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SCOTT FORESMAN

InvestigationsIN NUMBER, DATA1 AND SPACE

Information and Ideas for Parents

Investigations in Number Data, and Space® is a K-5 mathematics curriculum designed toengage students in making sense of mathematical ideas. It has just been revised by the TERCauthors through a National Science Foundation Grant. This 2 edition curriculum is designed to:

• Support students to make sense of mathematics and learn that they can bemathematical thinkers

• Focus on computational fluency with whole numbers as a major goal of the elementarygrades

• Provide substantive work in important areas of mathematics — rational numbers,geometry, measurement, data and early algebra — and connections among them

• Emphasize reasoning about mathematical ideas• Engage the range of learners in understanding mathematics

Underlying these goals is a guiding principle for the Investigations authors as theyapproached students as agents of their own learning:

• Students have mathematical ideas. Students come to school with ideas about numbers,shapes and measurements, patterns, and data. If given the opportunity to learn in anenvironment that stresses making sense of mathematics, students build on the ideasthey already have and learn about new mathematics they have never encountered.Students learn that they are capable of having mathematical ideas, applying what theyknow to new situations, and thinking and reasoning about unfamiliar problems.

ProgramInvestigations is based on experience from research and practice, including field testing thatinvolved documentation of thousands of hours in classrooms, observations of students, inputfrom teachers, and analysis of student work. As a result, the curriculum addresses the learningneeds of real students in a wide range of classrooms and communities. The investigations arecarefully designed to invite all students into mathematics — girls and boys; members of diversecultural, ethnic, and language groups; and students with a wide variety of strengths, needs, andinterests.

Based on this extensive classroom testing, the curriculum takes seriously the time studentsneed to develop a strong conceptual foundation and skills based on that foundation. Eachcurriculum unit focuses on an area of content in depth, providing time for students to developand practice ideas across a variety of activities and contexts that build on each other. Dailyguidelines for time spent on class sessions, Classroom Routines (K-3), and Ten Minute Math(3-5) reflect the commitment to devoting adequate time to mathematics in each school day.

PEARSONInvestigations in Number, Data, and Space 211(1 editionhttp://godigital.scottforesman.comlinvestigations/

Things You May Observe in an Investigations Classroom

ci Students are actively involved in all aspects of the lesson

ci Students use concrete mathematical manipulative objects as a natural part of instruction

ci Students solve problems as their primary purpose in math class

ci Students work fewer computations, but more problems that require higher-order thinking

ci Students use calculators as a tool, as called for in the class sessions

ci Students engage in activities that help develop spatial and number sense

ci Students participate in individual, small group and whole class learning experiences

ci Students record and reflect their thinking in math journals/logs/recording papers

ci Students’ estimation skills are incorporated in routines and investigations

ci Students learn math facts through repeated work in activities and games

ci Students use Shapes/LogoPaths software for computer work in geometry

ci Students demonstrate and explain their strategies for the teacher to notate and display

ci Students are assessed with formal and informal assessment

ci Students work on extended problems

ci Students study an algorithm to analyze & compare to strategies they know and understand

ci Students reinforce mental mathematics daily

ci Students participate in data collection and analysis

ci Students ask questions of their peers and their teacher

ci Students take home Family Math Letters regularly

ci Students are asked to justify and explain their thinking

Investigations in Number, Data, and Space 2nd editionhttp://godigitaLscottforesman.comlinvestigations/

Family Letters in Investigations

Just as it is important for children to read at home, it is essential for them to do math at home andto sometimes involve family. The first Family Letter in each Unit called, About the Mathematics inThis Unit introduces families to the Benchmark expectations for mastery and shows what themathematics looks like that the children will be doing.

A second letter in each Unit called, Related Activities to Try at Home is sent home a few days afterthe first letter. It suggests related activities that families can do together. It also has a list ofchildren’s books that support students’ work in mathematics. These books may be available atyour public library.

An additional letter in the first Unit called, About Mathematics Homework, gives suggestions forhelping students with their homework, setting up a good working environment, and askingproductive questions.

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Investigations in Number, Data, and Space 2nd editionhttp://godigitaLscottforesman.com!investigations/

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Investigations’ Student Math Handbook

The Student Math Handbook is for students, teachers and parents to use. TheHandbook has 2 kinds of pages, Math Words and Ideas, and Games.

The Math Words and Ideas pages highlight the major mathematical words and ideas,skills and concepts of the grade. It is a concise and visual summary of mathematics.Each Daily Page and Homework page has a Note to Parents with a Student MathHandbook reference page when appropriate. At home students can use the Handbookto review or for reference, or to share their mathematical thinking and ideas withparents. Parents can use the Handbook to browse through the mathematics of thegrade level, see visual representations their students are using and refreshmathematical terms and ideas they may have forgotten.

All of the games of Investigations for that grade are in the back of the Student MathHandbook! If the game has a recording sheet, it is pictured as a mini-page so everyoneknows what needs to be recorded.

The Handbook may be a Big Book used in the classroom in grades K-2. The HandbooksK-5 are also accessible online.

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All the players inciuding the player who calledour [he number search for cards that are multiplesof that number, Write hose multiples on therecording sheet and urn the cords Facedown.

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PEARSONInvestigations in Number, Data, and Space 2d editionhttp://godigital.scottforesrnan.com/investigations/

Factors of 24rectengukwarray

Each dimension of these rectangles is a factor of 24.

[istod in order the factors of 24 are:

Pairs of factors can be multiplied to get a product of 24:

1x2424 2x1224 3x824 4x62424x1=24 12x2—24 8x3=24 6x4=24

10 sec

Grade 4

What are some other foctorc of 32?

Grade 4

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Homework and Daily Practice in Investigations

In Investigations, Homework and Daily Practice pages from the Student Activity Book arevehicles for connecting school mathematics with students’ everyday lives. Homework and DailyPractice are extensions of classroom work that extend and solidify their mathematicalunderstanding. Sometimes they offer review and practice of work done in class, sometimespreparation for upcoming activities, and sometimes numerical practice that revisits work inearlier units. It may include:

• Number games that may be played more than once to give students multiple opportunitiesto clarify mathematical ideas and reinforce basic facts.

• Problems to solve that ask students to use their prior knowledge of math skills and ideas.• Tasks such as collecting data or taking measurements to be used solving a problem in class• Facts to practice to become competent in estimating, and accurate and fluent in

computation.

Homework and Daily Practice play roles both in supporting students’ learning and in helpinginform families about the ways in which students work with mathematical ideas in Investigations.Also, each Daily Page and Homework page has a Note to Parents with a Student MathHandbook reference page when appropriate.

Grade 2 Grade 4

Investigations in Number, Data, and Space 211(1 editionhttp://godigital.scottforesman.com!investigations/

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The Importance of Playing Games More Than Once

Games are used throughout theInvestigations program as a way to engagestudents in important mathematical ideas.The game format is one that students enjoy,so the potential for repeated experienceswith a concept or skill is great. Because mostgames involve at least one otherplayer, students are likely to learn strategiesfrom each other whether they are playingcooperatively or competitively.

The more times students play amathematical game, the more opportunitiesthey have to practice important skills and tothink and reason mathematically. The firsttime or two that students play, they focus onlearning the rules. Once they have masteredthe rules, their real work with themathematical content begins.Grade 4

Students need many opportunities to playmathematical games, not just during mathtime but other times as well Games playedas homework can be a wondertul way ofcommunicating with parents.

The game directions may come home ashomework, or as a student sheet used inclass. The game directions may also beaccessed online.

Grade 1

PEARSONInvestigations in Number, Data, and Space 2’ editionhttp://godigital.scottforesman.comlinvestigations/

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Technology in Investigations

The Investigations curriculum incorporates two forms of technology in the classroom:calculators and computers.

Calculators are assumed to be standard mathematical tools, available for student use asappropriate. Students need to learn how to use the calculator effectively andappropriately as a tool, just as they need to learn to read a clock, interpret a map,measure with a ruler, or use coins. They might use calculators at home for sensiblepurposes — just as you do — not as a replacement for mental calculations or for paperand pencil calculations they are learning to do. Calculators are recommended for only afew specific activities in the units.

Computers are explicitly linked to one or more curriculum units at each grade level.Shapes software is for grades K-2. LogoPaths software is for grades 3-5. Students’activities on the computers allow them to approach and visualize mathematical situationsin new ways. With Shapes students have free exploration and structured activities. Theycan compose and decompose shapes, pattern a quilt, or tile a plane, and print copies ofthe entire workspace for you to see. explore the properties of geometric figures bydrawing and manipulating them. LogoPaths provides an interactive environment wherestudents can learn about math and computer programming through exploration activities.They can explore distance and angles, supplementary angles and regular polygons,symmetry and similarity.

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PEARSONInvestigations in Number, Data, and Space 2’ editionhttp ://godigital.scottforesman.comlinvestigations/

Assessment in Investigations

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Assessment plays a critical role in teaching and learning, and it is an integral part of theInvestigations Curriculum. A set of Benchmarks for each grade for each Unit establish what isexpected to be mastered. These are shared in the first Family Letter of each Unit.

Assessment is an ongoing process toward the Benchmarks. Teachers may use ObservationChecklists as they observe students’ discussions and explanations of their strategies on a dailybasis and examine their work as it evolves. Daily Practice gives the teacher a snapshot of skillsand concepts learned. Individual assessment activities involve writing and reflecting, adiscussion or brief interaction between student and teacher, or the creation and explanation of aproduct. And the End-of-Unit Assessment gives another opportunity to show mastery of theBenchmarks. Teachers have sample student work (see above) provided by the authors to helpassess student’s mastery of the benchmarks.

Teachers may also use ExamView practice sheets and tests, and SuccessTracker online tests toassess skills and concepts in a more standardized test format.

Investigations in Number, Data, and Space 2nd editionhttp://godigital.scottforesman.comlinvestigations/

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Encouraging Students to Think, Reason and Share Ideas

In the Investigations program students need to take an active role in mathematics. They mustdo more than get the correct answers; they must think critically about their ideas, give reasonsfor their answers, and communicate their ideas.

You can help your student develop their thinking and reasoning by asking questions such as:Does this remind you of other problems you’ve worked?What have you come up with so far?Where do you think you should start?What is the problem asking you to do?Would drawing a picture help?How can I help you?How did you find your answer?Why does that work?Is there another way?How do you know it solves the problem?

Over time, students become more comfortable thinking about their solution, recording it, andexplaining it to others. Your interest in their thinking is a great motivator!

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Grade 3

Investigations in Number, Data, and Space 2 editionhttp://godigitaLscottforesman.comlinvestigations/

P EARSO N

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More Children’s Literature

Investigations uses children’s literature to support the mathematical ideas the studentsinvestigate. The second Family Letter in each unit will give you suggestions for related literature.Below are some more suggestions to look for at the local public library.

K-i 2-3 4-5

Allen, Pamela. Carle, Eric. Anno, Mitsumasa.Who Sank the Boat? The Very Hungry Caterpillar Anno’s Magic Seeds

Burns, Marilyn. Dee, Ruby. Birch, David.The Greedy Triangle Two Ways to Count to Ten The King’s Chessboard

Crews, Donald. Emberley, Ed. Clement, Rod.Ten Black Dots Ed Emberley’s Picture Pie Counting on Frank

Henkes, Kevin. Giganti, Paul, Donald Crews. Leedy, Loreen.Chrysanthemum Each Orange Had 8 Slices Fraction Action

Grossman, Virginia Hong, Lily Toy. Math is, Sharon Bell.Ten Little Rabbits Two of Everythjq The Hundred Penny Box

Lankford, Mary. Hutchins, Pat. Pittman, Helena Clare.Hopscotch Around the World The Doorbell Rang A Grain of Rice

Reid, Margarette. Merriam, Eve. Schwartz, David.The Button Box 12 Ways to Get to 11 If You Made a Million

Sturges, Philemon. Pinczes, Elinor 3. Tom pert, Ann.Ten Flashing Fireflies One Hundred Hungry Ants Grandfather Tang’s Sto

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Try-Me Activities

K-I 2-3 4-5Money: Recognize, name, know Make change, make 25 Help grocery shop,

the value and count and 50 cents multiple compare prices, budgetcoins ways, manage an allowance for

allowance saving/spending short/longterm

Counting: Count things around the Count by 2, 5, 10, counthome, past 10 past 100, look for patterns, Practice skip counting —

Identify numbers on practice skip counting starting at 2, 3, 7, 9, countsigns and in an elevator; past 1000 counting by 25,set the table for your 50, 250family size

Math Facts: Learn single digit facts, Know addition and Know multiplication andstart with doubles 1+1, subtraction facts to 20, division facts to 12, fluently2+2, 3+3, 5-5, 4-4, 3-3 begin learning and accurately

multiplication and divisionfact families (3x4=12,4x3=12, 12/3=4, 12/4=3)

Time: Read clocks on the hour Know minutes in an hour, Practice scheduling, timeand half hour; name days hours in a day, days in a management; determineof week, months of the week; read an analog elapsed timeyear, seasons clock

Measurement: Compare household Using measurement tools: Participate in cooking,items in length, weight, ruler, tape measure, scale, building, measuring;mass etc. rearrange your bedroom

Data: Count and compare: cars Survey and graph family Discuss newspaper graphsvs trucks; record and members “favorites”, or charts, discuss thecompare: sunny/cloudy describe the data, and ask probability of likely anddays “why” and “how” questions unlikely events

Geometry: Name shapes (circle, Name and describe Draw up a proposal forsquare, rectangle) and differences of 2- and 3-D new carpet and paint forfind representations in objects in the home, your bedroom; determinethe home and outside explore area and volume the cost

of cereal boxes

Investigations in Number, Data, and Space 2nd editionhttp://godigital.scottforesman. comlinvestigations/

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