Numbers and Operations

Transcription

1 Grade 7 MATH Unit Number 1 Numbers and Operations Title Big Ideas/Enduring Understandings Problems can be solved easier when using variety of equivalent forms. All numbers fall within the real number system. Suggested Time Frame 1 st Six Weeks 15 Days Guiding Questions How do I add and subtract with rational numbers? How do I multiply and divide with rational numbers? To what extent can rational numbers represent real world concepts? Where do numbers fit in the real number system? *TEKS one level below* Vertical Alignment Expectations TEA Vertical Alignment 5 th Grade Algebra I Sample Assessment Question *TEKS one level above* COMING SOON The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material.

2 Ongoing TEKS Math Processing Skills 7.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; Focus is on application (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; Students should assess which tool to apply rather than trying only one or all (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas (F) analyze mathematical relationships to connect and communicate mathematical ideas; and Students are expected to form conjectures based on patterns or sets of examples and non-examples (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Precise mathematical language is expected.

3 Knowledge and Skills with Student Expectations District Specificity/ Examples Vocabulary Supplemental Vocabulary: Rational Number, Bar Notation, Common Denominator, Least Common Multiple, Least Common Denominator, Repeating Decimal, Nonrepeating Decimal, Unlike Fraction, Dividend, Divisor, Terminating Decimal, Reciprocal, Multiplicative Inverse, Reasonableness, Justify, Absolute Value, Zero Pair, Evaluate, Simplify, Irrational Numbers, Real Numbers Expected Learner Outcomes Describe integers as quantities. Define sets and subsets of real numbers counting numbers, whole numbers, integers, rational numbers and irrational numbers using a graphical representation such as a Venn Diagram. Select an appropriate form of rational number to solve real-life problems. Based on the problem situation (context clues), select and use an appropriate operation to solve problems. Explain and justify the selection of operations and the problemsolving process used to solve problems. Apply a problem-solving method to solve multi-step problems. Use vocabulary such as integers, place value, greater than, less than, equal or equivalent and absolute value. Describe the order of operation in a given numerical expression including integers. Simplify numerical expressions using order operations (parentheses, exponents, multiply, divide, add, and subtract) Integers Negative Nonnegative Nonpositive Positive Rational numbers Sets Subsets Venn Diagram Whole Numbers Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. Chapter 1 Mathematical Processes Handbook Web Resources: Region XI: Livebinder NCTM: Illuminations

4 including integers. Based on the problem situation (context clues), select an appropriate operation to solve the problem. Explain and justify the selection of operation, problem-solving process, and reasonableness of answer, especially in terms of the estimate. Use a variety of techniques to evaluate the reasonableness of a solution. TEKS Clarifications: 7.02 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. 7.02A In 6th grade, students classify sets of numbers (whole, integers, and rational numbers). In 7th grade, the verb changes to describe relationships between sets of rational numbers. Students need to have experiences using visual representations (such as a Venn diagrams) to classify number systems

5 Common Misconceptions: 1. Knowing only a limited number of models for interpreting fractions; for example, not recognizing fractions as locations on a number line or as division calculations. 2. Understanding the symbol - Used to signify subtraction and a negative Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. 7.03A - add, subtract, multiply, and divide rational numbers fluently 7.03B - apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers 7.03AB Extend the fluent computation with positive rational numbers from 6th grade to 7th grade by now including all rational numbers (includes negative). Apply rational number operations in problem situations. Students will need to have a solid understanding of integer rules to be able to apply to rational numbers. While students need to be fluent in operations with both positive and negative rational numbers, the application problems will may tend to focus on positive numbers for meaningful examples, such as change in temperature, stock market loss and gains Chapter 1 Mathematical Processes Handbook Web Resources: Region XI: Livebinder NCTM: Illuminations

6 Example 1: A recipe that makes 1.5 dozen cookies requires 0.75 cups of sugar. Shanika wants to make 6 dozen cookies. How many cups of sugar will she need? Example 2: Ocean water freezes at about degrees C. Fresh water freezes at 0 degrees C. Antifreeze, a liquid used to cool most car engines, freezes at 64 degrees C. Imagine that the temperature is exactly at the freezing point for ocean water. How many degrees must the temperature drop for the antifreeze to turn to ice? Common Misconceptions: 1. Students may believe that all rational numbers are positive. 2. Students have trouble using models to illustrate operations or to connect operations on objects to algorithms.