# Unit 6 expressions and equations answers

This week your student will be learning to visualize, write, and solve equations. They did this work in previous grades with numbers. In grade 6, we often use a letter called a variable to represent a number whose value is unknown. Diagrams can help us make sense of how quantities are related. Here is an example of such a diagram:. Expand Image. A solution to an equation is a number used in place of the variable that makes the equation true. In the previous example, the solution is 5. Solving an equation is a process for finding a solution.

This week your student is writing mathematical expressions, especially expressions using the distributive property.

Rectangle A has a vertical side length of 3 and horizontal side length of 2. Rectangle B has a horizontal side length of x. The large rectangle can be partitioned into two smaller rectangles, A and B, with no overlap. Draw and label a partitioned rectangle to show that each of these equations is always true, no matter the value of the letters.

This week your student will be working with exponents. In this example, 7 is called the base. The exponent tells you how many factors of the base to multiply. In grade 6, students write expressions with whole-number exponents and bases that are. Find the solution to each equation from the list provided.

This week your student will study relationships between two quantities. Points located at 1 comma 25, 2 comma 50, 3 comma 75, 4 comma5 commaand 6 comma Unit 6 Family Materials Expressions and Equations. Equations in One Variable. Here is an example of such a diagram: Expand Image. Equal and Equivalent. Expressions with Exponents.

What would we have to divide by 9 to get 27? Relationships Between Quantities.Quadratic Equations. Unit 6: Quadratic Equations. After this unit, how prepared are your students for the end-of-course Regents examination? The end of unit assessment is designed to surface how students understand the mathematics in the unit. It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.

Please comment below with questions, feedback, suggestions, or descriptions of your experience using this resource with students. Big Idea 1: Quadratics can be written in multiple, equivalent ways.

Big Idea 2: Quadratic equations have 0, 1 or 2 real solutions. Big Idea 3: Quadratic equations can be solved by rearranging the equation into an equivalent form.

## Grade 6 » Expressions & Equations

Big Idea 4: The structure of a quadratic equation provides insights about its key characteristics. Re-engagement for Unit 6. Browse Components. End of Unit Assessment:. Open Resource. End of Unit Assessment. Teacher Feedback Please comment below with questions, feedback, suggestions, or descriptions of your experience using this resource with students. All Resources From:.For this lesson I want students to review the vocabulary of the previous lesson.

I ask students to share which answers are incorrect for and how they know. For 1, a common mistake I see is that students select c as there answer, not realizing that k-8 and 8-k are two distinct expressions. I created problem 3 so that students are thinking about the relationship between the number of tickets purchased and the cost. After the Do Now, I have a student read the objectives for the day. I tell students that they will be creating expressions and equations to model situations.

### Expressions & Equations

To get students making the connections between skills in manipulating numbers and variables, I have students work on the problems on page 2. Typically my students are able to easily answer a-d for the first situation. Some students struggle to take those same skills and use them with variables, like in the second example. If he is x years old now, how old will he be in 4 years? If students continue to struggle, I make connections back to the first example.

How did you find out how old Ms. Palmer was 5 years ago? I am looking for students to say that they subtracted 5 from 28 to get Then I push students to apply that same strategy to find Mr.

After students have had a few minutes to work, we review the answers. I give students values for Mr. What if Mr. What if he is 41 years old now?

Students are using substitution to find the answers. In this lesson students will set the foundation for the next two lessons where they are writing expressions and equations to model situations and then using those equations to answer further questions. I have a student read the first paragraph on p.

I ask a series of questions to help students write an expression. For each visitor that comes to the farm, they collect how much money? How much money would they collect if there were 6 visitors? Then how can we represent the amount of money they will collect if there are n visitors?

I want students to connect the operation they are using to answer questions with numbers to the expression. I ask for different ways to write the expression switching the order of the number and variable, using a dot, using parentheses, using 8n. I tell students that they need to substitute values for n into the expression in order to find the amount of money collected.In Module 6, students delve further into several geometry topics they have been developing over the years.

Grade 7 presents some of these topics, e. Module 6 assumes students understand the basics. The goal is to build a fluency in these difficult problems. The remaining topics, i. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials. Resources may contain links to sites external to the EngageNY. Skip to main content. Find More Curriculum Print. Grade 7 Mathematics.

Grade 7 Mathematics Module 6. Grade 7 Module 6: Geometry In Module 6, students delve further into several geometry topics they have been developing over the years. The student materials consist of the student pages for each lesson in Module 6. Like Grade 7 Mathematics Module 6: Teacher Materials Related Resources Resource Document. Curriculum Map Toggle Module 1 Module 1. Lesson 1. Lesson 2. Lesson 3. Lesson 4.Juliani - 14 Projects! Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials.

Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? All Categories. Grade Level. Resource Type. Log In Join Us. View Wish List View Cart. Results for expressions and equations project Sort by: Relevance. You Selected: Keyword expressions and equations project. Grades PreK. Other Not Grade Specific. Higher Education. Adult Education. Digital Resources for Students Google Apps. Internet Activities. English Language Arts. Foreign Language. Social Studies - History. History World History. For All Subject Areas. See All Resource Types. Expressions and Equations Project. Make math meaningful with this no prep real world expressions and equations mini-project and classroom makeover! In this project, students work at a coffee shop while practicing their skills at writing expressions, solving equations, and working with inequalities.

If you so choose, there are also in. WorksheetsProjects. Add to cart. Wish List.Turn content from Match Fishtank lessons into custom handouts for students in just a few clicks. Download Sample. The essential concepts students need to demonstrate or understand to achieve the lesson objective.

Understand that in the process of solving for a variable, whatever is done to one side of the equation must also be done to the other side in order to maintain the balance. Use models and diagrams to solve for a variable.

Solve one-step addition and subtraction equations algebraically. Write and solve one-step addition and subtraction problems for real-world contexts. Students first solve equations by using diagrams; they then generalize their actions to solve equations algebraically without diagrams. Though some students may find they can mentally solve these equations, encourage students to organize and show their thinking algebraically.

This will support them later as the equations become more and more complex. Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding. Do the answers you get from the diagrams match the answer you got from mentally solving the problem?

How are you keeping the balance in the equation? Students should understand that as they work with equations, they should do the same on both sides to maintain the equality. This would provide the opportunity for students to use precise language in explaining their solution process MP. As the equations become more complex in seventh and eighth grades, students often work vertically, so it is helpful to introduce this approach in sixth grade; however, with one-step equations, some students may benefit from seeing a horizontal approach.

### Working with Expressions and Equations Part 1

See EngageNY for examples of a horizontal approach. Describe a real-world situation that could be represented by the equation. How is this problem different from Anchor Problem 1? How is this problem similar to Anchor Problem 1? Accessed Dec. Name a value that is too high and name a value that is too low.

A set of suggested resources or problem types that teachers can turn into a problem set. Worksheet of practice problems related to the objective of the lesson. To edit this document use the student handout editor.

The following resources include problems and activities aligned to the objective of the lesson. They can be used to create a problem set for class for non-Fishtank Plus usersor as supplementary or additional resources to the pre-made Problem Set for Fishtank Plus users. Include problems with procedural practice in solving addition and subtraction problems.

Include problems where students write an equation from a context addition or subtraction only and solve the equation. Include error analysis problems of mistakes made in solving equations.Apply and extend previous understandings of arithmetic to algebraic expressions. A : Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

B : Identify parts of an expression using mathematical terms sum, term, product, factor, quotient, coefficient ; view one or more parts of an expression as a single entity. C : Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.

Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order Order of Operations. Reason about and solve one-variable equations and inequalities. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Represent and analyze quantitative relationships between dependent and independent variables.

Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. All links are deemed relevant and are not placed merely for profit. Purchase through these links helps to keep this educational website online and free. Grade 1. Grade 2. Grade 3. Grade 4. Grade 5. Grade 6.

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