Content Standard(s):
Mathematics 8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.
Unpacked Content
Evidence Of Student Attainment:
Students:
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
Interpret solutions of problems with rational numbers in the context of the problem.
Assess the reasonableness of answers using mental computation and estimation strategies.
Use variables to represent quantities in a real-world or mathematical problem. Teacher Vocabulary:
Rational numbers Integers Estimation Knowledge:
Students know:
techniques for converting between fractions, decimals, and percents.
Techniques for estimation, mental computations, and how to assess the reasonableness of their answers. Skills:
Students are able to:
convert between different forms of a rational number.
Add, subtract, multiply and divide rational numbers.
-translate verbal forms of problems into algebraic symbols, expressions, and equations.
Use estimation and mental computation techniques to assess the reasonableness of their answers. Understanding:
Students understand that:
One form of a number may be more advantageous than another form, based on the problem context.
Using estimation strategies helps to determine the reasonableness of answers. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.8.1: Define estimation, rational numbers, and reasonable.
M.7.8.2: Recall mental calculation strategies.
M.7.8.3: Recall estimation strategies.
M.7.8.4: Analyze the given word problem to set up a mathematical problem.
M.7.8.5: Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
M.7.8.6: Recognize the rules of operations of positive and negative numbers.
M.7.8.7: Recognize properties of numbers (Distributive, Associative, Commutative).
M.7.8.8: Recall problem solving methods.
Prior Knowledge Skills:
Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
Define integers, positive and negative numbers.
Define rational number.
Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 9. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. [Grade 7, 5]
Unpacked Content
Evidence Of Student Attainment:
Students:
Apply knowledge of addition and subtraction of rational numbers to describe real-world contexts.
Solve multi-step problems using numerical expressions that involve addition, subtraction, multiplication, and/or division of rational numbers, including problems that involve complex fractions. Teacher Vocabulary:
Rational numbers Complex fractions properties of operations Knowledge:
Students know:
Include situations involving elevation, temperature changes, debits and credits, and proportional relationships with negative rates of change.
Develop greater fluency with evaluating numerical expressions, using the properties of operations to increase their flexibility in approach. Skills:
Students are able to:
Interpret products and quotients of rational numbers by describing real-world contexts.
Solve real-world and mathematical problems involving the four operations with rational numbers. Understanding:
Students understand that:
it important to be able to write numeric expressions in multiple ways.
Rational numbers can represent values in real-world situations.
properties of operations learned with whole numbers in elementary apply to rational numbers Diverse Learning Needs:
Mathematics 17. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. [Grade 7, 8]
Unpacked Content
Evidence Of Student Attainment:
Students:
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
Interpret solutions of problems with rational numbers in the context of the problem.
Assess the reasonableness of answers using mental computation and estimation strategies.
Use variables to represent quantities in a real-world or mathematical problem. Teacher Vocabulary:
Rational numbers Integers Estimation Knowledge:
Students know:
Multiplying by 0.1 is the same as multiplying by 1/10 , the value of 10 percent can also be found by simply dividing by 10.
1% = 0.01 = 1 100 .
Since multiplying by 0.01 is the same as multiplying by 1/100 , the value of 1 percent can also be found by simply dividing by 100.
Adding a percent of a number onto the original number is the same thing as adding that percent to 100 and then finding that new percent of the number.
Finding more than 100% of a number must yield an answer that is larger than the original number. Skills:
Students are able to:
Convert between different forms of a rational number.
Add, subtract, multiply and divide rational numbers. Understanding:
Students understand that:
One form of a number may be more advantageous to use in a problem context than another form.
Using estimation strategies helps to determine the reasonableness of answers.
Finding one percent or ten percent of a number can facilitate solving percent problems. Diverse Learning Needs:
