Essential Questions:
Lesson Plan B.7: Writing and Solving Equations
Lesson Seed B.5: Treasure Hunt
Lesson Seed B.6: Pool Problem
Lesson Seed B.7: Write and Solve Equations
Unit Overview
Content Emphasis By Clusters in Grade 6
Progressions from Common Core State Standards in Mathematics
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Students begin to understand that solving an equation or inequality is the process of substituting values for given variables that make the equation or inequality true. Students focus on solving equations that represent authentic situations in the forms of x + p = q and of px = q, where these variables represent nonnegative rational numbers. Similarly, students write inequalities that represent authentic situations with constraints or specific conditions in the forms of x > c or x < c.
At the completion of this unit on applying and extending students’ previous understanding of arithmetic to algebraic expressions, the student will understand that:
The student will be able to:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Students may
Interdisciplinary Connections:
Interdisciplinary connections fall into a number of related categories:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
Part I – Focus Cluster Represent and Interpret Data Reason About and Solve One-Variable Equations and properties of equality:
Rules which allow you to balance, manipulate, and solve equations.
Reflexive property: x = x Example: 2 = 2 or I am equal to myself
Symmetric property: If x = y, then y = x Example: Suppose fish = tuna, then tuna = fish
Transitive property: If x = y and y = z, then x = z Example: Suppose John's height = Mary's height and Mary's height = Peter's height, then John's height = Peter's height
Addition property: If x = y, then x + z = y + z Example: Suppose John's height = Mary's height, then John's height + 2 = Mary's height + 2 Or suppose 5 = 5, then 5 + 3 = 5 + 3
Subtraction property: If x = y, then x − z = y – z Example: Suppose John's height = Mary's height, then John's height − 5 = Mary's height − 5 Or suppose 8 = 8, then 8 − 3 = 8 − 3
Multiplication property: If x = y, then x × z = y × z Example: Suppose Joe's weight = Dana's weight, then Joe's weight × 4 = Dana's weight × 4 Or suppose 10 = 10, then 10 × 10 = 10 × 10
Division property: If x = y, then x ÷ z = y ÷ z Example: Suppose Joe's weight = Dana's weight, then Joe's weight ÷ 4 = Dana's weight ÷ 4 Or suppose 20 = 20, then 20 ÷ 10 = 20 ÷ 10
Substitution property: If x = y, then y can be substituted for x in any expression Example: x = 2 and x + 5 = 7, then 2 can be substituted in x + 5 = 7 to obtain 2 + 5 = 7
Part II – Instructional Connections outside the Focus Cluster
measurement concept: This is referring to division of fractions. Reviewing,4 ÷ 3 with this concept means, “How many sets of 3 are in 4?” If you have 4 pints of ice cream to divide among 3 people, how much does each person receive?
partition concept: Modeling a quotient, using the partitive concept, requires that only the dividend be modeled. The divisor represents the number of equal parts into which the dividend is to be partitioned. Thus, the modeling materials representing the dividend are rearranged, partitioned, or sub-divided into equal groups. The quotient is the number shown in each of the equal groups. Due to the very nature of the partitive concept, the divisor of a quotient must be a whole number ≥ 2.
So 1 ^{1}/_{2} can be divided into 6 equal groups by dividing each part in 6 equal pieces. Take 1/6 of each part and add those together.
Each group is equal to ^{1}/_{4}. If, after some of the materials are rearranged into equal groups, there are materials remaining, the remaining materials should be traded for equivalent smaller pieces and the partitioning continued. If a number, less than the divisor, of the smallest pieces in your model remain after the partitioning has been completed, a fraction may be expressed where the remainder (the remaining number of smallest pieces) is the numerator and the divisor is the denominator. The quotient is the number in each equal set plus this fraction.
common denominator algorithm: The common-denominator algorithm is repeated subtraction concept of division. Example : ^{5}/_{4} ÷ ^{1}/_{2}
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