In this learning activity, students will learn to solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. The students will apply properties of operations to calculate numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.
This learning activity can be used as a stand-alone activity but is best used as a Before Activity, the During and After Activities can be found in the Tools or Recommendations section.
In this learning activity, students will learn to solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. The students will apply properties of operations to calculate numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. This learning activity can be used as a stand-alone activity but is best used as a During Activity, the Before and After Activities can be found in the Notes or Recommendations section.
Students will use the Quizizz response system to review solving multi-step problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) and to use tools strategically. This Multi-Step Real-Life and Mathematical Practice Problems Quizizz game has fifteen questions to test the understanding of solving multi-step real-life problems and is intended to be used as an after-activity. Quizizz allows the teacher to conduct student-paced formative assessments through quizzing, collaboration, peer-led discussions, and presentation of content in a fun and engaging way for students of all ages.
(This learning activity can be used as a stand-alone activity but is best used as an After Activity, the During and After Activities can be found in the Notes or Recommendations section.)
In this video lesson, students recall one way of understanding equivalent expressions, that is, the expressions have the same value for any number substituted for a variable. Then they use properties they have learned to write an equivalent expression using fewer terms. Students informally practice combining like terms, though the language is not yet introduced.
In this video lesson, students are working toward gaining fluency in writing equivalent expressions. The goal of this lesson is to highlight a particularly common error: mishandling the subtraction in an expression like 8–3(4+9x). To this end, students first analyze and explain the error in several incorrect ways of rewriting this expression. Then, they consider the effect of inserting parentheses in different places in an expression with four terms.
In this video lesson, students have an opportunity to demonstrate fluency in combining like terms. They also look for and make use of structure (MP7) to apply the distributive property in more sophisticated ways.
In Module 3, Topic B, students use linear equations and inequalities to solve problems. They continue to use bar diagrams from earlier grades where they see fit but will quickly discover that some problems would more reasonably be solved algebraically (as in the case of large numbers). Guiding students to arrive at this realization on their own develops the need for algebra. This algebraic approach builds upon work in Grade 6 with equations (6.EE.B.6, 6.EE.B.7) to now include multi-step equations and inequalities containing rational numbers (7.EE.B.3, 7.EE.B.4). Students solve problems involving consecutive numbers, total cost, age comparisons, distance/rate/time, area and perimeter, and missing angle measures. Solving equations with a variable is all about numbers, and students are challenged with the goal of finding the number that makes the equation true. When given in context, students recognize that a value exists, and it is simply their job to discover what that value is. Even the angles in each diagram have a precise value, which can be checked with a protractor to ensure students that the value they find does indeed create a true number sentence.
