Grade 4
Unit
Summaries
Units also include:
- 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.
Many units also include Adventure Books and recommendations for using related trade books and children’s literature.
Home Practice
The Home Practice (HP) in the Discovery Assignment Book consists of short problems that can be assigned as homework or assessment throughout the unit. The HP includes skill practice and problems related to the current unit or previous units. Problems can be solved in a variety of ways with a variety of tools including calculators, data tables and charts, graphs, manipulatives, and paper-and-pencil strategies.
Daily Practice and Problems
The Daily Practice and Problems (DPP) is a vital component of the curriculum and can be found at the beginning of each unit in the Unit Resource Guide. These exercises require less time to complete than a full activity. They provide ongoing practice, review, and study of a variety of topics. These include basic facts, computation, time, money, number sense, data, measurement, and geometry. Many word problems are included. Two DPP 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 that 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 Summary
This unit introduces students to fourth-grade mathematical content
and establishes a positive classroom atmosphere for the beginning
of the school year. The activities are designed to be adaptable
to individual, pair, or group work. They establish a basis for
learning mathematics by solving problems and communicating mathematical
thinking and solution strategies. In the first two activities,
students study categorical and numerical variables and their values.
Students organize data in tables and analyze it using a graph.
They learn to represent sets of data using medians as an average.
The four steps of the TIMS Laboratory Method are reviewed through
an Adventure Book story, The Four Servants. Then, in a lab, Arm
Span vs. Height, students use the four steps of the TIMS Laboratory
Method to investigate the relationship between fourth-graders’
arm spans and heights. This investigation sets a tone of inquiry
and exploration in mathematics. The DPP for this unit reviews
the addition facts.
Concept Focus
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Unit Summary
This unit has two major goals: to develop basic geometry concepts
and to provide opportunities to gather information about students’
mathematical abilities and attitudes at the beginning of the school
year. In the first activity, students review length, width, perimeter,
and area. In the second activity, Perimeter vs. Length, students
use the TIMS Laboratory Method to investigate the relationship
between the length and width of rectangles and their perimeters.
Using the Student Rubric: Telling as a guide, students then communicate
their discoveries. To solve a problem, Helipads for Antopolis,
they must apply area and perimeter concepts and then communicate
their problem-solving strategies. Each student starts a collection
folder and places work in a portfolio to establish a baseline
for documenting growth throughout the year. Students also explore
angles in this unit. They identify acute, right, and obtuse angles
by exploring the amount of turning in an angle. The DPP for this
unit reviews the subtraction facts.
Concept Focus
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Unit Summary
This unit develops several topics involving numbers and operations.
Students are introduced to Roman numerals. The study of a different
number system helps them further understand the Hindu-Arabic number
system and place value. They gain an appreciation of the evolution
of numbers and mathematics. Place value with ones, tens, hundreds,
and thousands then becomes the focus. Addition and subtraction
algorithms are reviewed using connecting cubes and base-ten pieces,
grouping, trading, and regrouping. Negative numbers are introduced
in the context of temperature. The DPP for this unit begins the
strategies-based year-long process of learning the multiplication
facts. This unit focuses on the multiplication facts for the fives
and the tens.
Concept Focus
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Unit Summary
This unit is the first of three multiplication and division units
in fourth grade. The array model for multiplication is used to
illustrate factors and multiples. The study of factors and multiples
then leads to a study of prime numbers and square numbers. Work
with factors gives students an opportunity to explore the relationship
between multiplication and division, as well as to practice the
multiplication facts. The DPP for this unit focuses on the multiplication
facts for the twos and threes. This unit includes two games, Floor
Tiler and Product Bingo, which provide practice with the multiplication
facts.
Concept Focus
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Unit Summary
In this unit, students use data from different sources to make
predictions. They interpret point graphs, draw best-fit lines,
and make predictions where appropriate. The Bouncing Ball lab
reinforces the four steps of the TIMS Laboratory Method while
introducing the terms manipulated, responding, and fixed variables.
Students collect data, organize it in a data table, and plot points
on a graph. They fit a line to the points, then make predictions
using their lines. Students solve a problem, Professor Peabody
Invents a Ball, using data similar to Bouncing Ball and communicate
their problem-solving strategies in words, tables, and graphs.
An Adventure Book, Two Heads Are Better Than One, illustrates
the lab and a problem students might encounter while completing
it. Students are also introduced to a new kind of average, the
mean. Students learn to calculate the mean and compare the median
and the mean of the same set of data. The DPP for this unit provides
practice with the multiplication facts for the square numbers.
Concept Focus
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Unit Summary
This unit focuses on number sense and numeration. Students explore
numbers in the thousands, ten thousands, hundred thousands, and
millions. They collect articles from newspapers that have big
numbers and place them in order on a newswire. They also work
together as a class to build models that extend the base-ten pieces
to the millions. Collecting data from the real world extends students’
opportunities to develop an intuition about numbers. Students
learn to read and write big numbers, which naturally leads to
computing with larger numbers. They practice two types of estimation:
estimating sums and differences and estimating the number of objects
in a collection. Computational estimation is guided by using convenient
numbers, benchmarks, and rounding techniques. When students estimate
“how many,” they determine if an estimate is close to the actual
number by using 10% as a guide. In the succeeding units, 10% continues
as a standard for estimation. In the context of an ancient story
about the inventor of the game of chess, students explore the
patterns of the powers of 2 using diagrams, data tables, and graphs.
The DPP for this unit focuses on the multiplication facts for
the nines.
Concept Focus
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Unit Summary
This unit focuses on multiplication facts, order of operations,
divisibility rules, and estimation strategies. Students explore
multiplication patterns with zeros when multiplying a one-digit
number by numbers that end in zeros. They also use the all-partials
algorithm to multiply one-digit by two-digit numbers. Multiplication
strategies are further explored as students pretend that certain
keys on calculators are broken. They must list keystrokes to obtain
products in different ways in the assessment lesson, Oh, No! My
Calculator Is Broken. Students also learn the conventional rules
for the order of operations in number sentences. They also identify
patterns in the multiples of a number while skip counting on a
100 chart. This leads to rules they can use to determine if one
number is divisible by another. Finally, students practice estimation
and identify how, when, and why it is appropriate to use. The
DPP for this unit introduces the last six multiplication facts
(4 x 7, 4 x 8, 4 x 6, 6 x 7, 6 x 8, 7 x 8).
Concept Focus
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Unit Summary
This unit reviews the concepts developed in the first seven units
while revisiting volume, a concept explored in earlier grades.
The activities included in the unit are designed to assess students’
learning in a variety of ways. Assessments are individual as well
as group oriented. Short, medium, and longer activities are included.
This unit includes an assessment laboratory investigation called
Volume vs. Number, which asks students to demonstrate their progress
in carrying out a laboratory investigation. Students also complete
a shorter task, Hour Walk, which allows you to evaluate their
problem-solving abilities as well as their ability to communicate
their solution strategies. The Mid-Year Test is also included
in this unit. The DPP for this unit includes a test for all the
multiplication facts studied in Units 3–7.
Concept Focus
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Unit Summary
The underlying theme of this unit is representing and describing
shapes in two and three dimensions. Students begin the unit by
reviewing some of the basic concepts of two-dimensional geometry.
They learn to name and describe lines and angles. They also explore
line and turn symmetry. Exploring three-dimensional geometry,
they draw prisms and investigate nets. An Adventure Book, Journey
to Flatopia, tells the tale of a three-dimensional person traveling
to a two-dimensional world. An assessment activity is included
to observe students’ understanding of prisms, symmetry, angles,
and volume. The DPP for this unit reviews the multiplication facts
with fives, tens, and square numbers.
Concept Focus
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Unit Summary
The main goal of this unit is to help students develop connections
between physical models, pictures, real situations, symbols, and
words for decimals. Students explore decimals as they measure
lengths in meters, decimeters, centimeters, and millimeters. They
learn to read, write, and order decimals to the hundredths. They
make connections between common fractions and decimals. Students
use the TIMS Laboratory Method to complete the Downhill Racer
lab. This unit also includes a game to compare decimals. The Adventure
Book, Alberto in TenthsLand, tells the story of a child who falls
asleep in a library and dreams of a world where everything involves
tenths. The DPP for this unit reviews the multiplication facts
with twos, threes, and nines.
Concept Focus
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Unit Summary
Students learn to multiply two-digit by two-digit numbers using
paper-and-pencil methods. The all-partials method of multiplication
is expanded, and the traditional method (compact method) of multiplication
is discussed. Students learn that there are many ways to complete
multiplication problems. Egyptian multiplication, called duplation,
is shown in the Adventure Book, Phil and Howard’s Excellent Egyptian
Adventure. Students also identify patterns in multiplying numbers
that end in zeros. The DPP for this unit reviews the last six
multiplication facts (4 x 7, 4 x 8, 4 x 6, 6 x 7, 6 x 8, 7 x 8).
Concept Focus
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Unit Summary
Through the use of manipulatives, students continue to build a
strong conceptual understanding of fractions. Part-whole fractions
are the main focus; however, there is some work with fractional
measurements. Students explore part-whole fractions with fraction
strips and pattern blocks. Comparing, ordering, adding, and subtracting
fractions with like denominators using manipulatives are stressed.
An open-ended problem involving fraction pattern block puzzles,
Puzzle Problem, is included as an assessment lesson. This unit
also includes a midterm test which covers concepts from this and
past units. The DPP for this unit reviews the multiplication facts
for the twos, threes, fives, and tens.
Concept Focus
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Unit Summary
This unit focuses on developing students’ conceptual understanding
of division and introduces a paper-and-pencil method (the forgiving
method) for computing division. Through stories, division is reviewed
before computation with symbols is introduced. Using the context
of TV Survey, students solve multiplication and division problems
involving time. They model division with base-ten pieces and then
make the connection to the forgiving method. The Plant Growth
lab is also begun in this unit. Students plant seeds and begin
collecting data that will be analyzed in Unit 15. The DPP for
this unit reviews the multiplication facts for the nines, square
numbers, and the last six facts.
Concept Focus
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Unit Summary
This unit investigates probabilities using a probability line,
number cubes, and spinners. Students learn to describe probabilities
qualitatively in words such as “likely,” “unlikely,” and “impossible”
and with probability lines. Students also describe probabilities
quantitatively using fractions. This unit includes a laboratory
investigation, Rolling A Number Cube, where students explore the
outcome of a random process. It also includes an Adventure Book,
Probe Quest, to review probability concepts. The DPP for this
unit reviews all the multiplication facts.
Concept Focus
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Unit Summary
This unit engages students in thinking about and using patterns.
Students explore, analyze, and extend patterns in many contexts.
Students complete their Plant Growth lab, which began in Unit
13, in this unit and explore the patterns that result in their
data tables and graphs. An Adventure Book, In the Shade of the
Old Meranpi Tree, relates the lab to a scientific investigation
with the rain forest. The investigation of patterns is continued
as students record patterns in data tables as functions. The unit
also reviews mass in the Taste of TIMS laboratory investigation.
In this lab, the pattern is a decreasing function where the mass
of the sandwich decreases as bites are eaten. The DPP for this
unit reviews all the multiplication facts.
Concept Focus
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Unit Summary
This unit reviews, extends, and assesses concepts students learned
throughout the school year. The activities in this unit are similar
to those in other assessment units. Students begin by reviewing
past laboratory investigations. This prepares them for completing
the experiment, Area vs. Length, which assesses their ability
to use and apply the TIMS Laboratory Method. An open-ended problem,
The Many-Eyed Dragonfly, is included in this unit to see if students
can combine many of the skills they’ve acquired to solve a problem.
Students then complete a short item test composed of a variety
of concepts taught in previous units. Finally, students review
past work in their portfolios and compare it to recently completed
work to see growth over time. The DPP includes a test on all the
multiplication facts.
Concept Focus
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NOTE: Above text taken from Math Trailblazers Teacher Implementation
Guide (TIG)
Copyright © 1998 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