.

In Math 6+, students continued their work with writing algebraic equations from real-world scenarios. Students were assigned partners and worked collaboratively to both write and solve equations from word problems.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non negative rational numbers.

Have fun!

Day 49: Write and Solve Addition and Subtraction Equations

Students in Math 6, used their work with properties of equality to begin solving equations with addition and subtraction. Once students began to understand how to solve one and two step equations, Mr. Giomini modeled how to write algebraic equations from word problems.

In Math 6+, students continued their work with writing algebraic equations from real-world scenarios.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non negative rational numbers.

Day 48: Apply Properties of Equality

Students in Math 6, students worked with the properties of equality from last Friday to help with balancing equations.

In Math 6+, students continued their work with solving multi-step equations as well as learning how to write equations from story problems.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• identify equations and variables.
• use substitution to find solutions to equations.

Day 47: Understand Equations and Solutions

Students in Math 6 reviewed their work from Friday and Lesson 4.1: Understand Equations and Solutions. Mr. Giomini provided the class with some examples to help refresh their memory from Friday's work. Class then worked in small groups to work on pages 181 and 182 to help improve their fluency with the skill.

In Math 6+, students had a multistep equation to solve upon entering into class. Students then worked with an enrichment piece from Lesson 4.1 to help deepen their understanding of equations and solutions.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• identify equations and variables.
• use substitution to find solutions to equations.

Day 46: Review What You Know - Introduction to Topic Four

During Math 6 -1°, students received their Topic Three Posttest back from the previous day. Mr. Giomini went through the assessment with the students. Mr. Giomini clarified any questions that the students may have had regarding the assessment. Topic Four - Represent and Solve Equations and Inequalities was introduced to the students. Students had an opportunity to show Mr. Giomini what they already knew about equations by completing some small tasks.

In Math 6+, students began to work with multistep equations that involved positive and negative numbers, decimals, fractions, and the distributive property.

Students in Math 6 - 3/7° spent time discussing different Properties of Equality before beginning Lesson 4.1: Understand Equations and Solutions.

Lesson Objectives: The student will be able to...

• understand solving an equation as a process.
• identify equations and variables.
• use substitution to find solutions to equations.

Day 45: Topic Three Posttest / Front-Load Topic Four

In Math 6(1°), students completed the Topic Three Posttest.

Students in Math 6(3/7°) and Math 6+ discussed their assessments from yesterday as well as front-loaded material for Topic Four.

 Lesson Objectives: The student will be able to...

• identify parts of an expression using mathematical terms (sum, term, factor, quotient, product, coefficient)
• evaluate expressions at specific values of their variables.
• perform arithmetic operations including those involving whole-number exponents.
• apply the properties of operations to generate equivalent expressions.
• identify when two expressions are equivalent.

Day 44: Test Preparation / Topic Three Posttest

In Math 6(1°), Mr. Giomini students spent time reviewing concepts for tomorrow's Topic Three Posttest.

Students in Math 6(3/7°) and Math 6+ completed the Topic Three Posttest.

 Lesson Objectives: The student will be able to...

• identify parts of an expression using mathematical terms (sum, term, factor, quotient, product, coefficient)
• evaluate expressions at specific values of their variables.
• perform arithmetic operations including those involving whole-number exponents.
• apply the properties of operations to generate equivalent expressions.
• identify when two expressions are equivalent.

Day 43: Simplify Algebraic Expressions / Topic Three Performance Task

In Math 6(1°), Mr. Giomini introduced Lesson 3.7: Simplify Algebraic Expressions. The focus of this lesson was to combine like terms in an attempt to simplify algebraic expressions. Students needed to identify like terms by using variables and coefficients. 

Students in Math 6(3/7°) and Math 6+ worked on the Topic Three Performance Task that is pictured below. 

 Lesson Objectives: The student will be able to...

• identify parts of an expression using mathematical terms (sum, term, factor, quotient, product, coefficient)
• evaluate expressions at specific values of their variables.
• perform arithmetic operations including those involving whole-number exponents.
• apply the properties of operations to generate equivalent expressions.
• identify when two expressions are equivalent.

Day 42: Generate Equivalent Expressions / Simplify Algebraic Expressions

Today, during Math 6(1°), students worked with Lesson 3.6: Generate Equivalent Expressions. To begin, Mr. Giomini introduced various properties of operations for the students to record in their notebooks. Modeling and knowing these provided the groundwork for the activity.

Students were then given an algebraic expression and asked to use one of the properties of operations to create an equivalent expression. To justify their equivalent expression, students needed to substitute multiply values to ensure that both provided the same value.

In Math 6(3/7°) and Math 6+, Mr. Giomini introduced Lesson 3.7: Simplify Algebraic Expressions. The focus of this lesson was to combine like terms in an attempt to simplify algebraic expressions. Students needed to identify like terms by using variables and coefficients. 

 Lesson Objectives: The student will be able to...

• identify parts of an expression using mathematical terms (sum, term, factor, quotient, product, coefficient)
• evaluate expressions at specific values of their variables.
• perform arithmetic operations including those involving whole-number exponents.
• apply the properties of operations to generate equivalent expressions.
• identify when two expressions are equivalent.