Mathematics Curriculum Guide Fifth Grade GO- Math! - Investigations August 14 - October 9, 2014 Unit 1 Suggested Pacing: First Nine Weeks- 40 days (40-55 Minutes on Routines and Lesson) Unit At A Glance: The focus of this unit is to develop ideas and meaning of operations with whole numbers, the development of computational fluency, the structure of place value and base-ten number system, and generalizations about numbers and operations. This unit assumes students know addition combinations and related subtraction problems and are fluent with addition strategies for solving multi-digit problems. In order to access all available resources, click on the hyperlink by holding down the Ctrl key. Once the small hand appears, click on the mouse (you must hold the ctrl key as you click). ACOS/CCRS Standard- Prepares students for: Operations and Algebraic Thinking Write and interpret numerical expressions. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5-OA] 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2] Examples: Express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product. Analyze patterns and relationships. 1
3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5-OA3] Example: Given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Number and Operations in Base Ten Understand the place value system 4. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. [5- NBT1] 5. Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. [5-NBT2] 6. Read, write, and compare decimals to thousandths. [5-NBT3] Perform operations with multi-digit whole numbers and with decimals to hundredths. 8. Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5] 9. Find whole-number quotients of whole numbers with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5-NBT6] 10. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5-NBT7] Use equivalent fractions as a strategy to add and subtract fractions. 11. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5-NF1] Example: 2/3 + 5/4= 8/12 + 15/12= 23/12. (In general, a/b+c/d=b + cd = ( ) ad bcbd+.) Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 2
13. Interpret a fraction as division of the numerator by the denominator (ab = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5-NF3] Examples: Interpret 3/4 as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between which two whole numbers does your answer lie? Represent and interpret data. 19. Make a line plot to display a data set of measurements in fractions of a unit ( ½,1/4, 1/8).Use operations on fractions for this grade to solve problems involving information presented in line plots. [5-MD2] Example: Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. 22. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume. [5-MD5] 26. Classify two-dimensional figures in a hierarchy based on properties. [5-G4] Essential Question(s): Essential questions causes genuine and relevant inquiry into big ideas, generates deep thought, provokes meaningful connections to prior experiences and lively discussion. How can you describe the relationship between two place-value positions? How do you read, write, and represent whole numbers through hundred millions? How can you use properties of operations to solve problems? How can you use a basic fact and a pattern to multiply by a 2-digit number? Learning Objective(s): I can statements provide students with the verbiage needed to understand their learning adventure. These powerful statements give students the opportunity to take control of their learning. I can use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. I can fluently multiply multi-digit whole numbers using the standard algorithm. I can interpret a fraction as division of the numerator by the denominator. Key Vocabulary: Content Specific: evaluate compare period numerical expression order of operations distributive property 3
base exponent inverse operation *Please add vocabulary to word wall For suggestions on how to effectively implement a word wall please visit http://olc.spsd.sk.ca/de/pd/instr/strats/wordwall/index.html See glossary from Curriculum Guide to the Alabama Course of Study: Mathematics March 2012- page 190 for additional vocabulary and definitions Assessments: During the implementation of this unit teachers will use a variety of assessment strategies to check for understanding in an effort to differentiate instruction that caters to the needs of students. The following bulleted items are examples of summative and formative assessments that can be used during the implementation of this unit. Formative assessments can be used to adjust teaching and learning while they are happening within the classroom. They also inform both teachers and students when instructional adjustments should be made and helps teachers determine next steps during the learning process. Summative assessments can be used to gauge students learning relative to content standards. They are given to determine what students have mastered. Some examples of summative assessments include, but are not limited to the following: state assessments, district benchmarks, weekly test, end of unit tests, and end of term exams. Summative Assessment I: Pre-Test, August 25- September 5, 2014 Post-Test, October 1-15, 2014 Beginning of Course Assessment located at www.pearsonsuccessnet.com (Located under the Success Tracker heading) Investigations Beginning of Year Test (TE) Assessment Guide p.7 Introduction/Pretest GO Math! 4
On-line Assessment System for GO Math! Lesson Quick Check Mid-Chapter Checkpoint Chapter Review/Test Performance Assessment Chapter Test Math Journals- Student should journal at least two times a week- refer to pacing guide for relevant journal topics. Instructional Considerations: Students can complete the data collecting activity in their journals. For data collecting activities visit mathematics resources found www.bhm.k12.al.us under Mathematics Resources for fifth Grade. [5-MD5] *These activities can be displayed on the promethean board via computer with internet access. The document camera is an excellent way to project a read aloud story via promethean board. The clickers can be used with a variety of lessons from promethean planet. Think Aloud-[5-NBT5] Purpose Monitor comprehension of a mathematical concept and direct thinking. Procedure 1. Teacher write a multistep problem on the board and begin computing it while periodically stopping explaining each significant step. Teacher model the use of computational fluency and mathematics vocabulary 2. Student then practice think aloud with a partner Question-Answer Relationship (QAR) is a way to help students realize that the answers are related to the type of question that is asked; it encourages them to be strategic about their strategies for computing answers. [5-OA] 1. Right There- explain the some computations require mental math and there is no pencil and paper calculation needed. 2. Think and Search- Some mathematical problems require grasp of multiple conceptsexplain that in those situation student should use what they know to figure out the 5
unknown. 3. Partner and You- Offers opportunities for students to use each other a resource to gather understanding of mathematical concepts. How to Teach Fractions-[5-NF1] http://www.mathgoodies.com/articles/teach_fractions.html http://www.teachingideas.co.uk/maths/contents_fractions.htm Differentiation: Intervention: Interactive Notebook activity. Students will identify fractional parts using colors of any multi-colored item. Possible items may be a handful of fruit loops, skittles, and/or poms. Teacher may use any item they feel will work for this activity. On Level: Table Talk Purpose: 1. Activate prior computational knowledge 2. Encourage active listening 3. Create a plan to solve a problem Procedure: 1. Write a thought provoking mathematical equation for student to see, in pairs or any grouping of your choice allow student talk time to discuss the problem, type of problem, best strategies to solve the problem quickly and efficiently. 2. Student are allowed time to solve the problem. 3. Student s share their response with partner or group to determine accuracy. Acceleration: Student are given opportunities to be peer leaders by assisting students who need extra assistance with particular mathematics concepts. 6
Accommodations: ELL/SPED The descriptors found at www.wida.us/standards/can DOS/ provide a starting point for working with ELL. It serves as a tool for planning. The descriptors provide continuum of English language development. As teachers become aware of their students English levels of proficiency, the descriptors provide sensory, graphic, and interactive support needed to facilitate ELL access to content. Proximity seating, manipulatives/calculator, visual aids/flash cards, auditory aids/tape recorder, peer tutoring, frequent comprehension checks, repeated directions (orally) for understanding, verbal prompts, guided repetition, modeling, flow charts, cue cards with problem-solving strategies, and/or examples. Additional accommodations may be specific to the student s specially designed instruction within the IEP. Technology: (Hardware) (Software) Promethean Board Promethean Clickers Document Camera computer *See instructional considerations for suggestions on how to incorporate into daily practice. Investigations-Digital Resources Go Math! Digital Patch Materials Investigations Materials Student Math Handbook Supplemental Resources What Fraction of this shape is red? Online Resources *The information contained in these websites is for educational purposes only. We make no representations or warranties of any kind, express or implied, about the completeness, accuracy, reliability, suitability or 7
Student Activity Book Scott Foresman GO Math! Materials GO-Math! Centers Kit GO Math!- TE- Chapter 1-2 https://www.teachingch annel.org/videos/teachin g-fractions Multiplying Whole Numbers and Fractions https://www.teachingch annel.org/videos/multipl ying-fractions-bywhole-numbers-lesson availability with respect to the sites. http://www-k6.thinkcentral.com www.alex.alsde.edu http://funkyfractionsforfifthgrade.wo rdpress.com/lesson-plans/ A Passion for Fractions https://www.teachingch annel.org/videos/multipl ying-fractions-lesson Teacher Notes: As you welcome your students to fifth grade consider the implementation of this unit will require the use of several manipulatives. Allow time to prepare these materials prior to teaching each lesson. An easy way to accomplish this is to have your manipulatives labeled with clearly visible easy to read labels. Create a classroom job as materials distributor/ collector. Teach the class a routine on how to retrieve, pack, and store manipulatives, and use it consistently. Manipulatives can be kept in small trays for cooperative group use and 8
distributed as needed. Please consider introducing each manipulative that student will use for the first time prior to your instruction, This introduction will erase the excitement and allow you to gather and keep student attention when it s time to use the material. It is also an opportunity to create excitement about the next day s lesson. Reading and writing in the mathematics classroom is essential. During the implementation of this unit consider the following books as a springboard for literacy during mathematics instruction. Childrens mathematics picture books Division and fractions Geometry Multiplication Time Ordinal numbers Size Subtraction is an acronym for Science, Technology, Engineering and Math education. We focus on these areas together not only because the skills and knowledge in each discipline are essential for student success, but also because these fields are deeply intertwined in the real world and in how students learn most effectively. STEM is an interdisciplinary and applied approach that is coupled with hands-on, problem-based learning.*check out this site which uses a sample lesson plan to show you how to break down a lesson to integrate STEM. Common Core Standards for Mathematical Practices is a way to approach teaching so that students develop a mathematical mindset and see math in the world around them. We are making problem-solvers. No matter what your objectives, textbook, or grade level, the eight mathematical practice standards are a guide to good math instruction. Please view the following link for explanation, examples and suggestions on how to implement into your practice. 9
http://www.scholastic.com/teachers/top-teaching/2013/03/guide-8-mathematical-practice-standards Looking Forward Fifth grade students will find patterns in products when multiplying by powers of 10. They will also model multiplication of whole numbers and decimals. [CC.5.NBT.7] 10
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