Mathematics Station Activities
MathematicsStation Activitiesfor Common Core State StandardsGrade 7WALCH EDUCATION
The classroom teacher may reproduce materials in this book for classroom use only.The reproduction of any part for an entire school or school system is strictly prohibited.No part of this publication may be transmitted, stored, or recorded in any formwithout written permission from the publisher. Common Core State Standards for Mathematics. Copyright 2010. National Governor’sAssociation Center for Best Practices and Council of Chief State School Officers. All rights 8 9 10ISBN 978-0-8251-6927-4Copyright 2011J. Weston Walch, PublisherPortland, ME 04103www.walch.comPrinted in the United States of AmericaWALCH EDUCATION
Table of ContentsStandards Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiMaterials List. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xRatios and Proportional Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Set 1: Ratios and Proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Set 2: Problem Solving with Rational Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Set 3: Analyzing and Describing Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Set 4: Graphing Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Set 5: Representing Patterns and Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37The Number System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Set 1: Adding and Subtracting Rational Numbers. . . . . . . . . . . . . . . . . . . . . . . . . .Set 2: Multiplying and Dividing Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . .Set 3: Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45455361Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Set 1: Solving Linear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Set 2: Multi-Step Real-Life Problems with Rational Numbers. . . . . . . . . . . . . . . .Set 3: Using Variables to Construct Equations and Inequalities . . . . . . . . . . . . . .68688088Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Set 1: Constructing Plane Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Set 2: Similarity and Scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Set 3: Sketching, Modeling, and Describing 3-D Figures . . . . . . . . . . . . . . . . . . . 110Statistics and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Set 1: Collecting, Organizing, and Analyzing Data . . . . . . . . . . . . . . . . . . . . . . . .Set 2: Theoretical Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Set 3: Experimental Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117117125132iii 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
Standards CorrelationsThe standards correlations below support the implementation of the Common Core Standards.This book includes station activity sets for the Common Core domains of Ratios and ProportionalRelationships; The Number System; Expressions and Equations; Geometry; and Statistics andProbability. The table below provides a listing of the available station activities organized byCommon Core standard.The left column lists the standard codes. The first number of the code represents the grade level.The grade number is followed by the initials of the Common Core domain name, which is thenfollowed by the standard number. The middle column of the table lists the title of the station activityset that corresponds to the standard, and the right column lists the page number where the stationactivity set can be found.StandardSet titlePage number7.RP.1.Ratios and Proportions17.RP.2.Ratios and Proportions17.RP.2.Analyzing and Describing Relationships217.RP.2.Graphing Relationships287.RP.2.Representing Patterns and Relationships377.RP.3.Ratios and Proportions17.RP.3.Problem Solving with Rational Numbers147.EE.3.Problem Solving with Rational Numbers147.NS.1.Adding and Subtracting Rational Numbers457.NS.1.Absolute Value617.NS.2.Multiplying and Dividing Rational Numbers537.NS.3.Absolute Value617.EE.1.Solving Linear Equations68(continued)v 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
Standards CorrelationsStandardSet titlePage number7.EE.2.Solving Linear Equations687.EE.3.Multi-Step Real-Life Problems with Rational Numbers807.EE.4.Using Variables to Construct Equations and Inequalities887.G.1.Similarity and Scale1027.G.2.Constructing Plane Figures957.G.2.Similarity and Scale1027.G.3.Sketching, Modeling, and Describing 3-D Figures1107.SP.5.Collecting, Organizing, and Analyzing Data1177.SP.5.Theoretical Probability1257.SP.6.Collecting, Organizing, and Analyzing Data1177.SP.6.Theoretical Probability1257.SP.6.Experimental Probability1327.SP.7.Collecting, Organizing, and Analyzing Data1177.SP.7.Experimental Probability1327.SP.8.Collecting, Organizing, and Analyzing Data117viStation Activities for Common Core Mathematics, Grade 7 2011 Walch Education
IntroductionThis book includes a collection of station-based activities to provide students with opportunitiesto practice and apply the mathematical skills and concepts they are learning. It contains sets ofactivities for each of the five Grade 7 Common Core Mathematics strands: Ratios and ProportionalRelationships; The Number System; Expressions and Equations; Geometry; and Statistics andProbability. You may use these activities in addition to direct instruction, or instead of directinstruction in areas where students understand the basic concepts but need practice. The DiscussionGuide included with each set of activities provides an important opportunity to help students reflecton their experiences and synthesize their thinking. It also provides guidance for ongoing, informalassessment to inform instructional planning.Implementation GuideThe following guidelines will help you prepare for and use the activity sets in this book.Setting Up the StationsEach activity set consists of four stations. Set up each station at a desk, or at several desks pushedtogether, with enough chairs for a small group of students. Place a card with the number of thestation on the desk. Each station should also contain the materials specified in the teacher’s notes,and a stack of student activity sheets (one copy per student). Place the required materials (as listed)at each station.When a group of students arrives at a station, each student should take one of the activity sheetsto record the group’s work. Although students should work together to develop one set of answersfor the entire group, each student should record the answers on his or her own activity sheet. Thishelps keep students engaged in the activity and gives each student a record of the activity for futurereference.Forming Groups of StudentsAll activity sets consist of four stations. You might divide the class into four groups by havingstudents count off from 1 to 4. If you have a large class and want to have students working in smallgroups, you might set up two identical sets of stations, labeled A and B. In this way, the class canbe divided into eight groups, with each group of students rotating through the “A” stations or “B”stations.vii 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
IntroductionAssigning Roles to StudentsStudents often work most productively in groups when each student has an assigned role. You maywant to assign roles to students when they are assigned to groups and change the roles occasionally.Some possible roles are as follows: Reader—reads the steps of the activity aloud F acilitator—makes sure that each student in the group has a chance to speak and posequestions; also makes sure that each student agrees on each answer before it is written down aterials Manager—handles the materials at the station and makes sure the materials are put Mback in place at the end of the activity imekeeper—tracks the group’s progress to ensure that the activity is completed in the Tallotted time Spokesperson—speaks for the group during the debriefing session after the activitiesTiming the ActivitiesThe activities in this book are designed to take approximately 15 minutes per station. Therefore,you might plan on having groups change stations every 15 minutes, with a two-minute interval formoving from one station to the next. It is helpful to give students a “5-minute warning” before it istime to change stations.Since the activity sets consist of four stations, the above time frame means that it will take aboutan hour and 10 minutes for groups to work through all stations. If this is followed by a 20-minuteclass discussion as described below, an entire activity set can be completed in about 90 minutes.Guidelines for StudentsBefore starting the first activity set, you may want to review the following “ground rules” withstudents. You might also post the rules in the classroom. ll students in a group should agree on each answer before it is written down. If there is a Adisagreement within the group, discuss it with one another. You can ask your teacher a question only if everyone in the group has the same question. I f you finish early, work together to write problems of your own that are similar to the ones onthe student activity sheet. L eave the station exactly as you found it. All materials should be in the same place and in thesame condition as when you arrived.viiiStation Activities for Common Core Mathematics, Grade 7 2011 Walch Education
IntroductionDebriefing the ActivitiesAfter each group has rotated through every station, bring students together for a brief classdiscussion. At this time, you might have the groups’ spokespersons pose any questions they hadabout the activities. Before responding, ask if students in other groups encountered the samedifficulty or if they have a response to the question. The class discussion is also a good time toreinforce the essential ideas of the activities. The questions that are provided in the teacher’s notesfor each activity set can serve as a guide to initiating this type of discussion.You may want to collect the student activity sheets before beginning the class discussion.However, it can be beneficial to collect the sheets afterward so that students can refer to themduring the discussion. This also gives students a chance to revisit and refine their work based on thedebriefing session.ix 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
Materials ListStation SetsClass Sets 2 bags (to hold cubes/blocks/etc.) calculators 2 spinners (one divided evenly into red,green, blue, and yellow sections; theother divided evenly into black and whitesections) compasses 3 blocks (red, green, and blue) 3 marshmallows box of toothpicks clay c olored cubes (one each of red, blue, andgreen; two yellow) protractors rulersOngoing Use i ndex cards (prepared according tospecifications in teacher notes for many ofthe station activities) graph paper n umber cubes (several numbered 1–6; onenumbered 4, 2, 2, 1, 3, 3; one numbered6, 1, 3, 5, 4, 8) integer chips pencils l ist of 100 randomly generated numbers(1–9) pennies marbles (24 green, 16 yellow) scrap/scratch paper model car with scale factor o ptional: tape measure; water; separatecontainers to hold 1 cup, 1 quart, and1 gallon of water plastic knives rectangular prism set of at least 5 congruent triangles t iles or small pieces of paper (several smallsquare tiles; several small round tiles;8 large blue algebra tiles; 20 small yellowalgebra tiles)xStation Activities for Common Core Mathematics, Grade 7 2011 Walch Education
Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsInstructionGoal: To provide opportunities for students to develop concepts and skills related to unitconversion, finding percents, simplifying algebraic ratios, and solving algebraicproportionsCommon Core StandardsRatios and Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths,areas and other quantities measured in like or different units.7.RP.2.Recognize and represent proportional relationships between quantities.a. Decide whether two quantities are in a proportional relationship, e.g., by testing forequivalent ratios in a table or graphing on a coordinate plane and observing whetherthe graph is a straight line through the origin.b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,diagrams, and verbal descriptions of proportional relationships.c. Represent proportional relationships by equations.7.RP.3. Use proportional relationships to solve multi-step ratio and percent problems.Examples: simple interest, tax, markups and markdowns, gratuities and commissions,fees, percent increase and decrease, percent error.Student Activities Overview and Answer KeyStation 1Students will be given 12 index cards with pairs of equivalent units of measurement written on them.They will work together to match the cards that are an equivalent unit of measurement. Then theywill perform unit conversion.Answers1. 10 mm 1 cm; 12 in. 1 ft; 3 ft 1 yd; 2 pints 1 quart; 4 quarts 1 gallon; 1 ton 2,000 pounds2. 8 pints in a gallon; 2 pints 1 quart and 4 quarts 1 gallon, so 2(4) 8 pints3. 18 inches; 1/2 yard 1.5 feet and 12 inches 1 foot, so 12(1.5) 18 inches4. 5,000 pounds5. 850 mm1 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7Ratios and Proportional Relationships
Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsInstruction6. 13.5 feet7. 3 quarts 0.75 gallons8. Answers will vary. Possible answers include: cooking, when modifying recipes for more or fewerpeople; carpentry, when creating custom-size cabinetryStation 2Students will be given a calculator to help them solve the problems. They work as a group to solvereal-world applications of unit conversions.Answers1. His friend measures temperature in Celsius, and Evan measures it in Fahrenheit. F 95 2. P 36.67 yards; P 1,320 inches, A 77.78 yds2; A 100,800 76.55Meters91.44121.9570Time12 seconds12 seconds12 secondsJeremy, Tim, Martin; Tim 25 feet/sec, Jeremy 33.33 feet/sec; Martin 19.14 feet/secStation 3Students will be given a bag containing 24 green marbles and 16 yellow marbles. They will use themarbles to create ratios and percents. They will then solve percent problems.Answers1. Answers will vary. Possible answers include: green 1; yellow 7; total 8. Find 1/8 0.125 12.5%; 12.5% were green. Subtract 12.5% from 100% to get 87.5% or 7/8 87.5%; 87.5% wereyellow.2. There are 40 marbles so 24/40 60% green marbles; 100% – 60% 40% or 16/40 40%3. 9 yellow marbles; student drawings should depict 9 yellow marbles and 12 green marbles.4. 24(1/4) 6 or 24(0.25) 65. 17(2/1) 34 or 17(2.0) 346. 10(14) 140 in2; increased dimensions by 200% then found the area of the photograph2Station Activities for Common Core Mathematics, Grade 7 2011 Walch Education
Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsInstructionStation 4Students will be given 8 large blue algebra tiles and 20 small yellow algebra tiles. Students visuallydepict ratios and proportions with the algebra tiles. They then solve proportions for a specifiedvariable including a real-world application.Answers8 blue2 1.20 yellow 52 blue4 blue 2.3 yellow 6 yellow3. 8/20 x/100, so x 40 blue4. 8/20 x/15, so x 6 blue5. x 46. x 40blue63 yellow 10 5Let x number of blue pencils and 24 – x number of yellow pencils.7.3x , so x 9 blue pencils and 24 – x 15 yellow pencils5 ( 24 x )Materials List/SetupStation 112 index cards with the following written on them: 10 millimeters, 12 inches, 3 feet, 2 pints, 4 quarts, 1 ton, 1 centimeter, 1 foot,1 yard, 1 quart, 1 gallon, 2,000 poundsStation 2calculatorStation 324 green marbles; 16 yellow marblesStation 48 large blue algebra tiles; 20 small yellow algebra tiles3 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsInstructionDiscussion GuideTo support students in reflecting on the activities and to gather some formative information aboutstudent learning, use the following prompts to facilitate a class discussion to “debrief” the stationactivities.Prompts/Questions1. How do you perform unit conversion?2. When would you use unit conversion in the real world?3. What are two ways to find the percent of a number?4. What is a ratio?5. How do you know if two ratios are equivalent?6. What is a proportion?7. When would you use ratios and proportions in the real world?Think, Pair, ShareHave students jot down their own responses to questions, then discuss with a partner (who was notin their station group), and then discuss as a whole class.Suggested Appropriate Responses1. Use ratios and proportions to convert units.2. Answers will vary. Possible answers include: creating scale models of buildings; using themetric system instead of U.S. Customary units; converting Celsius to degrees Fahrenheit andvice versa3. Multiply the number by a decimal or fraction that represents the percentage.4. A ratio is a comparison of two numbers by division.5. Two ratios are equivalent if, when simplified, they are equal.6. A proportion is when two ratios are set equal to each other.7. Answers will vary. Possible answers include: enlarging photos; scale models; modifyingquantities of ingredients in a recipe4Station Activities for Common Core Mathematics, Grade 7 2011 Walch Education
Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsInstructionPossible Misunderstandings/Mistakes Not keeping track of units and using incorrect unit conversions Not recognizing that terms must have the same units in order to compare them S etting up proportions with one of the ratios written with the incorrect numbers in thenumerator and denominator Not recognizing simplified forms of ratios in order to find equivalent ratios5 2011 Walch EducationStation Activities for Common Core Mathematics, Grade 7
NAME:Ratios and Proportional RelationshipsSet 1: Ratios and ProportionsStation 1You will be given 12 index cards with the following written on them:10 millimeters, 12 inches, 3 feet, 2 pints, 4 quarts, 1 ton, 1 centimeter, 1 foot, 1 yard,1 quart, 1 gallon, 2,000 poundsShuffle the index cards and deal a card to each student in your group until all the cards are gone. Asa group, show your cards to each other and match the cards that are an equivalent unit of measurement.1. Write your answers on the lines below. The first match is shown:10 mm 1 cm2. Find the number of pints in a gallon. Explain how you can use your answers in problem 1 tofind the number
activity set can be found. Standard Set title Page number 7.RP.1. Ratios and Proportions 1 7.RP.2. Ratios and Proportions 1 7.RP.2. Analyzing and Describing Relationships 21 7.RP.2. Graphing Relationships 28 7.RP.2. Representing Patterns and Relationships 37 7.RP.3. Ratios and Proportions 1 7.RP.3. Problem Solving with Rational Numbers 14 7.EE.3.
Station 3: Five-Finger Retell card Station 3: Green Questions card Station 3: Key Words card Station 3: Problem-Solution card Station 3: Red Questions card Station 3: Shared Retelling Cards Station 3: Story Retelling Rope Station 3: SWBS card Station 3: Track the Character’s Feelings card Station 3: V.I.P. Fiction card Station 3: V.I.P .
7 Station No. Station Name in Chinese Station Name in English A1 臺北車站 Taipei Main Station A2 三重站 Sanchong Station A3 新北產業園區站 New Taipei Industrial Park Station A4 新莊副都心站 Xinzhuang Fuduxin Sation A5 泰山站 Taishan Station A6 泰山貴和站（明志科大） Taishan Guihe Station A7 體育大學站 National Taiwan Sport University Station
Total Station (Geodimeter/Trimble) 4 Total Station (Leica TPS Series) 10 Total Station (Leica Robotic) 15 Total Station (Leica/Wild Older Models) 23 Total Station (Nikon) 24 Total Station (Pentax) 25 Total Station (Sokkia Set) 27 Total Station (Sokkia Robotic) 31 Total Station (Spectra Focus 30) 33 Total St
years - depending on how often the system is powered down. The more the system's power is off, the shorter the battery's life. Connection points for the CO and station DDK connectors. 82400 - 36 Station 1 Trunk 4 Battery Trunk 3 Trunk 2 Trunk 1 Station 2 Station 3 Station 4 Station 5 Station 6 Station 7 Station 8 HDWR1B.QXD 5/18/98 4:51 PM .
3 1st station: jesus is condemned to death 2nd station: jesus takes up his cross 3rd station: jesus falls for the first time 4th station: jesus meets his mother 5th station: simon of cyrene helps jesus to carry the cross 6th station: veronica wipes the face of jesus 7th station: jesus falls for the second time 8th station: jesus consoles the women of jerusalem 9th station: jesus falls for the .
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
