Grade 3
Unit
Summaries
Many units also include:
- Adventure Books and recommendations for using related trade books and children’s literature;
- Suggestions for journal writing;
- Recommended homework assignments for most activities, labs, and games;
- Parent letters that discuss the important ideas within the unit and provide suggestions for home activities that support lessons in school;
- Special notes to parents discussing homework activities;
- Assessment, both through formal instruments and through the informal observations that a discourse-based curriculum makes possible.
Daily Practice and Problems
The Daily Practice and Problems is a vital component of the curriculum and is incorporated into each unit. These exercises require less time to complete than a full activity. They provide ongoing practice, review, and study of a variety of topics, including basic facts and operations, time, money, number sense, and geometry. Many word problems are included. Two Daily Practice and Problems items are presented each day. TIMS Bits are short items that provide quick reviews of a topic or focused practice on a specific skill. TIMS Tasks and TIMS Challenges are problems which ask students to use previously learned concepts in a new context or to extend those concepts in a challenging new situation. The content includes:
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Unit Summaries
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Unit 11
Unit 12
Unit 13
Unit 14
Unit 15
Unit 16
Unit 17
Unit 18
Unit 19
Unit 20
Unit Summary
This unit aims both to introduce significant mathematics content
and to establish a positive classroom atmosphere for the beginning
of the school year. Activities are adaptable to a range of abilities.
Working cooperatively in small groups and handling manipulatives
appropriately are encouraged. The first activity is a brief investigation
of the number of letters in the first names of students in the
class. In the lab, First Names, students apply basic techniques
of data collection and analysis—organizing data in tables, making
graphs, and discussing the meaning of results—in a familiar context.
Students also solve problems involving addition and subtraction,
practice mental computation while playing a game, and solve puzzles
to develop logical reasoning skills. In the second lab of this
unit, students create and study a population. In the lab, Kind
of Bean, students take a sample of a population of beans and make
predictions using the TIMS Laboratory Method. The unit ends with
the Adventure Book, You Can’t Do That, a cautionary tale about
group work and individual responsibility.
Concept Focus
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Unit Summary
This unit provides baseline measures about a broad range of students’
mathematical understandings and competencies. The activities include
opportunities for teachers to assess students’ arithmetic skills,
mathematical concepts, and abilities to solve problems and communicate
solutions. They also lay the foundation for ongoing work in the
Daily Practice and Problems to gain facility with the subtraction
facts. Problems involving probabilities with spinners are used
as a context for two of the activities. Portfolios of student
work are organized during this unit. The information from the
formal assessment instruments in this unit will complement samples
of student work to provide a comprehensive and balanced picture
of students’ mathematical understandings near the beginning of
the school year. The unit also includes the Adventure Book, Yü
the Great, which introduces students to magic squares.
Concept Focus
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Unit Summary
This is the first of a series of multiplication and division units
which are distributed throughout the year. Building on the informal
experiences with these operations in first and second grades,
third-grade students begin a more formal study of the concepts,
applications, notation, and procedures involved in multiplying
and dividing. The first activity provides a context for using
multiplication. Students solve problems about decorating T-shirts
using the data on first names collected in Sampling and Classifying
(Unit 1). Then, they investigate things which come in 2s, 3s,
4s, etc., and use this information to solve problems such as finding
the total number of wheels on five trucks. In another investigation,
they use counters to divide numbers into groups in as many ways
as possible. Students write story problems to illustrate multiplication
and division expressions, using manipulatives, paper-and-pencil
drawings, or computer graphics to tell their stories. The ongoing
activity, Multiples on the Calendar, is used to introduce multiples
and to begin work with the multiplication facts.
Concept Focus
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Unit Summary
This unit extends students’ work with place value to four-digit
numbers and helps them build their understanding of our number
system. The activities lay the conceptual groundwork for performing
addition and subtraction involving four-digit numbers, which will
be formally introduced in Unit 6. Base-ten pieces provide a concrete
representation of the relationship between the different digits
in our number system and help students visualize how different
digits in a number are used to represent different quantities.
In addition to place value, students practice writing and telling
time on analog and digital clocks. They continue to practice this
skill in the Daily Practice and Problems and in future units.
Concept Focus
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Unit Summary
Students’ concept of area is strengthened through a series of
activities where they find the area of irregular shapes by counting
square centimeters. In the introductory activity, students piece
together fractional parts of square centimeters into full units.
In the experiment, The Better “Picker Upper,” students apply this
skill toward understanding which of several brands of paper towel
is the best for soaking up water. The lab also provides a context
for mathematical problem solving and for an extended discussion
of the roles of fixed (controlled) variables in experiments. Students
also read the Adventure Book, The Haunted House, a story about
a team of amateur detectives who solve a mystery by measuring
the area of a ghost’s footprint.
Concept Focus
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Unit Summary
Students’ experiences with two-digit addition and subtraction,
base-ten pieces, and a standard algorithm are extended to three-
and four-digit addition and subtraction. The aims of this unit
are twofold: (a) for students to continue developing their own
strategies for adding and subtracting big numbers, and (b) for
students to discuss standard procedures and become comfortable
with using them in meaningful ways. The emphasis is on solving
problems involving addition and subtraction in context rather
than on using these operations in isolation from any context.
The Adventure Book, Leonardo the Blockhead, looks at the historical
and multicultural roots of the base-ten number system we use today.
Concept Focus
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Unit Summary
This unit has two main goals. The first is to provide a problem-solving
setting for students to continue developing their conceptual understanding
of multiplication and division. The second is to have students
explore multiples of small numbers using graphs. To do this, students
collect and graph linear data. This activity is students’ first
experience making point graphs. Students work with a recipe for
lemonade and use multiplication, division, and graphing to solve
problems related to increasing quantities in the recipe. Mathhoppers,
imaginary creatures that jump specified numbers of units on a
number line, help students explore multiplication and division
concepts. Students begin to use the division symbol when they
solve problems in the context of planning a birthday party. In
the culminating activity, students investigate the multiplicative
relationship between the number of sides of a regular figure and
its perimeter. They measure a side and the perimeter of the figures,
record and graph the data, and analyze the results using multiplication
and division.
Concept Focus
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Unit Summary
Students learn to locate objects using coordinates. A plastic
figure, named Mr. O, is used to specify the origin and coordinate
directions. For example, in the first activity, students are given
coordinates such as “four steps right” and “six steps front” and
then, using Mr. O as the origin, they locate objects in the room.
They practice finding the distance between objects on a map using
a scale by finding distances between familiar objects on a map
of a student’s desk. Then, to apply their knowledge, they build
a miniature town using connecting cubes and make a coordinate
map of the town on graph paper. Throughout these activities, students
measure distances using units of measure from both the metric
system and the customary system. Also included in the unit is
an Adventure Book, The Ghost Galleons, a story about a family
who uses coordinates to help them find sunken treasure in the
Caribbean.
Concept Focus
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Unit Summary
Students use a two-pan balance and standard masses to find the
mass of various objects. Then, in the lab, Mass vs. Number, they
investigate how to predict the total mass of a number of identical
objects. For example, if one pencil has a mass of 11 grams, then
multiplication or repeated addition yields 44 grams for the mass
of 4 pencils. They see that such procedures give a good, though
possibly inexact, prediction. For example, the measured mass of
the 4 pencils might turn out to be 46 grams. Students discuss
the concept of experimental error, possible sources of experimental
error, and explore ways to make predictions when the data contains
experimental error. In particular, point graphs are used to make
predictions when data points are close to a straight line. The
unit provides a context for a variety of problem-solving situations
involving multiplication and division.
Concept Focus
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Unit Summary
The formal assessment activities in this unit, together with ongoing
informal and formal assessment activities in the other units,
help teachers monitor student progress. Paper-and-pencil problems
and short tasks provide information about certain understandings
and skills that students should be developing. A review of student
portfolios presents an opportunity to examine student progress
across a broad spectrum of outcomes. Student work in designing
and carrying out the lab, Stencilrama, enables teachers to assess
many of the skills and concepts developed in the preceding units.
Students’ ability to communicate mathematical ideas is also assessed..
Concept Focus
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Unit Summary
Students investigate part-whole fractions by solving word problems,
playing games, working with geoboards, and making and using paper
models. Basic fraction concepts are emphasized; procedures are
not. A fundamental idea in several activities is that the meaning
of a fraction depends on what the whole is (e.g., half an inch
is much less than half a mile). Other important ideas are that
the whole must be divided into equal parts, that fractions can
have more than one name, and that ordering fractions by size requires
attention to both the numerator and denominator. The use of one-half
as a benchmark for comparing fractions is emphasized. The utility
of fractions in everyday life is highlighted in several activities
and in the homework.
Concept Focus
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Unit Summary
Students make, draw, measure, describe, and analyze plane geometric
figures. Much of the work involves figures that can be made with
small sets of constituent pieces; we say the figures are “dissected”
into the pieces. In the first activity, students use Tangrams
to solve puzzles and create shapes. In Building with Triangles,
students build plane geometric shapes with triangles and then
investigate the ideas of congruence, transformations (turns and
flips), area, perimeter, and symmetry. Relationships between attributes
of shapes (e.g., the number of sides and the number of corners)
are studied. As culminating activities, students solve geometric
puzzles and play a geometric game similar to tic-tac-toe.
Concept Focus
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Unit Summary
The study of multiplication and division continues by solving
problems about an amusement park called Lizardland. Students also
look for patterns in the multiplication table and build rectangular
arrays in order to develop strategies for learning the multiplication
facts. They apply these patterns to the multiplication of multiples
of 10 and 100. The Adventure Book, Cipher Force, discusses addition,
subtraction, multiplication, and division involving zero.
Concept Focus
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Unit Summary
A major objective of this unit is to give students more autonomy
as they work on a lab and solve problems. In the lab, Make Your
Own Survey, students work with a group to conduct a survey using
the TIMS Laboratory Method. With as little assistance as possible,
they choose a variable to study and then organize, collect, display,
and analyze the data. In this unit the class also works cooperatively
to plan and implement a “reading drive,” whereby the class sets
goals for the amount of reading they will do over a given period
of time. They keep track of their reading by collecting data and
displaying the data. The data provides a context for problem solving
using addition and subtraction of larger numbers, reading a clock
to the nearest minute, and finding elapsed time.
Concept Focus
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Unit Summary
This unit presents a formal introduction to decimals. (Informal
work with decimals began in first grade.) Decimals for tenths
and hundredths are presented as another way of writing certain
common fractions. One important context for this initial work
is measuring to the nearest tenth. To complete the lab, Number
vs. Length, students measure to the nearest tenth of a centimeter.
Work with skip counting by tenths is included. Students also explore
what happens when there are more than ten tenths. Base-ten pieces
are used to help students understand the relationship between
decimals and common fractions (e.g., 0.1= 1/10). Using this relationship,
they tell whether a fraction is more than, less than, or equal
to a given decimal.
Concept Focus
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Unit Summary
To begin the unit, students estimate the volume of small objects
by building models with centimeter connecting cubes. They then
check their estimates using a graduated cylinder and measuring
the volume of the objects by displacement. In the lab Fill ’er
Up!, students measure the volume of several containers, record
the measurements in a data table, and graph the results. They
use the data to predict how many of one container will be needed
to fill another. This provides a context for investigating division
with remainders and solving problems involving multiplication.
In the Adventure Book, Elixir of Youth, two investigators use
their volume skills when the liquid inside an ancient jar is stolen
from a museum’s collection. Students also discover the relationships
between U.S. customary units of measuring volume—the cup, pint,
quart, and gallon.
Concept Focus
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Unit Summary
Students explore relationships between fractions, focusing on
the importance of the unit whole and on the concept of equivalence.
The activities include the use of pattern blocks and paper folding.
Students investigate how the quantity represented by a fraction
depends on what the unit is: half of a hexagon pattern block is
not the same as half of a blue rhombus. They also find that the
same quantity can be represented by different fractions and may
even begin to notice patterns in those fractions. They are encouraged
to think about relationships between fractions other than equivalence,
including greater than, less than, and comparisons with benchmarks
such as 0, 1, and 1/2. In the Adventure Book, The Clever Tailor,
misunderstandings about fractions arise when the size of the unit
whole is neglected.
Concept Focus
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Unit Summary
This unit deals with visualizing and describing three-dimensional
objects. Students describe three-dimensional objects (e.g., rectangular
prisms and objects made with connecting cubes) in words by talking
about the faces, edges, and vertices (corners). They give information
about 3-D objects by measuring and recording the height, volume,
and area of the faces. They also use three methods for representing
three-dimensional shapes in two dimensions: sketching cubes and
other boxes, making cube model plans, and recording three views
of the cube models—the top, front, and right-side views.
Concept Focus
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Unit Summary
Students solve multiplication problems by breaking products into
the sum of simpler products. This decomposition is modeled using
rectangular arrays drawn on grid paper. They begin with one-digit
by one-digit problems and move to two-digit by one-digit problems.
Students write and solve multiplication story problems with particular
attention given to partitioning numbers into tens and ones. These
problems act as a catalyst for the conceptual development of an
algorithm for multiplication involving two-digit by one-digit
numbers. In this unit, students also solve division problems that
deal with remainders in various ways and multistep problems that
involve both multiplication and division.
Concept Focus
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Unit Summary
This unit provides summative evaluation information by engaging
students in several tasks. As in the previous assessment units,
Units 2 and 10, students complete both paper-and-pencil and hands-on
activities. A class discussion of the labs completed during the
year sets the stage for the final lab, Tower Power. A shorter
activity, Earning Money, can be used to assess students’ ability
to apply their knowledge of the operations in a problem-solving
situation and then to communicate their problem-solving strategies.
Two traditional paper-and-pencil tests and a review of student
portfolios are also part of this assessment menu. Students are
given many opportunities within this unit to demonstrate the variety
of concepts and skills which they have developed over the year.
Concept Focus
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NOTE: Above text taken from Math Trailblazers Teacher Implementation
Guide (TIG)
Copyright © 1997 by Kendall/Hunt Publishing Company. Used with
permission.
Copyright © 1999 Institute for Mathematics and Science Education.
All rights reserved.
UIC—University of Illinois at Chicago