unit iv: evolution - mountain lakesfc.mtlakes.org/.../fav2-00102e40/fov2-0… · web view ·...

3RD Grade MathCourse Description and Philosophy

In Grade 3, instructional time will focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes. The course has been updated to meet the 2010 Common Core Math Standards for 3rd Grade Math. http://www.corestandards.org/Math/Content/3/introduction

Throughout the year, students focus on development of problem solving strategies, rote knowledge of facts, and understanding of math through writing, illustrating, and discussing concepts. Math is taught using a combination of text-based lessons, teacher-directed activities, and hands-on learning centers. This course is intended for all students. Basic problem-solving strategies are reinforced throughout each unit including: looking for patterns, making tables, drawing a picture, guessing and checking, using manipulatives, role-playing, and using logical reasoning.

Evaluation of studentsʼ performance will be conducted utilizing pre-testing and post-testing for each unit, on-going facts review and quizzes, homework, class participation, mid-year cumulative test, and end-of-year state testing results.

Teacher Resources: Illustrative Mathematics Content Standards: High School http://www.illustrativemathematics.org/standards/k8 The Teaching Channel (Common Core Math Channel) https://www.teachingchannel.org/videos?

page=1&categories=subjects_math,topics_common-core&load=1 The Mathematics Common Core Toolbox (http://ccsstoolbox.agilemind.com/resources_samples.html) has both sample scope and sequence

documents as well grades 4-12 PARRC assessment tasks.

Text Reference:enVisionMath 2012 Pearson Education, Inc. Upper Saddle Rover, NJ/ USA

Written 2013

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http://ccsstoolbox.agilemind.com/resources_samples.html

https://www.teachingchannel.org/videos?page=1&categories=subjects_math,topics_common-core&load=1



http://www.illustrativemathematics.org/standards/k8

http://www.corestandards.org/Math/Content/3/introduction

Unit I: Place ValueEssential Question: How do you use place value understanding and properties of operations to perform multi-digit arithmetic?

Objectives: Students will be able to: Read and write numbers in the hundreds Explore place value relationships Read and write numbers through thousands Read and write numbers through hundred thousands Understand, identify, and write numbers in expanded, standard, and word form Compare whole numbers Order numbers Round 2-digit and 3-digit numbers to the nearest 10 Round numbers to the nearest hundred and up to hundred thousands Understand & use Place Value terminology: place value, digits, expanded, standard, word form, period, compare, order, estimate & round Identify patterns on a number line and calculate the missing number

Unit I: Topic/Content Skills Assessment Resources Instructional Method

Tech Infusion CCS: Unit 1

Topic 1: Numbers Through Hundred Thousand

Test/QuizzesHome/ClassworkClass ParticipationProjects

TextResource booksManipulatives

Whole-group instructionHands-On ActivitiesDiscussionGroup Collaboration

www.firstinmath.comwww.aaaknow.com/grade3 Smart Exchange

3.NBT.A.1

Topic 2: Ordering Numbers Test/QuizzesHome/ClassworkClass ParticipationProjects




3.NBT.A.2

Topic 3: Rounding Numbers Test/QuizzesHome/ClassworkClass ParticipationProjects




3.NBT.A.1

Topic 4: Adding and subtracting





3.NBT.A.2

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http://www.aaaknow.com/grade3


http://www.firstinmath.com/










Differentiated Learning ActivitiesTo promote differentiation among students, view this Teaching Channel video, Sharing Strategies for Counting Collections. Watch how the teacher differentiates with students by abilities to help them record and share strategies when skip counting. https://www.teachingchannel.org/videos/counting-collections-lesson

Ethical Decision Making/Character EducationExploring where and when numbers become rounded to make problems easier to solve promotes discussion in social groupings, self-awareness and allows for connections to world and self.

21st Century Skills: Initiative and Self-Direction OUTCOME: Students monitor, define, prioritize, and complete tasks independently, while balancing tactical and strategic goals to solve mathematical problems. EXAMPLE: Students work alone or in small groups to look for a method of finding the sum of all whole numbers from 1 to 100 without adding up all the numbers individually. Students who need help getting started might first wish to examine ways of adding up the numbers from 1 to 10.

Unit II: Adding Whole NumbersEssential Question: How do you apply the facts you know and your place value understanding to solve various addition problems?

Objectives: Students will be able to Explore adding on a hundred chart Explore algebra to by finding the missing number Use rounding to estimate sums and to solve Explore addition with regrouping Add 2-digit numbers Add 3-digit numbers Add 4-digit numbers Find the sum of more than 2 addends Solve problems by guessing and checking Use mental math to find sums Find the value of groups of coins Write money amounts Use calculators to add Recall basic addition facts Understand and use addition terminology: sum, addend, and regroup, commutative, associative Decide if both parts of an equation are equal Draw pictures to help solve a problem

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https://www.teachingchannel.org/videos/counting-collections-lesson

Unit 2: Topic/Content Skills Assessment Resources Instructional Method


Topic 1: Developing Addition Sense




www.firstinmath.comwww.aaaknow.com/grade3 Smart Exchangewww.fun4thebrain.com

3.NBT.A.2

Topic 2: Word problems Test/QuizzesHome/ClassworkClass ParticipationProjects




3. OA.D.83.OA.D .9

Topic 3: Extending Addition Test/QuizzesHome/ClassworkClass ParticipationProjects




3. OA.D.83.OA.D .9

Differentiated Learning ActivitiesIn many lessons using addition, students are allowed to self-pace so they can complete exercises, move through various challenges, and receive individual or group help, as needed. Using addition fact quizzes and work to show progress and improve his or her own time. Pre-testing at the beginning of the unit allows for individual needs in this area to be determined and some activities to be tailored by the teacher.

Ethical Decision Making/Character EducationIncorporate addition skills into tracking progress of on going class projects to help the less fortunate in our town, our state and our country.

21st Century Skills: Critical Thinking To promote critical thinking among students, view this Teaching Channel video, Discover Number Patterns With Skip Counting. Watch how the teacher uses different color markers to look for patterns when counting by 200s. https://www.teachingchannel.org/videos/teaching-number-patterns

21st Century Skills: Innovation OUTCOME: By discovering fresh insights and communicating them to others, students come to understand that mathematics is a creative endeavor that builds on previous knowledge. EXAMPLE: Students explore Mayan mathematics(www.hanksville.org/yucatan/mayamath.html). They compare and contrast how numbers are represented in our Arabic system and in the Mayan system. They practice writing Mayan numerals and create addition and subtraction problems in theMayan system for one another to solve (http://mathforum.org/k12/mayan.math/index.html ).

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http://mathforum.org/k12/mayan.math/index.html

http://www.hanksville.org/yucatan/mayamath.html

https://www.teachingchannel.org/videos/teaching-number-patterns

http://www.fun4thebrain.com/












Unit III: Subtracting Whole Numbers

Essential Question: How do you apply the facts you know and your place value understanding to solve various subtraction problems?

Objectives: Students will be able to: Explore subtraction on a hundred chart Estimate differences using rounding Explore regrouping Explore subtracting 2-digit numbers Explore subtracting 3-digit numbers Subtract 3-digit numbers (whole numbers or currency) Subtract with 2 regroupings Subtract across zeros Subtract 4-digit numbers Understand and use subtraction terminology: difference, fact family Recall basic subtraction facts Solve problems by writing a number sentence Subtract using mental math Decide if both parts of an equation are equal



Topic 1: Developing Subtraction Concepts




www.firstinmath.comwww.math-play.comSmart Exchangewww.fun4thebrain.com

3.NBT.A.2

Topic 2: Subtracting currency Test/QuizzesHome/ClassworkClass ParticipationProjects




3.NBT.A.2

Topic 3: Extending Addition Test/QuizzesHome/ClassworkClass ParticipationProjects




3. OA.D.83.OA.D .9

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http://www.math-play.com/








Differentiated Learning ActivitiesIn many lessons using subtraction, students are allowed to self-pace so they can complete exercises, move through various challenges, and receive individual or group help, as needed. Using subtraction fact quizzes, students work to progress and improve his or her own time. Pre-testing at the beginning of the unit allows for individual needs in this area to be determined and some activities to be tailored by the teacher.

Ethical Decision Making/Character EducationIn class exercises using subtraction, students are asked to make purchasing choices to calculate money payments required to stay within a budgeted amount. This activity encourages development of ability to make choices about spending money and paying bills.

21St Century Skills: Productivity and Accountability OUTCOME: Students set goals, establish priorities and schedules, and meet goals to complete a project. EXAMPLE: Students work in groups to solve a mathematics problem. Each group is assigned a problem on a different topic and identifies the mathematical knowledge needed to solve it. Groups are then reorganized so that in each new group, each student is responsible for reviewing the mathematics for the problem they worked on in the first group, presenting a solution to their problem to the others in the group. Each student is likewise responsible for helping others in their new group understand their topic.

Unit IV: Multiplication Concepts and FactsEssential Questions: What is multiplication, how do you use it, and how do you use it to solve problems?

Objectives: Students will be able to: Explore multiplication stories Write and illustrate multiplication stories Write multiplication sentences for arrays Multiply with 2 as a factor Multiply with 5 as a factor Explore patterns for 2ʼs and 5ʼs on a hundred chart Explore patterns when multiplying with 0 and 1 Multiply with 9 as a factor Understand and use multiplication terminology: array, factor, product, multiple, square number and grouping property Recall basic multiplication facts Multiply with 3, 4, 5, 6, 7, and 8 as a factor Explore patterns for 3ʼs and 6ʼs on a hundred chart Explore patterns on a fact table Multiply with 3 factors and use associative properties Explore multiplying tens Explore multiplication patterns

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Estimate products Explore multiplication with arrays Multiply with 2-digit numbers Multiply with 3-digit numbers Multiply money Solve for one problem and use the answer to solve a second problem Use distributive properties to simplify multiplication problems by breaking arrays apart Use objects, pictures, and multiplication to find the number of possible combinations of data Solve multistep problems



Topic 1: Understanding multiplication




www.firstinmath.comwww.multiplication.comSmart Exchangewww.fun4thebrain.com

3.OA.A.1

Topic 2: Multiplying Test/QuizzesHome/ClassworkClass ParticipationProjects




3.OA.A.3

Topic 3: Extending multiplication





3.OA.A.4

Topic 4: Developing multiplication # sense





3.OA.B.53.OA.C.73.OA.D.83.OA.D.93.NBT.A.3

Differentiated Learning ActivitiesIn many lessons using multiplication, students are allowed to self-pace so they can complete exercises, move through various challenges, and receive individual, or group help, as needed. Using multiplication fact quizzes and students’ work to show progress and improve his or her own

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http://www.multiplication.com/











time. Pre-testing at the beginning of the unit allows for individual needs in this area to be determined and some activities to be tailored by the teacher.Ethical Decision Making/Character EducationExploring groupings of items that come in specific sets encourages discussion of social groupings, group dynamics, aesthetics in design, and self-awareness.

21st Century Skills: Collaboration To promote collaboration among students, view this Teaching Channel video, Reasoning About Multiplication & Division. Watch how the teacher fosters an understanding of multiplication and division among his students by having them learn from each other and give students opportunities to revise their thinking. https://www.teachingchannel.org/videos/multiplication-division-in-the-core?fd=1

Unit V: Division Concepts and FactsEssential Question: How do you divide numbers and recall division facts to use in problem solving?

Objectives: Students will be able to: Explore division as sharing Explore division as repeated subtraction Explore and write division stories Explore division patterns Understand and use division terminology: dividend, quotient, divisor, remainder Use multiplication to divide Divide by numbers 0 – 9 Recall basic division facts Explore even and odd numbers Estimate quotients Explore division with remainders Divide to fine quotients and remainders Explore algebra by balancing scales Use models to solve division problems using repeated subtraction Use multiplication tables to solve division problems Solve word problems by writing equations to represent the solution Give multiplication fact and relate it to a division fact Solve multistep problems Determine if both sides of an equation are equal Use fact families to solve problems

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https://www.teachingchannel.org/videos/multiplication-division-in-the-core?fd=1



Topic 1: Understanding Division




www.firstinmath.comSmart Exchangewww.fun4thebrain.com

3.OA.A.2

Topic 2: Using Multiplication to solve division





3.OA.A.3

Topic 3: Finding Division Facts Test/QuizzesHome/ClassworkClass ParticipationProjects




3.OA.A.43.OA.B.63.OA.C.73.OA.D.8

Differentiated Learning ActivitiesIn many lessons using division, students are allowed to self-pace so they can complete exercises, move through various challenges, and receiveindividual, or group help, as needed. Using division fact quizzes and students’ work to show progress and improve his or her own time. Pre-testing at the beginning of the unit allows for individual needs in this area to be determined and some activities to be tailored by the teacher.

Ethical Decision Making/Character EducationExploring groupings of items that come in specific sets encourages discussion of social groupings, group dynamics, aesthetics in design, and self-awareness.

21st Century Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures. (9.1)

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Unit VI: FractionsEssential Question: How do you understand fractions as numbers, and how do you use them in the every day world?

Objectives: Students will be able to: Explore and identify equal parts Name and write fractions Explore equivalent fractions Explore comparing and ordering fractions Estimate fractional amounts Find a fraction of a set Explore finding a fraction of a number Write fractions greater than 1 Explore adding and subtracting fractions Understand and use fraction terminology Associate the model, symbol, and words used to describe a fractional part of a whole region and a set Identify fractional parts and mixed numbers on a number line Identify and use benchmark fractions to estimate fractions Look at a table to find a pattern to solve a problem. Compare fractions with same numerator and denominator Use benchmark fractions to compare fractions Use a number line to compare fractions and to identify equivalent fractions Order fractions to solve problems Use fraction strips to find fraction names for whole numbers



Topic 1: Understanding Fractions

Test/QuizzesHome/ClassworkClass Participation


Whole-group instructionHands-On ActivitiesGroup Collaboration

www.firstinmath.comSmart Exchangewww.coolmath4kids.com

3.NF.A.13.NF.A.2

Topic 2: Comparing Fractions Test/QuizzesHome/ClassworkClass Participation




3.NF.A.2.a 3.NF.A.2b

Topic 3: Equivalent fractions Test/QuizzesHome/Classwork

TextResource books

Whole-group instructionHands-On Activities

www.firstinmath.comSmart Exchange

3.NF.A.3a, 3.NF.A.3b3.NF.A.3c,

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http://www.coolmath4kids.com/




Class Participation Manipulatives Group Collaboration www.coolmath4kids.com 3.NF.A.3dEthical Decision Making/Character EducationThe use of small group and partner activities provides experience with cooperation and respect for one another while working together. Fraction lessons using hands-on materials encourage discussion and experience for students in sharing. Activities used to teach the concept of probability encourages discussions about fairness as it may relate to social issues for students, such as game playing.

21st Century Skills: Innovation & Creativity OUTCOME: Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. EXAMPLE: The teacher presents the class with the problem: Five friends are planning a pizza party. If each of them will eat 3 pizza slices and each pizza is cut into 8 slices, how many pizzas will be needed for the party? Students work in small groups: (1) One group looks at how many pieces of pizza will be needed. They reason that 5 people eating 3 slices each will require 5 x 3 = 15 slices. The group then examines how many pizzas will be needed to get 15 slices. (2) Another group approaches the problem by asking: If each person eats 3/8 of a pizza, what fraction will 5 people eat? (3) A third group creates paper “pizzas”: Each student draws a large circle and draws 4 lines through the center to create 8 equal-size wedges, or “pizza slices.” Students sort the wedges into piles of 3. They see that 5 piles of 3 wedges each provide a total of 15 “pizza slices.” Since each slice is 1/8 of a pizza, they reason that 15 slices is 15 x 1/8, or 15/8 of a pizza. They find that 15/8 = 1 7/8, which is just under 2 pizzas.

Unit VII: GeometryEssential Question: What are key attributes and relationships of solids and shapes? How do you determine perimeter, area, and volume of geometric shapes?

Objectives: Students will be able to: Explore solids; explore connecting solids and shapes Identify lines, line segments, rays, parallel lines, and intersecting lines Explore, identify and classify angles Explore slides, flips, and turns; explore symmetry Explore perimeter and use standard units to find the perimeter of a shape Explore area & volume Understand and use geometry terminology Find and name points on a coordinate grid Solve problems by solving simpler problems and finding patterns Solve problems by making decisions about area Identify and classify polygons, quadrilaterals and triangles Create new shapes by combining or rearranging separate shapes Use appropriate tools to find the perimeter and area of an object Solve problems through try, check and revise Measure the area of a shape by counting square units Use square units to make figures with given areas

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Find the area of other regular and irregular shapes

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Topic 1: Shapes and Solids Test/QuizzesHome/ClassworkClass Participation




3.G.A.1, 3.G.A.2. 3.MD.C.53.MD.C.5.a, 3.MD.C.5.b

Topic 2: Perimeter, Area and Volume





3.MD.C.6, 3.MD.C.73.MD.C.7.a3.MD.C.7.b, 3.MD.C.7.c3.MD.C.7.d, 3.MD.D.8

Differentiated Learning ActivitiesVaried levels of challenge are integrated into hands-on activities using shapes and solids and exploring perimeter, area, and volume. Students are allowed to self-pace so they can complete exercises, move through various challenges, and receive individual or group help, as needed. Pre-testing at the beginning of the unit allows for individual needs in this area to be determined and some activities to be tailored by the teacher.

Ethical Decision Making/Character EducationExploring and drawing geometric shapes and designs that are found in our environment, our neighborhoods, and our world encourages aesthetic appreciation and self-awareness.

21st Century Skills: Creativity and Intellectual Curiosity/Technology Students can first use digital cameras to photograph representations of geometry concepts from their surroundings; then transfer the photo images to create a math slide show; and give a presentation for an audience to explain geometry concepts. Tools that can be used: digital cameras, laptop computers, multimedia presentation software, graphing calculators, probes/Cbrs, Website development software

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Unit VIII: Measurement and DataEssential Question: How do I solve problems involving measurement and estimation?

Objectives: Students will be able to: Tell time to the nearest five minutes Tell time to the nearest minute Tell time to the nearest half hour and quarter hour Find ending time and the time between events Write time in digits and word form Properly use AM and PM identifiers Develop understanding of correlation of digital and analog clock Perform simple conversations for units of time Find elapsed time in intervals of minutes Measure to the nearest half and quarter inch Explore length in feet and inches Estimate and compare measurement in inches, feet, yard and miles Explore centimeters and decimeters Estimate and compare measurement in meters and kilometers Explore capacity in customary units Estimate and compare measurement in liters and milliliters Explore weight in customary units Estimate and compare measurement in grams and kilograms Estimate and compare measurement in degrees Fahrenheit and Celsius Read a bar graph Read a line graph Explore organizing data Explore making pictographs Explore making bar graphs Collect and analyze data Understand and use graph terminology: bar graph, scale, line graph, survey, tally mark and data Read a pictograph Explore and make a line plot Solve problems by using tables and graphs to draw conclusions Choose appropriate unit and tool to estimate and measure objects Identify objects that hold a cup, milliliter, pint, quart and gallon, gram, kilogram, ounce, pound and ton Solve problems using units of capacity and mass

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Topic 1: Time (Telling time & Understanding elapsed time)





3.MD.A.1

Topic 2: Graphs (How to use graphs, collecting data, creating graphs)





3.MD.B.3

Topic 3: Measurement (Customary linear measurement; Metric measurement; Capacity, weight, temperature; Using rulers)





3.MD.A.23.MD.B.4

Ethical Decision Making/Character EducationThe process of interviewing and gathering information about classmates develops understanding of differences and similarities within the class and encourages positive social interaction.

21st Century Skills: Critical Thinking & Collaboration OUTCOME: Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. EXAMPLE: Students work in small groups to design a parking lot. Given a flat, rectangular space with set dimensions, each group arranges rows of parking spaces to be easily accessible while allowing for a maximum number of cars to park. Students may visit an actual parking lot to assess and measure parking space width and angles. Each group creates a drawing of its design and presents it to the class.

Sustainability: Health Literacy OUTCOME: Students gain a fundamental understanding of the legal and ethical issues surrounding the access, use, and potential distortion of mathematical information, terms, and concepts. They recognize the common tendency to treat quantitative data as truth and to infer patterns where none exist. EXAMPLE: Students examine the numbers on food labels. Each student lists the serving size on a bag of chips, the amount of fat per serving, and the “daily value” percentage. Then the student estimates the number of servings he or she would actually eat, and recalculates fat per serving and “daily value” based on the number of servings (see sample below). Students do a similar estimation and calculation for cereal, cookies, salad dressing, milk, or other foods. Students can also calculate estimates for saturated fat, sugar, or sodium. Students talk about their findings and discuss the fact that (as footnoted on food labels) “daily value” is based on a 2,000-calorie-per-day diet—and some people need more than 2,000 calories per day while others need less.

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unit iv: evolution - mountain lakesfc.mtlakes.org/.../fav2-00102e40/fov2-0… · web view ·...

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