Grade 5
Unit
Summaries
Units also include:
- Suggestions for journal writing;
- Recommended homework assignments for most lessons;
- Parent letters that discuss the important ideas within the unit and provide suggestions for home activities that support lessons in school;
- 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. A recommended software list also accompanies most units. Many of the units in the first semester include activities which review materials from fourth grade so students new to the curriculum will have the necessary skills and concepts for fifth grade.
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 which are related to the current unit or previous units. Problems can be solved in many 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 short exercises 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 provided for each class session. 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 is designed to help you start the year off right by
establishing a positive classroom atmosphere, introducing critical
mathematics, and gathering baseline assessment data about your
students’ mathematical abilities. Students begin the unit with
a lab called Eyelets. This lab sets a cooperative atmosphere and
reviews concepts used in earlier grades. Two activities from fourth
grade are also included which review finding the median and collecting,
organizing, and graphing data in bar graphs. Throughout the unit,
students translate between graphs and real-world events. The Searching
the Forest lab, which will help you gather baseline data on students’
mathematical abilities, focuses on populations and samples. The
Adventure Book, A Matter of Survival, also explores these concepts.
The DPP for this unit will allow you to assess students’ facility
with the addition and subtraction facts.
Concept Focus
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Unit Summary
This unit focuses on place value, big numbers, estimation, and
computation. It also provides opportunities to gather baseline
data on students’ mathematical abilities in these areas. Students
complete a variety of activities that involve reading and writing
big numbers, using convenient numbers to estimate products, multiplying
using paper and pencil, and reading scientific notation. Activities
from the fourth grade are included so students can use base-ten
pieces to review place value and addition and subtraction as needed.
An Adventure Book, Sand Reckoning, tells the story of Archimedes
and his estimate for the number of grains of sand needed to fill
the universe. A short assessment problem, Stack Up, is also included
to provide baseline data on students’ abilities to solve multistep
problems and communicate their solution strategies. The Student
Rubrics: Telling and Solving are reintroduced and students begin
collection folders to make portfolios. The yearlong review of
the multiplication facts and the study of the division facts begin
in this unit. Students use fact families to review the multiplication
facts for the fives and tens and to develop strategies for learning
the related division facts.
Concept Focus
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Unit Summary
In this unit, students build a strong conceptual foundation for
work with fractions and ratios. They review fraction concepts
with pattern blocks and use the concepts to develop skills and
procedures such as finding equivalent fractions, ordering fractions,
writing mixed numbers for improper fractions, and writing improper
fractions for mixed numbers. Students also explore ratios using
data tables, graphs, and symbols. This unit includes the lab Distance
vs. Time. In this lab, speed is defined as the ratio of distance
moved to time taken. Students use this definition as they apply
their knowledge of fractions and ratios. The Student Rubric: Knowing
is reintroduced. The DPP for this unit reviews the multiplication
facts for the twos and threes and uses fact families to introduce
the division facts for the twos and threes.
Concept Focus
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Unit Summary
This unit extends and applies students’ knowledge of several topics:
division, measuring area, averages (means and medians), and accuracy
in measurement and estimation. Division is explored first by modeling
with the base-ten pieces, then by a paper-and-pencil method called
the “forgiving” method. Students explore area and use it as a
basis for making estimates. They check the accuracy of their estimates
using 10% as a benchmark. For the first time in fifth grade, students
use the mean to average a set of data. This unit also includes
the lab Spreading Out. This lab draws upon many of the concepts
in the unit including area, 10% as a standard for error analysis,
and averages. As part of the lab, students decide when it is appropriate
to use a bar graph and when it is appropriate to use a point graph.
The Adventure Book: George Washington Carver: Man of Measure explores
many of the variables involved in math and science. This unit
also marks the midpoint of the semester. A midterm test is included
that assesses many of the concepts and skills studied thus far.
The DPP for this unit reviews the multiplication facts for the
square numbers and introduces the division facts for the square
numbers.
Concept Focus
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Unit Summary
This unit makes connections between two important strands in the
curriculum: the study of fractions and the use of data to solve
problems. Students review and expand their knowledge of fraction
concepts to include models for finding common denominators. Students
use rectangles on dot paper, geoboards, and pattern blocks as
their primary fraction models. They then use these models to develop
procedures for comparing, adding, and subtracting fractions with
unlike denominators. These concepts are further explored in the
lab A Day at the Races. In this lab, students use the TIMS Laboratory
Method and their knowledge of fractions to compare speeds by comparing
ratios. The DPP for this unit reviews the multiplication facts
for the nines and introduces the division facts for the nines.
Concept Focus
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Unit Summary
In this unit, students investigate patterns and concepts in geometry.
They draw triangles and other plane figures and discover properties
of the shapes. Students discover the relationship between the
number of sides of a polygon and the sum of the angles. Then,
they describe and classify shapes. Tessellations are explored
using quilt designs. This unit contains a short assessment, Making
Shapes, in which students draw shapes when given specific properties
and measurements. To complete the assessment, they use the Telling
Rubric as a guide for their writing as they explain the strategies
they used to draw the shapes. The DPP for this unit reviews the
last six multiplication facts (4 x 6, 4 x 7, 4 x 8, 6 x 7, 6 x
8, and 7 x 8) and introduces the 12 related division facts.
Concept Focus
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Unit Summary
A major goal of this unit is to help students understand that
often a quantity can be expressed as a fraction, decimal, and
a percent. Students use two models to help them make connections
between fractions and decimal symbols: centiwheels (circles divided
into hundredths) and squares divided into tenths, hundredths,
and thousandths. Students work with these grids to reinforce place
value concepts, compare decimals, round decimals, and model addition
and subtraction of decimals. They use an area model to learn to
place decimals in products of decimal multiplication problems.
Students use their knowledge of decimals to explore probabilities.
They complete a lab, Flipping Two Coins, in which they explore
the results of coin flipping experiments. The lab is related to
a real-life story with the Adventure Book, Unlikely Heroes. The
DPP for this unit reviews all the multiplication and division
facts.
Concept Focus
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Unit Summary
This unit expands and applies concepts and skills learned in the
first seven units. Students are assessed on these concepts and
skills as they work on the activities and labs. They demonstrate
their knowledge by solving problems that arise in several contexts
that have strong connections to science and social studies. Students
review labs completed in the first half of the year in preparation
for completing the assessment lab, Comparing the Lives of Animals
and Soap Bubbles. As part of the lab, students apply their knowledge
of percents and interpret graphs. They also read the Adventure
Book, Florence Kelley, which describes the work of a social reformer
in the late 1800s who—through data collection—was able to contribute
to the passage of child labor laws in Illinois. This Adventure
Book sets the stage for an assessment activity called Florence
Kelley’s Report in which students interpret Florence Kelley’s
data as she reported it to the governor. This unit also includes
the Mid-Year Test and a portfolio review session. The DPP for
this unit tests all the multiplication and division facts.
Concept Focus
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Unit Summary
This unit focuses on division and its applications as well as
its connections to other areas of mathematics. Students begin
by exploring the relationship between fractions and division in
order to learn strategies for finding decimal equivalents for
fractions. They extend paper-and-pencil division (the forgiving
method) to two-digit divisors. Extending the forgiving method
in a context provides a setting for interpreting remainders in
meaningful ways. In the context of checking division by using
multiplication, this unit includes an optional activity which
introduces a different multiplication method: lattice multiplication.
The lattice method is connected to the compact and all-partials
algorithms. Students also use calculators to divide larger numbers
and devise strategies to find whole number remainders with calculators.
To conclude the unit, students again connect fractions and division
by employing calculator strategies to add and subtract fractions.
The DPP for this unit reviews the division facts for the fives
and tens.
Concept Focus
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Unit Summary
This unit starts with a discussion of negative numbers within
several real-world contexts, including measuring temperature and
tracking money in a bank account. Then, positive and negative
numbers are applied to the task of making coordinate maps. The
activity, Mr. O, continues students’ investigation of coordinates
begun in first grade. An Adventure Book Wherefore Art Thou, Romeo?
emphasizes the importance of the positive and negative signs in
coordinate pairs. Students develop their spatial visualization
skills and understanding of geometric concepts by investigating
the results of flips and slides on shapes in the coordinate plane.
The DPP for this unit reviews the division facts for the twos
and the squares.
Concept Focus
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Unit Summary
In this unit students investigate some of the underlying structures
of arithmetic, often referred to as number theory. They play a
game in which they must find all the factors of the numbers from
one to forty. They identify prime and composite numbers using
a hundreds chart and a process developed by Eratosthenes, a famous
Greek mathematician. They then examine and describe patterns in
the chart. Students complete an assessment activity, A Further
Look at Patterns and Primes, using the same process on a different
chart. In a different activity, students investigate patterns
in square numbers. In the latter part of the unit, students use
common factors and common multiples to rename, compare, and reduce
fractions. The DPP for this unit reviews the division facts for
the threes and nines.
Concept Focus
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Unit Summary
In this unit, students continue their study of fractions by using
pattern blocks and other models to represent fractions in different
ways. This helps students generalize concepts and procedures which
they can then apply in new situations. For example, they use pattern
blocks to model addition of mixed numbers and multiplication of
fractions in order to develop pencil-and-paper methods for these
operations. Students also use pattern blocks to solve an assessment
problem, Pattern Block Candy. They read an Adventure Book, Peanut
Soup, which uses the context of the work of George Washington
Carver to explore the use of fractions in a real-life setting.
The unit concludes with a Midterm Test, which assesses concepts
and skills studied in this and previous units. The DPP for this
unit reviews the 12 division facts related to the last six multiplication
facts (4 x 6, 4 x 7, 4 x 8, 6 x 7, 6 x 8, and 7 x 8).
Concept Focus
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Unit Summary
The goal of this unit is to use the previously studied concepts
of ratio and proportion as a foundation for developing more formal
concepts and procedures for solving problems that involve proportional
reasoning. Students first review the use of words, tables, graphs,
and symbols to express ratios. Then, they learn that a proportion
is a statement that two ratios are equivalent and develop strategies
for solving proportional reasoning problems. Students apply proportional
reasoning to the study of density in the activity Sink and Float
and the lab Mass vs. Volume. The DPP for this unit reviews the
division facts for the twos, fives, tens, and the square numbers.
Concept Focus
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Unit Summary
In this unit, students apply many previously learned skills and
concepts, and they explore the geometry of circles. They investigate
the relationship between the circumference and the diameter of
a circle, first informally, then more formally as they complete
a laboratory investigation, Circumference vs. Diameter. In this
lab they use data tables and graphs to find an accurate approximation
for the ratio circumference to diameter (C/D), or pi (π). Then, they use this ratio to find a formula for the circumference
of a circle. Students also learn to use a compass and a ruler
to copy and construct circles and other shapes. As they work through
each activity, they use geometric terms as needed to name parts
of the circle. Finally, they interpret and construct circle graphs.
The DPP for this unit reviews the threes, nines, and the 12 division
facts related to the last six multiplication facts (4 x 6, 4 x
7, 4 x 8, 6 x 7, 6 x 8, and 7 x 8).
Concept Focus
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Unit Summary
In this final unit on geometry, students build on previous knowledge
to develop and use formulas for the area and perimeter of a rectangle
and the area of a triangle. They first review strategies for finding
the area of a rectangle, then develop the formula. To develop
the formula for the area of a triangle, students build right triangles
using geoboards and dot paper. They use different strategies for
finding the area of the triangles, then record their measurements
in a table. Using patterns in the table, they create a formula
for the area of right triangles. Then, using similar strategies,
they extend the formula to all triangles. The formula for the
perimeter of a rectangle is developed through the observation
that opposite sides of a rectangle are equal in length. The DPP
for this unit reviews all the division facts.
Concept Focus
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Unit Summary
This unit is designed to review, extend, and assess the concepts
students have studied throughout the year. Students revisit each
of the labs they have completed during the year in preparation
for completing an assessment lab. The assessment lab is based
on the Adventure Book Bats! in which a family helps a scientist
estimate the number of bats in a cave. In the lab How Many Bats
in a Cave? students use beans in a container to model the sampling
procedures used in the story. Using a similar procedure and proportional
reasoning, students estimate the number of beans in their containers.
They also complete an open-ended assessment problem, Grass Act,
in which they again use sampling to estimate the number of blades
of grass in a given area. Finally, students take an End-of-Year
Test, which assesses concepts from Units 13–15. The unit ends
with a review of students’ portfolios. The DPP for this unit reviews
and assesses all the division 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