Topic Eight: Numerical Expressions, Patterns, and Relationships

Desired Results

Transfer:

1. Makes sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Established Goals:

5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

5.OA.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Pre-Requisite Skills:

4.OA.2:Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Student Friendly "I Can" Stataements

I can use parentheses and brackets in expressions.

I can write expressions I hear using ma thematic symbols and the order of operations.

Use numerical rules and patterns to form ordered pairs. Graph the ordered pairs on a coordinate plane.

Big Ideas:

Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.

Properties: For a given set of numbers there are relationships that are always true called properties, and these are the rules that govern arithmetic and algebra.

Variable: Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.

Solving Equations and Inequalities: Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations so solutions can be found.

Essential Questions:

How are the values of an algebraic expression and a numerical expression found?

Students will know...

Some mathematical phrases can be represented using a variable in an algebraic expression.

There is an agreed upon order for which operations in a numerical expression are performed.

To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplication and division calculations from left to right, followed by any addition and subtraction calculations from left to right.

Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

Patterns that repeat in predictable ways may be used to identify relationships.

Some mathematical phrases can be represented using a variable in an algebraic expression.

Some problems can be solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem.

Vocabulary: variable, algebraic expression, corresponding, sequence, term, order of operation

Students will be skilled at...

Writing numerical expressions with variables to represent relations expressed verbally.

Using given values for variables to evaluate numerical or algebraic expressions with three or more numbers and two or more operations.

Using the order of operations to simplify and solve basic algebraic expressions.

Using the order of operations to evaluate expressions with whole numbers and decimals.

Studying completed tables to determine a rule and write an expression.

Extending patterns in a table using given rules and looking for the relationship between corresponding terms in a sequence.

Translating words into algebraic expressions.

Solving problems by showing hot to act out the problem and using information given in the problem to draw conclusions.

Assessment Evidence

Performance Assessment:

Other Evidence:

Learning Plan

Learning Activities:

8-1: Some mathematical phrases can be represented using a variable in an algebraic expression.
8-2: There is an agreed upon order for which operations in a numerical expression are performed.
8-3: To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplication and division calculations from left to right, followed by any addition and subtraction calculations from left to right.
8-4: To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplication and division calculations from left to right, followed by any addition and subtraction calculations from left to right.
8-5: Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.
8-6: Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.
8-7: Extending patterns in a table using given rules and looking for the relationship between corresponding terms in a sequence.
8-8:Some mathematical phrases can be represented using a variable in an algebraic expression.
8-9:Some problems can be solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem.

## Topic Eight: Numerical Expressions, Patterns, and Relationships

## Desired Results

Transfer:1. Makes sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5.

Use appropriate tools strategically.6. Attend to precision.

7.

Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Established Goals:Pre-Requisite Skills:,e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.Student Friendly "I Can" StataementsBig Ideas:Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.Properties:For a given set of numbers there are relationships that are always true called properties, and these are the rules that govern arithmetic and algebra.Variable:Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.Solving Equations and Inequalities:Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations so solutions can be found.Essential Questions:How are the values of an algebraic expression and a numerical expression found?

Students will know...variable, algebraic expression, corresponding, sequence, term, order of operationVocabulary:Students will be skilled at...## Assessment Evidence

Performance Assessment:Other Evidence:## Learning Plan

Learning Activities:8-1: Some mathematical phrases can be represented using a variable in an algebraic expression.

8-2: There is an agreed upon order for which operations in a numerical expression are performed.

8-3: To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplication and division calculations from left to right, followed by any addition and subtraction calculations from left to right.

8-4: To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplication and division calculations from left to right, followed by any addition and subtraction calculations from left to right.

8-5: Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

8-6: Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

8-7: Extending patterns in a table using given rules and looking for the relationship between corresponding terms in a sequence.

8-8:Some mathematical phrases can be represented using a variable in an algebraic expression.

8-9:Some problems can be solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem.

Resources:Centers:Target Number Dash

Numerical Expressions Wall Clock

Verbal Expressions

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