Subject Math Grade Level 3 rd Mission Statement K-12 Mission Statement for <subject area: ie, English Language Arts (ELA); mathematics; science, social studies> Mission Statement for math: A standards-based math education at Littlestown Area School District will provide authentic experiences where students connect with their world by applying and integrating mathematical concepts throughout their daily experiences. On a social level, our mathematicians will be collaborative as well as independent, risk- takers, who are self-motivated and confident. o Therefore, students will have opportunities for authentic learning experiences where they will work together to transfer and apply math concepts to real world math problems. Assessments should be ongoing, diagnostic, and aligned with instruction. o Therefore, students will engage in multiple authentic assessment opportunities. Students will be lifelong learners. o Therefore, we will facilitate instruction and curriculum designed to develop students, who will be informed and active problem solvers. Instruction should be relevant, meaningful, and evidence-based. o Therefore, we will facilitate differentiated instruction and assessments based on evidence collected throughout the student experience. Course Description What is it that students will learn during this course? This module builds upon the foundation of multiplicative thinking with units started in grade 2. First, students concentrate on the meaning of multiplication and division and begin developing fluency for learning products and representing and solving problems involving multiplication and division involving factors of 2, 3, 4, 5, and 10. The restricted set of facts keeps learning manageable, and also provides enough examples to do one- and two-step word problems and to start measurement problems involving weight, money, length, capacities, and time in the second module.
Subject Math Grade Level 3 rd Title of Unit Unit 1 Multiplication and Division with Factors of 2, 3, 4, 5, and 10 Time Frame Stage 1 - Desired Results 6 Weeks Established Goals (Learning Outcomes) What content standards (designate focus standards with an F ) and program- or mission-related goal(s) will this unit address? What habits of mind and cross disciplinary goals will this unit address (example 21 st Century Skills)? Focus Standard: CC.2.2.3.A.1 Represent and solve problems involving multiplication and division. CC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division. CC.2.2.3.A.3 Demonstrate multiplication and division fluently. Important Standards: CC.2.1.3.B.1 Apply place value understanding and properties of operations to perform multi-digit arithmetic. CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Transfer What kinds of long term independent accomplishments are desired? Students will be able to independently use their learning to.. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure (Deductive Reasoning) Look for and express regularity in repeated reasoning (Inductive Reasoning) Meaning
Enduring Understandings What understandings about the big ideas are desired? What misunderstandings are predictable? Students will understand that... Essential Questions What provocative questions will foster inquiry, meaning-making and transfer? Students will keep considering. 1. The use of models is essential in helping students eliminate this understanding. 2. Presenting students with multiple situations in which they select the symbol and explain its meaning. 3. What the symbol represents will counter this misconception. Related misconceptions 1. Students think a symbol (? or []) is always the place for the answer. This is especially true when the problem is written as 15 3=? or 15=[]x3. 2. Students also think that 3 15=5 and 15 3=5 are the same equations. 3. The use of a symbol to represent a number once cannot be used to represent another number in a different problem/situation. How can multiplication and division be used to solve real world problems? How can the same array represent both multiplication and division? How can we connect multiplication facts with their array models? How can we model division? How can we model multiplication? How can we use patterns to solve problems? How can we write a mathematical sentence to represent a multiplication model we have made? How can we write a mathematical sentence to represent division models we have made? How is the commutative property of multiplication evident in an array model? Is there more than one way of multiplying to get the same quotient? What are strategies for learning multiplication facts? What do the parts of a division problem represent? What is the relationship between the divisor and the quotient? What facts and basic concepts should students know and be able to recall? This content knowledge may come from the established goals or address pre-requisite knowledge essential for this unit. Acquisition What discrete skills and processes should students be able to use? List the skills and/or behaviors students will be able to exhibit as a result of their work in this unit. Students will know... Students will be skilled at Place value and properties of operations Vocabulary: Division Estimate Multiplication Associative Property of Addition demonstrating an understanding of the relationship between multiplication and division. demonstrating fluency. identifying and explaining patterns in arithmetic (including addition and subtraction). representing and solving problems.
Quotient Column Commutative Property of Addition Difference Digit Equation Even Number Factor Multiple Inverse Operations Number Line Odd Number Order of Operations Parentheses Reasonableness Row Subtract Variable Fact family Product Related facts Sum Zero Property of Multiplication Pattern Unknown Square number Array Divisor Stage 2 Evidence Performance Task Through what authentic performance task will students demonstrate the desired understandings, knowledge, and skills? By what criteria will performances of understanding be evaluated? Students will show their learning by The students will solve several multiplication and division word problems. Other Evidence Through what other evidence (work samples, observations, quizzes, tests, journals Student Self-Assessment How will students reflect upon or self-assess their learning?
or other means) will students demonstrate achievement of the desired results? LITTLESTOWN AREA SCHOOL DISTRICT January 2015 Adapted from: Wiggins, G. and McTighe, J., (1998). Understanding by Design. Alexandria, VA: ASCD.