Table of Contents
Gourmet
Learning
®
3rd Grade Math Sample Packet
Sample #
1
Description
Appetizers
TEKS Instructional Targets for 3rd grade
2
3
Math Main Dishes Overview
Numbers and Operations - Table of Contents
4
Numbers and Operations Unit 2 Lesson 4 - represent equivalent fractions
using objects, pictorial models and number lines
5
Algebraic Reasoning - Table of Contents
6
Algebraic Reasoning Unit 2 Lesson 2
7
Geometry Table of Contents
8
Geometry Unit 1 Lesson 1
9
Measurement Table of Contents
Measurement Unit 3 Lesson 1
10
Personal Financial Literacy
Gourmet
Learning
®
Appetizers
TM
TM
Gourmet Learning’s menu for reading, math and science goes beyond the regular educational
“menu” and serves smooth, rich differentiated instruction that actively engages students in
their learning. The end result is students taking responsibility for their learning and ultimately
achieving significantly higher test scores! The Gourmet Lesson design provides teachers with
all the tools to learn how to teach more effectively and increases their teaching success with
significantly measurable data outcomes.
Appetizers are short, daily warm-ups that provide daily math problem-solving skills review.
The content for each grade level Appetizer has been carefully selected to include mathematical
process standards so that students have ample opportunities to demonstrate mathematical
understanding. These teacher-modeled Appetizers provide ongoing assessments of students’
abilities to communicate, use, , explain and justify, their mathematical understanding and skills.
More specifically Appetizers:
• provide high interest content, relating students’ experiences to the objective of the lesson
and putting the students in a receptive frame of mind for learning;
• focus students’ attention on the math skill, create a framework for students to
organize and metacognitively interact with text;
• extend students’ understanding and application of skills to real-world scenarios;
• review math skills in a short comprehensive format;
• empower teachers with thousands of opportunities to emphasize test-taking strategies;
• provide models that incorporate critical thinking strategies for responses by providing
evidence from the text that supports and justifies students’ understanding.
• written specifically to the New Texas TEKS/STAAR standards
There you have it, fully aligned to the Texas TEKS/STAAR, the “full meal deal” utilizing
a fun, different approach to learning. All materials are available in print or online. For
additional teaching ideas and suggestion for using Appetizers as part of your daily reading,
please refer to page iv. Additional information about other Gourmet products can be found
at www.gourmetlearning.com. There are no “left-overs” in the Gourmet Learning meals!
Have an extraordinary successful year using the Gourmet Menu of products.
Jan Garber
President and Publisher
Gourmet Learning
SAMPLE 1
Gourmet Curriculum Press, Inc.©
iii
Gourmet
Learning
®
Appetizers
TM
TM
Using Math Appetizers:
Model the following procedure and expectations with your entire class for several
weeks until students are comfortable with them.
Procedure and Expectations:
Step 1: Read each card’s passage from the print or the online LessonMaker .
Step 2: Next, read and discuss the question being asked. Read each of the possible
multiple-choice answers, and discuss whether that choice is a reasonable
answer. If it is a possibility, put a question mark next to the letter. If it is a
choice that can be eliminated, draw a √ or an X through the letter.
Step 3: As students eliminate possible answer choices, ask them to use information
from the text to justify their reasoning. This is a critical test-taking skill that
Appetizers help reinforce.
Step 4: Continue this process until one or two answers remain. Use direct questioning
to prompt students to redirect or fine tune their search for accurate justifications
from the text that clarify why an answer is correct or incorrect.
Step 5: Once a final answer is selected, ask students for verbal justification, specific
with information from the text, why this is the best possible answer.
After students are comfortable with these expectations, have students complete the
recipe cards and record their answers. Using spiral notebooks for this activity
allows students to accumulate their daily responses efficiently and simplifies
your grading and long-term assessment of their progress.
Procedural Example:
Sept. 5 page 14
Card 1 B
Card 2 H
Card 3 A
iv
Gourmet Curriculum Press, Inc.©
SAMPLE 1
3rd Grade Math Appetizers
TEKS/STAAR
TEKS/STAAR
Texas Essential Knowledge and Skills
(b) Knowledge and skills.
(1) Mathematical process standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A apply mathematics to problems arising in everyday life, society, and the
workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number
sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and language as
appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical
ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
(2) Number and operations. The student applies mathematical process standards to
represent and compare whole numbers and understand relationships related to
place value. The student is expected to:
(A)compose and decompose numbers up to 100,000 as a sum of so many ten
thousands, so many thousands, so many hundreds, so many tens, and so many
ones using objects, pictorial models, and numbers, including expanded notation
as appropriate;
(B) describe the mathematical relationships found in the base-10 place value system
through the hundred thousands place;
(C) represent a number on a number line as being between two consecutive multiples
of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in
order to round whole numbers; and
(D)compare and order whole numbers up to 100,000 and represent comparisons
using the symbols >, <, or =.
SAMPLE 1
Gourmet Curriculum Press, Inc.©
v
3rd Grade Math Appetizers
TEKS/STAAR
TEKS/STAAR
Texas Essential Knowledge and Skills
(3)Number and operations. The student applies mathematical process standards to
represent and explain fractional units. The student is expected to:
(A) represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using
(B) determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given [of] a specified point on a number line;
(C) explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number;
(D) compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b;
(E) solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8;
(F) represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines;
(G) explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model; and
(H) compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects,
(4) Number and operations. The student applies mathematical process standards
to develop and use strategies and methods for whole number computations in
order to solve problems with efficiency and accuracy. The student is expected to:
(A) solve with fluency one-step and two-step problems involving addition and
subtraction within 1,000 using strategies based on place value, properties of
operations, and the relationship between addition and subtraction;
(B) round to the nearest 10 or 100 or use compatible numbers to estimate
solutions to addition and subtraction problems;
(C) determine the value of a collection of coins and bills;
(D) determine the total number of objects when equally-sized groups of objects
are combined or arranged in arrays up to 10 by 10;
vi
Gourmet Curriculum Press, Inc.©
SAMPLE 1
3rd Grade Appetizers
TEKS/STAAR
TEKS/STAAR
Texas Essential Knowledge and Skills
(4) Number and operations (cont’d) The student applies mathematical process
standards to develop and use strategies and methods for whole number
computations in order to solve problems with efficiency and accuracy. The student
is expected to:
(E) represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting;
(F) recall facts to multiply up to 10 by 10 with automaticity and recall the
corresponding division facts;
(G)use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties;
(H)determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally;
(I) determine if a number is even or odd using divisibility rules ;
(J) determine a quotient using the relationship between multiplication and division
(K) solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.
(5) Algebraic reasoning. The student applies mathematical process standards to
analyze and create patterns and relationships. The student is expected to:
(A) represent [and solve] one- and two-step problems involving addition and
subtraction of whole numbers to 1,000 using pictorial models, number lines, and
equations;
(B) represent and solve one- and two-step multiplication and division problems
within 100 using arrays, strip diagrams, and equations;
(C) describe a multiplication expression as a comparison such as 3 x 24 represents 3
times as much as 24;
(D) determine the unknown whole number in a multiplication or division equation
relating three whole numbers when the unknown is either a missing factor or
product; and
(E) represent real-world relationships using number pairs in a table and verbal
descriptions .
SAMPLE 1
Gourmet Curriculum Press, Inc.©
vii
3rd Grade Appetizers
TEKS/STAAR
TEKS/STAAR
Texas Essential Knowledge and Skills (
(6) Geometry and measurement. The student applies mathematical process standards to
analyze attributes of two-dimensional geometric figures to develop generalizations
about their properties. The student is expected to:
(A) classify and sort two- and three-dimensional solids, including cones, cylinders,
spheres, triangular and rectangular prisms, and cubes, based on attributes using
formal geometric language;
(B) use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and
squares as examples of quadrilaterals and draw examples of quadrilaterals that do
not belong to any of these subcategories;
(C) determine the area of rectangles with whole number side lengths in problems using
multiplication related to the number of rows times the number of unit squares in
each row
(D) decompose composite figures formed by rectangles into non-overlapping
rectangles to determine the area of the original figure using the additive property
of area; and
(E) decompose two congruent two-dimensional figures into parts with equal areas
and express the area of each part as a unit fraction of the whole and recognize that
equal shares of identical wholes need not have the same shape.
(7) Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement. The student is expected to:
(A) represent fractions of halves, fourths, and eighths as distances from zero on a
number line;
(B) determine the perimeter of a polygon or a missing length when given perimeter
and remaining side lengths in problems;
(C) determine the solutions to problems involving addition and subtraction of time
intervals in minutes using pictorial models or tools such as a 15-minute event plus
a 30-minute event equals 45 minutes;
(D) determine when it is appropriate to use measurements of liquid volume (capacity)
or weight; and
(E) determine liquid volume (capacity) or weight using appropriate units and tools.
viii
Gourmet Curriculum Press, Inc.©
SAMPLE 1
3rd Grade Math Appetizers
TEKS/STAAR
TEKS/STAAR
Texas Essential Knowledge and Skills
(8) Data analysis. The student applies mathematical process standards to solve
problems by collecting, organizing, displaying, and interpreting data. The
student is expected to:
(A) summarize a data set with multiple categories using a frequency table, dot
plot, pictograph, or bar graph with scaled intervals; and
(B) solve one- and two-step problems using categorical data represented with a
frequency table, dot plot, pictograph, or bar graph with scaled intervals.
(9) Personal financial literacy. The student applies mathematical process standards
to manage one’s financial resources effectively for lifetime financial security.
The student is expected to:
(A) explain the connection between human capital/labor [capital] and income;
(B) describe the relationship between the availability or scarcity of resources and
how that impacts cost;
(C) identify the costs and benefits of planned and unplanned spending decisions;
(D) explain that credit is used when wants or needs exceed the ability to pay and
that it is the borrower’s responsibility to pay it back to the lender, usually
with interest;
(E) list reasons to save and explain the benefit of a savings plan , including for
college ; and
SAMPLE 1
Gourmet Curriculum Press, Inc.©
ix
3rd Math Appetizers
3rd Math
Appetizers
Samples
Gourmet Curriculum Press, Inc.©
Serves: 3rd grade
Appetizers
OBJECTIVE 3(5)(A)
Mr. Martinez wanted to divide our class into groups of four for our social
studies project. The first thing we had to do was to draw a number out of a jar.
Each number would fit in a series of numbers, and that would be your group
assignment. My number was 21. Which set of numbers will I belong to?
a. 8,12,16
b. 13,16,19
c. 5,11,18
Gourmet Curriculum Press, Inc.©
d. 12,15,18
Geometry
OBJECTIVE 3(7)(A)
Hector wasn’t paying attention to his teacher when the
assignment was given to the class. Each student was asked to draw a
fraction to represent 2/5 Which set might be reasonable for Hector to
have drawn?
a.
b.
d.
c.
OBJECTIVE 3(7)(A)
Which number represents C on the number line.
Mark your answer.
B
78
A
79
80
C
81
D
82
83
a. 79 1/2
b. 81
c. 81 1/2
1
d. 83 1/2
SAMPLE 1
Serves: 3rd grade
Appetizers
OBJECTIVE 3(5)(E)
Ms. Miller teaches summer school. She is going to buy enough
pencils so that each student has 5 pencils. Which table shows the
number of pencils Ms. Miller needs to buy if she has 6 students in
her first class, 8 students in her second class, and 9 in her last class?
OBJECTIVE 3(5)(E)
Gourmet Curriculum Press, Inc.©
Number of
Students
a.
6
8
9
Number of
Students
c.
6
8
9
Pencils
Needed
5
10
15
Number of
Students
b.
Pencils
Needed
30
40
50
6
8
9
Number of
Students
d.
6
8
9
Pencils
Needed
30
35
40
Pencils
Needed
30
40
45
OBJECTIVE 3(7)(C)
Yvonne didn’t eat breakfast this morning, and she is looking
forward to lunch. It is now 11:47 a.m.. Her class goes to lunch at
12:00 p.m. How long must she wait for lunch?
a. 1 hour
b. 30 minutes
c. 13 minutes
d. 10 minutes
SAMPLE 1
11 12 1
10
2
9
3
8
4
7 6 5
2
Gourmet
Learning
®
Math
Main Dishes
TM
TM
Gourmet Learning’s math lessons are organized by educational mathematic
objectives – the same objectives defined in the National Council for Teachers of
Mathematics Standards. We’ve organized these six objectives, as well as the lessons
within each objective, in a logical taxonomy for learning. The structure of each lesson
helps meet students’ differentiated needs. The variety of activities for each level of
mastery or intellectual expectation provides teachers with a multitude of instructional
activities for fostering successful learners.
Our books are both a teacher and a student resource. Each page is available as a hard
copy master. To make student instruction pages immediately accessible, these pages are
provided as transparencies and noted with a (T) next to the page number. Transparencies
are located immediately following each lesson’s hard copy master pages. So, the lesson
organization is: lesson tab, hard copy masters with answer keys, and transparencies.
Main Dishes are designed to provide everything a teacher needs to introduce,
practice and test mathematics objectives. Each lesson includes a Focus Activity, Initial
Instruction (including explicit instruction, vocabulary, an optional reading activity, and
guided practice), Checking for Understanding, Cooperative Learning, Enrichment,
Reteach, and Practice and Application problems. (Additionally, many lessons include
a bonus activity and/or game.) Detailed descriptions of each of these sections can be
found in the Menu of Components on cover page v. Following this, you will find ways
to introduce vocabulary in the classroom (cover pages vii-viii).
Bloom’s Taxonomy is embedded within Gourmet’s materials. For a review of the
taxonomy and an explanation on its inclusion in our materials, see cover pages ix-x.
The modular design of each lesson, plus the spiraling design of the overall curriculum,
provides multiple opportunities for differentiated instruction and flexible grouping.
Through formative and summative assessments, you can determine a path for each
student to follow through a lesson. Information on flexible grouping as a viable option in
the math classroom can be found on cover page xi.
Main Dishes may be used separately or in tandem with other materials including
our own Appetizers.
Gourmet Curriculum Press, Inc.©
SAMPLE 2
iii
Menu of Components within each Lesson
Study the TEKS:
Focus Activity:
Designed to assist teachers in Texas,
this information helps determine their
“piece of the puzzle” that this grade
level should be covering for the specific
student expectation. We’ve looked to
the past and to the future to help you
determine what to teach this year.
Designed to get the students actively
engaged from the start, this activity
provides an informal assessment of where
the students are in their development of
this concept or in their development of
other skills needed to achieve mastery of
the skill being introduced.
Initial Instruction:
Checking for Understanding:
Four components designed to help the
teacher instruct the concepts in the lesson
include vocabulary, direct questioning,
a children’s literature connection, and
guided practice. Together they give the
students ample opportunities to learn
through many senses, ask questions, and
practice.
Although the class remains in larger
group settings, this activity is designed
to allow the teacher to step away from
the direct instruction while promoting
a common understanding and learning
from the group. This is another chance
for informal assessment to see how
well the students responded to the new
information and strategies presented in
the Initial Instruction.
Cooperative Learning:
Enrichment:
In groups, students will work together
actively
discussing
and
sharing
knowledge with their partners to solve
problems.
Often students excel in the current skill
and are looking for a challenge. This
section is designed for the students ready
for a new or advanced spin on the same
topic. It is not meant for the entire class
and often goes beyond the standards for
this grade level.
Reteach:
Practice Problems:
Similarly, with the reteach, some
students need a fresh look at the same
information – presented in a new light.
This activity does not simply provide
more problems for practice, but provides
a new and engaging way to look at the
skill/problems.
The practice section is designed as a freeresponse and multiple-choice exam. It
is provided on overhead transparencies
so that teachers can use it as a learning
tool as students review the strategies
and information learned throughout this
lesson.
Application Problems:
Answer Key:
Similar to the practice, although not
presented on transparencies, these
problems are designed as a formative
assessment at the end of the unit.
SAMPLE 2
This section is provided for the teacher’s
guidance in helping students understand
the answers. Sometimes it is impossible to
provide answers due to the randomness
of a particular activity; however, a key is
provided whenever possible.
Gourmet Curriculum Press, Inc.©
v
Flexible Grouping in the Math Classroom
Focus Activity – designed to assess what the students’ prior knowledge includes as well
as provides an engaging activity to hook the students into the material to come
Initial Instruction – designed to teach the new topic—This is accomplished
with vocabulary, children’s literature, discovery activities and traditional
methods. At the end of each Initial Instruction is a Guided Practice
to informally assess each student’s level at the end of the instruction.
This can help decide the next instructional steps.
Zone 1:
Zone 2:
Zone 3:
Checking for
Understanding –
designed to keep
the teacher in a
facilitation role
while allowing
students time to
practice in larger
groups
Checking for
Understanding –
designed to keep
the teacher in a
facilitation role
while allowing
students time to
practice in larger
groups
Cooperative
Learning/Game –
with the teacher
out of the picture,
gives the students
an opportunity to
work together to
practice their new
skills
Cooperative
Learning/Game –
with the teacher
out of the picture,
gives the students
an opportunity to
work together to
practice their new
skills
Cooperative
Learning/Game –
with the teacher
out of the picture,
gives the students
an opportunity to
work together to
practice their new
skills
Reteach –
designed
to give the
students another
opportunity to
learn the material
using a different
approach
Enrichment –
designed to give
the students a
challenge within
the realm of the
same standard
Enrichment –
designed to give
the students a
challenge within
the realm of the
same standard
Checking for
Understanding/
Game –
from a higher
grade level
Practice – a think/pair/share review activity for the whole class—Mix all three zones
together as they “pair” up to enrich the discussions on how students solve the problems.
This is the last chance to ask questions in a whole-class review before the test.
Transparencies are provided.
Application – intended as a final assessment on the skill
SAMPLE 2
Gourmet Curriculum Press, Inc.©
xi
3 Grade
rd
Nu
s
on
m
s and Opera
r
e
b
ti
Numbers and Operations
Numbers, operations, and quantitative reasoning provide a
foundation for the rest of students’ development of math skills.
Through these lessons, students will create an understanding
of numbers – not just with digits, but with words and concrete
models. In-depth studies on and strategies for learning place
value and fractions direct the students to problem-solving in
these areas. These concepts include the four main operations
(addition, subtraction, multiplication, and division), turning
the student into a true problem-solver.
Gourmet Curriculum Press, Inc.©
SAMPLE 3
Table of Contents
Numbers and Operations - Volume I
NUMBERS and OPERATIONS
I. Unit 1 - Lesson 1 - 3.2 (A)&(B) (Place Value - Compose and Decompose)
Pages
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction (Optional Reading Activity - Page 20)
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
II. Unit 1 - Lesson 2 - 3.2 (D) (Compare and Order Whole Numbers)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
SAMPLE 3
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
1
2-4
5
6-32
See Above
33-34
35-37
38-41
42-51
52-55
56-60
61-62
63-64
65-68
1
2
3
4-23
24-25
26-27
28-30
31
32-33
34-36
37-39
40-42
43-44
45-47
xxi
Table of Contents
Numbers and Operations - Volume I
III. Unit 1 - Lesson 3 - 3.4 (C) (Determine the value of coins and bills)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
Study the TEKS
Focus Activity (Optional Reading Activity - Page 4)
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Bonus Activity
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
Pages
1
2-10
11
12-18
See Above
19-21
22-24
25
26
27-30
31-34
35-42
43-46
47-49
51-52
IV. Unit 2 - Lesson 1 - 3.3(A) (Representing fractions with concrete objects)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.
N.
O.
xxii
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Reteach - Part I
Reteach - Part II
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Guided Practice
Checking for Understanding
Cooperative Learning
Reteach
Enrichment
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
1
2
3
4-6
7-8
9-10
11-12
13-15
16-18
19-21
22
23-29
30
31-33
34-36
37-38
39-40
41-43
44-46
47-52
SAMPLE 3
Table of Contents
Number Concepts - Volume I
V. Unit 2 - Lesson 2 - 3.3(E),(G) &(H) (Partitioning sets of objects; equivalent
fractions and comparing fractions with like denonimators or numerators)
Pages
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
1
2-3
4
5-17
18-24
25-26
27-30
31-39
40-43
44-47
48-52
53-55
57-58
VI. Unit 2 - Lesson 3 - 3.3 (A) &(C) (Explaining fractions as parts of a whole)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
SAMPLE 3
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
1
2-3
4
5-8
9-18
19
20-24
25-29
30-31
32-33
34-36
37-38
39-41
xxiii
Table of Contents
Numbers and Operations - Volume I
VII.Unit 2 - Lesson 4 - 3.3(F) (Representing equivalent fractions with objectcs,
pictorial models and number line) Pages
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Study the TEKS
Initial Instruction Preparations
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
1
2
3
4
5-12
13-15
16-17
18
19-22
23-25
26-28
29-30
31-33
35-36
Teacher note: Numbers and Opertaions continues in Volume II of your Main Dish set.
xxiv
Gourmet Curriculum Press, Inc.©
SAMPLE 3
3rd Grade
Number and Operations
Student Expectation: Students will construct models of equivalent fractions using a
variety of objects and pictorial models including number lines TEKS 3(3)(F)
Unit 2 – Lesson 4
The student uses fraction names and symbols with denominators of 8 or less to describe
fractional parts of whole objects or sets of objects. The student is expected to construct
concrete and pictorial models of equivalent fractions for fractional parts of whole objects.
Teacher note: For tests, pictorial models are used.
Study the TEKS . . .
Prior Knowledge
Students have created and used fractions since
Kindergarten. However, the concept of equivalent
fractions has never previously been mentioned.
Caution: In 2nd grade, the students have just begun
to multiply. This TEKS statement does not say use
multiplication to create equivalent fractions. Students
use concrete models to make equivalent fractions.
Next Steps
3rd
In 4th grade, students will continue to use concrete
and pictorial models to generate equivalent
fractions. Not until 5th grade do the TEKS require
students to generate equivalent fractions without
the use of models.
Grade
In 3rd grade . . .
Students will not create equivalent fractions by multiplying numerators and
denominators by the same number this year. They will begin to understand that
1
1
given 2 pizzas of the same size and shape, if they eat two
pieces or one
piece,
8
4
they will have eaten the same amount. Hands-on, concrete models are used to teach this
concept. The rules for using multiplication with fractions are introduced in 5th grade.
Gourmet Curriculum Press, Inc.©
SAMPLE 4
21
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct models of equivalent fractions using a
variety of objects and pictorial models including number lines TEKS 3.3(F)
Initial Instruction Preparations
Manipulatives to Make Equivalent Fractions
Teacher note: Many teacher supply stores carry fraction circles and bars made in
sturdy foam or plastic. If you do not have access to these manipulatives, the Resource
Section pages 1-24 is provided at the end of Objective 1 for you to copy and create your
own sets of fraction circles and bars.
Group size: individual
Materials: 12 different colors of cardstock, fun foam, or another product that will run
through a copy machine, but is sturdier than normal writing paper; scissors; plastic
bags
Before class: Make copies of each size circle or bar on a different color of cardstock.
(For example, the wholes may be white, the halves yellow, thirds green, etc.) Although
each page has six manipulatives, each student’s set will only need one of each type of
bar or circle. Therefore, once you copy the first page, you have enough whole circles
for six sets of manipulatives. Make enough copies, so each student has a set.
Directions: Cut out the circles and bars, including each individual piece. Separate the
bars from the circles.
Each circle set should include:
#
one
two
three
four
five
six
seven
eight
nine
ten
eleven
twelve
22
fraction
whole circle
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
10
1
11
1
12
circles
Each bar set should include:
#
one
two
circles
three
circles
four
circles
five
circles
six
circles
seven
circles
eight
circles
nine
circles
ten
circles
eleven
circles
twelve
fraction
whole bar
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
10
1
11
1
12
bars
bars
bars
bars
bars
bars
bars
bars
bars
bars
bars
Gourmet Curriculum Press, Inc.©
Teacher note:
It is NOT a good idea to
allow the students to cut
out their own sets. Small
mistakes in cutting will
create different sizes
of frames, making it
more difficult to see the
equivalencies.
You will also want to
create a set for your
overhead. Please note:
Multiple colors will
not show up unless
multi-colored overhead
transparency film is
used.
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction circles
An
Focus Activity
Equivalent Fractions
S
Teacher note: This Focus Activity is designed to engage students with fractions they use
regularly (slices of pizza).
Group size: 12 groups of at least 2 students per group
Materials: Resource Section, pages 1-24; overhead set of fraction circles
Before class: Copy the fraction circle manipulatives in the Resource Section, pages 1-24,
on overhead transparency film, if needed.
Directions: Engage the whole class in a discussion using the following Instructional
Strategy.
Questioning Technique
Instructional Strategy
Say: Eight of us go to Pablo’s Pizzeria for lunch. We order a pizza which is cut into 8
slices. If we can each eat one slice, then we say we all ate the same amount. Why? (Engage
students in a discussion of the different sizes of pizza slices. Just because we all ate 1 of
8
a pizza does not make it equal! Some pieces may be larger than others.)
(Hand out a different fraction circle to each of 12 groups. (Group #1 receives halves; group
#2 receives thirds, etc. No group will receive the whole pizza.)
Say: We all have the same size of whole pizza now. One person from each group needs
to hold a “slice” or piece up. Look at other groups’ pieces around you.
Ask: If this is the one piece of pizza you received, can we now say we ate the same
amount? (No, the sizes of the slices are different.)
Ask: Which group’s slice shows
piece on the overhead.)
1
2
of the pizza? (A student from this group places the half
Ask: If I let you eat as many slices to equal the same amount as this group’s slice, how
many would you have to eat? (Allow each group to come up to the overhead and place
1
1
their slices on the half. Complete easy fractions first such as 2 - pieces, 3 - 6 pieces,
4
1
4 - 1 pieces, 5 - pieces.) (Direct students to show how many of their slices are the same
8
10
as the original half. Continue showing the number of slices that equal
1
11
pieces are more difficult to show, and there will be
1
2
1
2
. The
1
7
pieces or
of the last piece still showing.)
Say: By showing how many of one fractional amount equals another fractional amount,
we are creating equivalent fractions. This is what we are going to discuss today.
Gourmet Curriculum Press, Inc.©
SAMPLE 4
23
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will learn vocabulary for constructing concrete models
of equivalent fractions
Initial Instruction—Part I—Vocabulary
Equivalent Fractions
Definitions:
equivalent fraction: two or more fractions that name the
same amount
1 2
Example:
=
4 8
• numerator
• denominator
The following additional vocabulary words found in this unit
are defined by using either the fraction circles or fraction bars,
resource pages 1-24.
•
•
•
•
•
•
•
•
•
•
•
•
•
24 ( T )
halves
thirds
fourths
fifths
sixths
sevenths
eighths
ninths
tenths
elevenths
twelfths
fraction bars
fraction circles
SAMPLE 4
Gourmet Curriculum Press, Inc.©
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
K C
Ap
Initial Instruction—Part II
Equivalent Fractions
Teacher note: In this Initial Instruction, students will use their fraction bars and fraction
circles to create concrete models of equivalent fractions. Using multiple-colored transparencies
will work better than all clear transparencies when stacking fractions on the overhead.
Group size: individual and whole class
Materials: Instructional Strategy, pages 5-8; examples, transparency pages 9-12; overhead
sets of fraction circles and bars, Resource Section, pages 1-24; individual student sets of
fraction circles and bars
Before class: Locate or make an overhead class set of fraction circles and bars.
Directions: Use the Instructional Strategy provided to guide students in constructing
models of equivalent fractions.
Questioning Technique
Instructional Strategy
Place transparency page 9 on the overhead.
Example 1: Use your fraction circles to find fractions that are equivalent to
Ask: What do we need to show first? (what
4
8
looks like)
4
8
.
Ask: Which fraction circle will we use? (the eighths)
Ask: What tells us this? (The denominator tells us it is in 8 parts or names the fraction.)
Ask: How many pieces will we use? (4)
Ask: How do we know this? (The numerator tells us there are 4 pieces.)
4
• Once each student has
on his/her desk, place this on the overhead. Then encourage
8
1
them to find other fraction parts of circles that equal 4 . Anything equivalent to will
2
8
work (including 1 ). Have them prove their answers by stacking transparency pieces
2
on the overhead. Challenge students to find all of the equivalent fractions.
Example 2: Create a model that is equivalent to
Ask: Which bars will we need for
denominator names the fraction.)
1
3
1
3
using fraction bars for
1
6
.
? (those in 3) Why? (The denominator is 3. The
Say: Lay out all 3 bars, but separate the 1 just a bit. (Example:
Ask: What does the question ask us to use for the equivalent fraction? (sixths)
)
1
Say: Lay out all
pieces over the thirds. If using the overhead or colored transparent
6
fractions, stack the pieces. Place them directly below the thirds if using the paper models.
(Example:
)
Say: So
2
6
=
1
3
.
Gourmet Curriculum Press, Inc.©
SAMPLE 4
25
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
Initial Instruction—Part II
Equivalent Fractions
Questioning Technique
Instructional Strategy
Place transparency page 10 on the overhead.
1
5
Example 3: Which model shows a fraction equivalent to
1
5
?
Ask: What is ? (Have a student come to the overhead and show a fifths circle, separating
1
slightly one piece (or ) from all the others. Have him/her discuss how he/she knew this.)
5
Ask: Which circles are shown in each of the answer choices? (A = thirds; B = twelfths;
C = tenths; D = eighths) Create all these circle fractions on your desk.
Say: Test each shaded part against the
1
5
piece you separated earlier. Which fraction fits?
Ask: What is the name of this fraction? (two-tenths)
Ask: What does the 10 represent? (10 equal parts)
Ask: What does the 2 represent? (2 shaded parts)
Ask: How can we write this as 2 equivalent fractions showing they are equal?
(
1
5
=
2
10
or
2
10
=
1
5
)
Ask: Which answer is the same equivalent fraction for
Optional Review of inequalities. <, >, =
=
1
5
, are
Ask: How can we write that as an inequality? (
1
3
>
Ask: Using the information you know, that
Ask: Which is larger
Ask: If
Ask: Is
2
10
4
12
equals
1
5
1
3
or
2
?
10
(
1
3
)
2
10
? (circle;
2
10
larger, smaller, or equal to
1
3
? (equal to;
2
)
10
Ask: Using what you know, is
4
12
4
12
4
12
=
=
1
3
2
10
)
)
1
3
2
10
1
3
and
Ask: How can we write this as an inequality? (
>
Gourmet Curriculum Press, Inc.©
1
5
? (
1
3
1
3
>
? (No)
1
5
)
)
greater than, less than, or equal to
4
12
pieces)
pieces the same as
, then what inequality can we write about
Ask: How can this be written as an inequality? (
26
1
5
2
10
? (greater than)
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
Initial Instruction—Part II
Questioning Technique
Equivalent Fractions
Instructional Strategy
Ask: How can you prove this? (We can place
Say: Let’s compare answer J to answer H.
Ask: What fraction names answer J? ( 2 )
Ask: Is
2
8
8
equal to, greater than, or less than
2
10
2
10
4
12
over
;
4
12
are greater than
? (greater than)
Ask: How can you prove this using your models? (We can place
fraction.)
2
10
over
2
8
;
2
8
2
10
.)
is the larger
Place transparency page 11 on the overhead.
Example 4: What fraction is equivalent to this model?
Ask: What fraction model is shown? (sixths;
4
6
)
Ask: How do you know? (Of 6 parts, 4 are shaded. The denominator
SAMPLE 2shows the
number of parts or names the fraction; the numerator shows 4 parts shaded.)
Say: Create this model with your circles.
Say: Create each of the fractions shown in the answer options. (Allow time for the
1
2
3
4
students to create , ,
, and .)
2
3
4
Ask: Which one is equivalent to
5
4
6
? (
Ask: How can you prove this? (Stack
2
3
2
3
)
on top of
4
6
. They are equivalent.)
Ask: How can we write a math sentence that tells us they are equivalent?
(
4
6
=
2
3
or
2
3
=
4
6
)
Ask: Can you find other fractions equivalent to
their answers.
4
6
and
2
3
? (
Gourmet Curriculum Press, Inc.©
8
12
or
6
9
) Have students justify
SAMPLE 4
27
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
Initial Instruction—Part II
Equivalent Fractions
Questioning Technique
Instructional Strategy
Place transparency page 12 on the overhead.
Example 5: Find a fraction that is equivalent to
6
12
,
3
4
,
2
5
,
For the following example, students may use bars or circles.
4
7
, and
11
11
.
Students should create the fractions specified, one at a time. For each fraction, have a
student display it using the overhead set of manipulatives. Additionally, for each fraction,
ask students the following questions.
Ask: How do you know your model is the same as the fraction? (Be sure the students use
correct vocabulary as they discuss the numerator and denominator.)
Say: Prove your equivalencies by placing your answers on top of the parts of other circles
or bars. (Challenge them to find all of the equivalent fractions—not to just stop at one.)
6
12
3
4
2
5
4
7
*There are no equivalent fractions for
reason for this with students.
4
7
with denominators of 12 or less. Discuss the
Ask: What must be true in order to use models to create equivalent fractions? (The models
must be congruent, or the same size and same shape!)
28
6
12
=
5
10
=
4
8
3
4
=
6
8
=
9
12
2
5
=
4
10
4
7
11
11
= 1 =
=
2
2
=
3
6
=
3
3
SAMPLE 4
=
2
4
=
4
4
=
1
2
5
5
=
6
6
=
7
7
=
8
8
=
9
9
=
10
10
=
12
12
Gourmet Curriculum Press, Inc.©
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
Initial Instruction—Part II—Examples
Equivalent Fractions
Example 1:
Use your fraction circles to find fractions that are
equivalent to 4 .
8
Example 2:
1
Create a model that is equivalent to using the fraction
3
1
bars for
.
6
Gourmet Curriculum Press, Inc.©
29 ( T )
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct concrete models of equivalent fractions
using fraction bars and circles TEKS 3.3(F)
Initial Instruction—Part II—Examples
Equivalent Fractions
Example 5:
Find a fraction that is equivalent to each of the following:
6
12
3
4
2
5
4
7
11
11
30 ( T )
SAMPLE 4
Gourmet Curriculum Press, Inc.©
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will create equivalent fractions using pictorial models
Initial Instruction—Part III
Equivalent Fractions
Optional Reading Activity
Questioning Technique
Instructional Strategy
Part I:
Say: Let’s look at another set of equivalent fractions:
Say: Turn over your paper. Draw three more rectangles on this side. Again, make each
of the rectangles the same size. This time, though, draw them so that they are 4 squares
across and 3 squares down.
Say: Now divide the first rectangle into three equal parts.
Ask: What have we created? (thirds)
Ask: If we shade one of them, what is that fraction? (one-third)
Say: Shade one-third of the first rectangle.
Say: Now divide the second rectangle into six equal parts.
Ask: What have we created? (sixths)
Ask: If we shade two of them, what is the fraction? (two-sixths)
Say: Shade two-sixths of the second rectangle.
Say: Now divide the third rectangle into twelve equal parts.
Ask: What have we created? (twelfths)
Ask: If we shade four of them, what is the fraction? (four-twelfths)
Say: Shade four-twelfths of the third rectangle.
Ask: After comparing the three fractions we have created, what can you tell me about them?
(One-third, two-sixths, and four-twelfths are the same. They are equivalent fractions.)
Challenge: Start with a rectangle that is 4 across and 4 down. How many equivalent
1
fractions can you find using this rectangle for the fraction ? (Students should be able to
2
find 1 , 2 , 4 , and 8 using the squares on the graph paper.)
2
4
8
SAMPLE 4
16
Gourmet Curriculum Press, Inc.©
31
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will construct pictorial models of equivalent fractions
Initial Instruction—Guided Practice
Equivalent Fractions
K
C
Teacher note: This Guided Practice is designed to give the students an opportunity to
practice the concepts from the Initial Instruction. It is not intended to be a test; rather
it is one more chance for the students to ask questions as they work independently.
Compare students’ strategies, and discuss the problems with the class. An answer key
has been provided, page 35. Have fraction resources available; however, students do
not have to use them.
1. Which fraction is NOT equivalent to
your answer.
2
A
3
6
6
D
12
B
4
4
C
9
2. Shade the diagram to show your answer.
F
G
H
J
8
12
=
3
1
2
3
0
32 ( T )
SAMPLE 4
Gourmet Curriculum Press, Inc.©
? Explain
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will use fraction bars to make equivalent fractions
Checking for Understanding
Equivalent Fractions
“To What Are You Equal?”
Ap
Teacher note: In this Checking for Understanding, students will work in groups to use
fraction bars to find equivalent fractions.
Group size: two to three students
Materials: fraction bar set for each student, Resource Section, pages 13-24; notebook paper;
pencils; answer key, page 35
Before class: Place the transparency on overhead. Distribute sets of fraction bars.
Directions:
• Using fraction bars, find fractions equivalent for each problem.
• Record the equivalent fractions on a piece of notebook paper.
1
.
2
1.
2.Find 3 fractions that are equivalent to
3
1.
3. Find 2 fractions that are equivalent to
4
4. Find 1 fraction that is equivalent to 1 .
5
1.
5. Find 1 fraction that is equivalent to
6
2.
6. Find 3 fractions that are equivalent to
3
3.
7. Find 2 fractions that are equivalent to
4
2.
8. Find 5 fraction that are equivalent to
4
1. Find 5 fractions that are equivalent to
SAMPLE 4
Gourmet Curriculum Press, Inc.©
33 ( T )
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will find equivalent fractions using fraction circles
Cooperative Learning
Equivalent Fractions
K
“Equivalent Fraction Land”
Ap
Teacher note: In this Cooperative Learning, students will play a game in which they
move along a game board by finding the equivalent fractions.
Group size: two to four students
Materials: game board, page 20; game cards, pages 21-22; set of fraction circles for each
student, Resource Section pages 1-12; number cubes; game board markers, different color
for each player
Before class: Copy the game board and game cards onto cardstock. Before laminating the
board and cards, write a number or place a sticker on the back of each card that matches
the board for storage. Make 1 set for each group. Locate a number cube and game board
markers for each group.
Directions:
• Distribute a set of game cards, game board, and a number cube to each group. Students
should have their fraction circles out for use.
• One player will shuffle the cards and place them face-down on the playing surface.
• Each player rolls the number cube. The player with the highest number goes first, and
then play moves around to the right (or counterclockwise).
• Player #1 rolls the number cube and moves the specified number of spaces.
• If the player lands on a fraction space, his/her turn is over.
• If the player lands on a card space, he/she must draw a card. The student will then
recreate the picture on the card with his/her fraction circles. Next, the student must
find an equivalent fraction for the shaded part of the picture on the game board and
move to that space. Sometimes players will move forward and sometimes backward.
More than one player may occupy a space.
• The winner is the player who lands on the “You Win” space first. Players must roll the
exact number to land on this space. If the number rolled is more than this space, then
player cannot move, and play goes to the next player.
• If the cards run out before the game is over, players will reshuffle the cards and place
them face-down again.
34
Gourmet Curriculum Press, Inc.©
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will find equivalent fractions using fraction circles
Cooperative Learning—Game Board
Equivalent Fractions
“Equivalent Fraction Land”
T
1
AR
T
S
6
CARD
D
CAR
2
5
CARD
2
3
CA
R
D
1
5
1
2
CARD
DG
E
5
6
1
4
Ta
Ba Go
S
Sp ck
CARD ho ke
rt th aces2
cu e
t
4
5
BR
I
CARD
CARD
3
4
1
CARD
CARD
Welcome to
FRACTION
LAND
SAMPLE 4
CARD
You W
in!
EN
D
Gourmet Curriculum Press, Inc.©
1
3
35
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will find equivalent fractions using fraction circles
Cooperative Learning—Game Cards
Equivalent Fractions
“Equivalent Fraction Land”
36
Move to the fraction that is
equivalent to:
Move to the fraction that is
equivalent to:
Move to the fraction that is
equivalent to:
Move to the fraction that is
equivalent to:
Move to the fraction that is
equivalent to:
Move to the fraction that is
equivalent to:
Gourmet Curriculum Press, Inc.©
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will make a fraction and find its equivalent
Enrichment
Equivalent Fractions
“Speed Fractions”
S
E
Teacher note: In this Enrichment, students will use playing cards to make a fraction
and then find an equivalent fraction.
Group size: two to three students
Materials: fraction board, page 24; score cards, page 25; deck of playing cards; student set
of fraction circles and bars, Resource Section, pages 1-24
Before class: Copy the fraction board and score card for each group. Locate a deck of
cards for each group.
Directions:
• Distribute a fraction board, score card, and deck of cards to each group. Students
should have their fraction circles and bars out for use.
• One player will remove the kings in the deck and shuffle the cards. The ace stands
for 1. The jack is 11. The queen is 12.
• One player turns over the top two cards. The smaller number is the numerator and
the larger number is the denominator. He/She places them on the fraction board.
• Then this player uses either fraction bars or fraction circles to create the fraction
shown with the cards.
• Once the fraction is shown, each player, including the player who created the
fraction, finds an equivalent fraction. The student who finds an equivalent fraction
first receives 2 points. If there are not any fractions that are equivalent, then all
players receive 1 point.
• After 10 rounds, the player with the most points wins.
SAMPLE 4
Gourmet Curriculum Press, Inc.©
37
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will make a fraction and find its equivalent
Enrichment—Fraction Board
Equivalent Fractions
“Speed Fractions”
38
Gourmet Curriculum Press, Inc.©
SAMPLE 4
Unit 2 – Lesson 4
Numbers and Operations
Student Expectation: Students will tear apart fraction strips to create equivalent
fractions
Reteach
Equivalent Fractions
K
“Ripping Apart Fractions”
C
Teacher note: Students will use fraction strips in a different way. By tearing apart equivalent
parts on the fraction strips, the students will create numerous equivalent fractions. Students
will be able to use this visual in future years when they are finding common denominators to
add or subtract fractions.
Group size: pairs
Materials: Instructional Strategy, below and pages 27-28; crayons; sets of fraction bars,
Resource Section, pages 13-24
Before class: Make multiple copies of fraction bars for each pair on white paper.
Directions: Use the Instructional Strategy below to guide students in this activity.
Questioning Technique
Instructional Strategy
Step 1: Everyone makes the same equivalent fraction to one-half.
• Hand students the fraction strip divided into halves.
Say: Color one section red.
Ask: What does the red part represent? (
Say: Rip the red part into 3 equal pieces.
1
2
Say: Rip the white part into 3 equal pieces.
—one red part out of two total parts)
Ask: What fraction is represented by the red parts? (
parts)
Say:
3
6
is equivalent to
1
2
3
6
—three red parts out of six total
.
Say: Let’s all make a different equivalent fraction now.
Step 2: Everyone makes a different equivalent fraction to one-half.
• Hand students another copy of the fraction strip divided into halves.
Say: Color one section blue.
Ask: What does the blue part represent? (
1
2
—one blue part out of two total parts)
Say: Rip the blue part into as many equal pieces as you’d like. (Be sure the students are
choosing different numbers of parts to increase the discussion.)
Say: Whatever you do to the colored part, you must also do to the white part, so there are
equal pieces.
Ask: Why is it important that we have equal pieces? (The numerator and the denominator
are referring to equal parts of the whole.)
SAMPLE 4
Gourmet Curriculum Press, Inc.©
39
Unit 2 – Practice #4
Numbers and Operations
Teacher note: Allow students to have access to fraction bars and circles.
Directions: Read each problem carefully. Decide which answer best completes the
question. Show your work.
Problem #3
Problem #1
1
=
3
6
What number belongs in the numerator
1
to create a fraction equivalent to
?
3
Circle your answer choice, and then
shade parts of the circle to show your
answer.
A1
D4
Problem #4
Which fraction is equivalent to this
picture?
1
2
G
2
3
B6
D12
C3
F
A3
C9
B2
Problem #2
12
=
3
4
What number belongs in the numerator
3
to create a fraction equivalent to 4 ?
Circle your answer choice, and then
shade in the first picture to show your
answer.
Which picture shows a fraction that
is equivalent to 3 ?
4
F
G
H
J
H 3
4
J
1
3
40 ( T )
SAMPLE 4
Gourmet Curriculum Press, Inc.©
Unit 2 – Application #4
Numbers and Operations
Teacher note: Allow students to have access to fraction bars and circles.
Directions: Read each problem carefully. Decide which answer best completes the
question. Show your work.
Problem #1
Problem #3
2
=
3
6
What number belongs in the numerator to
create a fraction equivalent to 2 ?
3
Shade in the circle to show your answer is
equivalent.
2
4
Abigail and Gary each ordered the same
1
type of pizza. Abigail ate
of her pizza
4
2
and Gary ate
of his pizza. Who ate more
8
pizza? Use your fraction circles or bars to
help you determine the answer. Explain
your answer.
Abigail ate more pizza.
They both ate the same amount.
6
2
4
3
5
Problem #4
Problem #2
5
=
What number belongs in the numerator to
create a fraction equivalent to 6 ?
12
Shade in the box to show your answer is
equivalent.
3
6
12
Gary ate more pizza.
They both ate the whole pizza.
4
6
=
12
What number belongs in the numerator to
create a fraction equivalent to 4 ?
6
Shade in the box to show your answer is
equivalent.
2
6
4
8
Gourmet Curriculum Press, Inc.©
41
SAMPLE 4
3 Grade
ic R
rd
ra
b
e
g
l
A
easo
n
in
g
Algebraic Reasoning
This objective is the foundation of algebra. Students will use process
standards to analyze and create patterns and relationships which
are the foundations for more complex algebraic topics. Students will
use patterns to understand multiplication and division as well as
how all the operations are related.
SAMPLE 5
Table of Contents
Algebraic Reasoning
I.
Unit 1 - Lesson 1 - 3.5 (A) Solving addition and subtraction with pictorial
models, number lines and equations
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction (Optional Reading Activity - Page 8)
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
II. Unit 1 - Lesson 2 - 3.6 (B) (Patterns)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
SAMPLE 5
Gourmet Curriculum Press, Inc.©
1
2-3
4
5-16
See Above
17-18
19-25
26-30
31-34
35-37
38-40
41-42
43-47
1
2-3
4
5-7
8
9
10-15
16-20
21
22-27
28-29
30-32
33-34
35-39
xxi
Table of Contents
Algebraic Reasoning
III. Unit 1 - Lesson 3 - 3.6 (C )(Patterns)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
IV. Unit 2 - Lesson 1 - 3.7 (A) (Lists, Tables, and Charts)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
xxii
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
Pages
1
2-3
4
5-6
7-9
10
11
12-19
20-21
22-29
30-31
32-33
35-36
1
2-3
4
5-15
16-18
19-20
21-23
24-27
28-30
31-37
38-41
42-45
47-53
SAMPLE 5
Table of Contents
Algebraic Reasoning
V. Unit 2 - Lesson 2 - 3.7 (B) (Lists, Tables, and Charts)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
VI. End of Objective Material
A.
B.
C.
D.
E.
F.
Objective 2 Supply List
Journal Entries
End of Objective Review Game
Final Test Objective 2
Answer Key
Bloom’s Taxonomy
VII. Resource Section
A. Pattern Blocks
SAMPLE 5
Pages
1
2-6
7
8-13
14-15
16-17
18-28
29-35
36-39
40-41
42-44
45-47
49-54
1
2-8
9-26
27-32
33
34-41
1-4
Gourmet Curriculum Press, Inc.©
xxiii
3rd Grade
Algebraic Reasoning
Student Expectation: Students will identify and extend whole numbers and geometric
patterns to make predictions and solve problems
Unit 1 – Lesson 1
The student uses patterns to solve problems. The student is expected to identify
and extend whole-number and geometric patterns to make predictions and solve
problems.
Study the TEKS . . .
Prior Knowledge
In 1st grade, the student is expected to identify,
extend, and create patterns of sounds, physical
movement, and concrete objects. In 2nd grade, the
student extends the idea of patterns to numbers
(such as in a hundreds chart).
Next Steps
3rd
Beyond 3rd grade, there is no mention of identifying
and extending patterns. However, patterns are
used as an important tool in multiplication and
relating data in a table.
Grade
In third grade . . .
Solidifying the idea of patterns is important this year. It is not directly taught in future
years, so being able to identify patterns, use them, and apply knowledge of them must
become a tool that students can use without direction. This is the first year that the
students look at numeric patterns without a hundreds chart to direct them.
Gourmet Curriculum Press, Inc.©
SAMPLE 5
47
Unit 2 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will learn how to analyze a given pattern and determine
the next items in the sequence
Initial Instruction—Part IV
Identify and Extend Patterns
Questioning Technique
Instructional Strategy
Method 2: Number Line
Step 1: Write all the numbers between and including the first and last number in the
example on a number line.
5 6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Step 2: Circle the numbers that are included in the original example.
5 6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Step 3: Determine how many steps and in which direction you are moving on the number
line to get from one number to the next.
move 5 right
move 5 right
move 5 right
5 6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Step 4: Continue the number line until you reach the next number. Move 5 to the right
from 20, and you will arrive at the answer, 25.
Method 3: Discuss and Write
Say: A verbal method (discuss and write) is simply putting into words what we see in
the other methods. Using any of the other methods, you can determine the pattern. Once
you do, the method of discussing and writing will help you explain what you see.
For example in method 2, we saw on the number line that 5 + 5 = 10. 10 + 5 = 15, etc.
Ask: What are the important parts of this pattern? (The students should see that the numbers
go up by 5 each time. This is important – but JUST as important is where the pattern starts.)
Say: For example, knowing that the numbers increase by 5 each time doesn’t mean that
this is the entire pattern, since the sequence 7, 12, 17, 22 also increases by 5 each time. So, to
write a complete explanation, we’ll need both the starting point and what it is increasing
or decreasing by each time.
Ask: How can you explain in words what our pattern is in this example? (Answers may
vary slightly, but should be similar to the following: Our pattern starts at 5, and we add 5
each time.)
48
Gourmet Curriculum Press, Inc.©
SAMPLE 6
Unit 2 – Lesson 2
Geometry
Student Expectation: Students will use number lines to learn how to analyze a given
pattern and determine the next items in the sequence (TEKS 3.5(A)
Initial Instruction—Part IV
Identify and Extend Patterns
Questioning Technique
Instructional Strategy
Method 2: Number Line
Say: Using number lines, the smaller numbers must be to the left and the larger numbers
to the right.
Ask: How many steps and in which direction did you move on the number line? (move
3 left each time)
55 56 57 58 59 60 61 62 63 64 65 66 67
Answer!
Method 3: Discuss and Write
Explain that each number to the right in the sequence is 3 less than the previous
number. The pattern is subtract 3 each time. Take away 3 from 61, and you get 58. (To
check, take away 3 from 58, and you get 55.)
Method 4: Number Sentences
Say: To find the numeric relationship, identify each of the numbers between the two
target numbers. 67, 64, 61
67
64
64
61
Ask: What operation will get us from 67 to 64? from 64 to 61? (- 3)
Ask: Are these number sentences true? 67 - 3 = 64; 64 - 3 = 61 (Yes.)
Say: So, our pattern is subtract 3 each time.
Say: Continue the pattern with the last number. (61 - 3 = 58) To check, continue the
pattern. 58 - 3 = 55
Have students fold a second piece of paper into 4 equal quadrants and label them the
same way they did the previous piece. They will work through example 3 using the four
methods.
Example 3: 2, 3, 5, 8, 12,
Method 1: Concrete Models
2
3
4
5
6
7
8
9
10
11
12
Say: At first glance, we can see that something is different about this example.
SAMPLE 6
Gourmet Curriculum Press, Inc.©
49
Unit 2 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will use pictorial models, number lines and equations
to represent one- and- two-step problems involving additioini and subtraction of
whole numbers to 1,000 TEKS 3.5(A)_
Enrichment
Identify, Describe & Extend Patterns in Tables
An
“The Gingerbread Man”
S
Teacher note: In this activity, students will use their creativity to decorate a gingerbread
man with various shapes. Then, using their new creation, they will form tables, make
predictions, and solve questions.
Group size: individual, then groups of four
Materials: decoration costs and questions, transparency page 37; shapes, page 38; gingerbread
man, page 39; paper; rulers; pencils; colored pencils or markers; scissors; glue sticks
Before class: Copy the gingerbread man and shapes page for each student. Gather other materials.
Directions:
• Distribute a gingerbread man, page of shapes, and other materials to each student.
• (This following step can be assigned as homework if class time is not available.) Students
will color the shapes, cut them out, and glue them to the gingerbread man in any way
they’d like. (They may create buttons with the circles, a necklace with the stars, cuffs
with the squares . . . the possibilities are endless.) They do not have to use all of the
shapes - but must include some of each.
• Now students will act as professional bakers. Using his/her own gingerbread man as the
model, each students will create a table for each of the decoration shapes used. Each table
should include 3 columns and a minimum of 5 rows. The first column will be headed
“Number of Gingerbread Men.” The second will be “Number of (Shape).” The third will
be “Cost.” Each student will fill in the first two columns for each shape at this point.
Example: If a student’s gingerbread man had 4 circles as buttons and 8 stars in a necklace,
he/she would create 2 tables like these:
Gingerbread Men
1
2
3
4
Circles
4
8
12
16
Cost
Gingerbread Men
1
2
3
4
Stars
8
16
24
32
Cost
• Once all the tables have been created, place transparency page 37 on the overhead, and
have the students complete their tables and answer the questions. This can be done on
the same page as their tables or on additional blank paper.
• Once all students have finished their tables and questions, place the students in groups
of 4 to share their findings with each other. Students should discuss similarities and
differences in their work. Whose man was the most expensive? The least? Have one
“master baker” present the group’s findings to the class.
50
• Display the gingerbread men and tables on a bulletin board.
Gourmet Curriculum Press, Inc.©
SAMPLE 6
Unit 2 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will use pictorial models, number lines and equations
to represent one- and- two-step problems involving additioin and subtraction of
whole numbers to 1,000 TEKS 3.5(A)_
Enrichment—Decoration Costs and Questions
Identify, Describe & Extend Patterns in Tables
“The Gingerbread Man”
•
•
•
•
•
Cost of Decorations
Each shape costs the following:
stars cost a quarter each
circles cost a dime each
squares cost a nickel each
triangles cost 3 cents each
little rectangles cost a penny each
1. Complete the third column of each table using the
information in the box above.
2. Describe all the patterns you see in each table.
3. How many of each shape will you need for a dozen
cookies? Explain how you arrived at your answers.
4. How much do the decorations on one cookie cost
altogether? Show your calculations.
5. Create one more table with two columns: number of
cookies and cost of cookies. This table will have 10 rows.
6. How much will a dozen of each cookie decoration cost?
What is the total cost for decorations on one dozen
cookies? Explain how you arrived at your answers.
SAMPLE 6
Gourmet Curriculum Press, Inc.©
51 ( T )
Unit 2 – Application #4
Numbers and Operations
Directions: Read each problem carefully. Decide which answer best completes the
question. Show your work.
Problem #7
What is the rule for the pattern?
+3
+5
203, 207, 211, 215, 219
Problem #10
Jessica was laying tile on her kitchen floor.
She had to make sure she put the right tile
down to match the pattern.
+4
+6
What is the next tile that she needs to put
down to continue the pattern correctly?
Problem #8
Four students stood in a row. Each held a
card showing the number of pages that he/
she could read in 20 minutes.
10 20 30 40
If the pattern continues for all of these
students, how many pages can the 5th
student read?
40
50
Problem #11
What number is missing in this pattern?
45
30
55
Problem #9
What number is missing from the pattern?
57, 157,
200
257
, 357, 457, 557, . . .
52
57
39
48
66
56
60
250
277
What is the pattern?
52
Gourmet Curriculum Press, Inc.©
SAMPLE 6
3 Grade
rd
m
e
o
t
e
ry
G
Geometry
Look around! The world is based on geometry. Everything
we look at or touch is a shape, and students should be able
to recognize and name these geometric shapes. Formal
geometric language is important as it relates these concepts to
their everyday existence. Congruence and symmetry are also
important concepts used in geometry and spatial reasoning
that are developed in this objective.
Gourmet Curriculum Press, Inc.©
SAMPLE 7
I.
Table of Contents
Geometry
Unit 1 - Lesson 1 - 3.8 (Vocabulary/Attributes)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Pages
1
2-4
5-6
7-12
13-14
15-17
18-19
20-26
27-28
29-38
39-41
42-43
45
II. Unit 1 -Lesson 5- 3.6(A) Classify/sort two-three dimensional objects Pages
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
SAMPLE 7
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
1
2-4
5
6-14
15
16-17
18-21
22-25
26-29
30-34
35-37
38-39
41-43
xxi
Table of Contents
Geometry
II. Unit 3 - Lesson 1 - 3.7(A) Fractions on a Number Line
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Study the TEKS
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach #1
Reteach #2
Practice Application
Answer Keys
VI. End of Objective Material
A.
B.
C.
D.
E.
F.
Objective 3 Supply List
Journal Entries
End of Objective Review Game
Final Test Objective 2
Answer Key
Bloom’s Taxonomy
VII. Resource Section
A. Pattern Blocks
B. Number Line
Pages
1
2-3
4
5-15
16-18
19-20
21-25
26-28
29-33
34-36
37
38-39
40-41
43-45
1
2-6
7-24
25-30
31-32
33-39
1-4
Gourmet Curriculum Press, Inc.©
xvii
SAMPLE 7
3rd Grade
Geometry
Student Expectation: Students will identify, classify, and describe two- and threedimensional geometric solids including cones, cylinders, spheres triangular and
rectangular prisms, and cubes, based on attributes, using formal geometric language.
TEKS 3.6 (A)
Unit 1 – Lesson 1
The student uses formal geometric vocabulary. The student is expected to identify,
classify, and describe two- and three-dimensional geometric figures by their attributes.
The student compares two-dimensional figures, three-dimensional figures, or both
by their attributes using formal geometric vocabulary.
Study the TEKS . . .
Prior Knowledge
In 2nd grade, the students describe, compare, and identify
two- and three-dimensional figures using attributes such
as number of vertices, faces, edges, and sides, but they are
not required to use formal geometric vocabulary.
Next Steps
3rd
Grade
In 4th grade, the students will continue to use formal
geometric language, but the number of attributes will
increase to include identifying and describing different
types of angles as well as parallel and intersecting (including
perpendicular) lines.
In third grade . . .
Introducing formal geometric language will better prepare the students for learning more
complex terms used in later grades. Many of the terms taught in this unit appear on the
TAKS test. As the teacher, it is important, to model this using the geometric terms and
equally as important to require students to use the terms, so they will become a part of
the students’ math vocabulary.
Gourmet Curriculum Press, Inc.©
57 ( T )
SAMPLE 7
Unit 2 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will identify, classify, and describe two- and threedimensional geometric solids including cones, cylinders, spheres triangular and
rectangular prisms, and cubes, based on attributes, using formal geometric language.
TEKS 3.6(A)
Focus Activity—”What’s in Your Pantry or Refrigerator?” Chart
Attributes of Geometric Figures
Spheres
58
SAMPLE 7
Rectangular
Prisms
Cubes
Cylinders
Gourmet Curriculum Press, Inc.©
Cones
Square
Pyramids
Unit 1 – Lesson 1
Geometry
Student Expectation: Students will identify, classify, and describe two- and threedimensional geometric solids including cones, cylinders, spheres triangular and
rectangular prisms, and cubes, based on attributes, using formal geometric language.
TEKS 3.6 (A)
Initial Instruction—Part I—Vocabulary
Attributes of Geometric Figures
K
attribute: the specific characteristics and qualities that define each
geometric figure
plane figures: a figure in a plane that is formed by lines that are
curved, straight, or both—(A plane is a flat surface that goes on
and on in all directions.) Plane figures are 2-dimensional and flat.
There is no depth. An example of a plane figure is a square, a
triangle, a circle.
solid figures (or space figures): a figure that has length, width
and height—Solid figures are 3-dimensional and actually take up
“space.” An example of a solid figure is a ball, a box of Kleenex, a
a can of soup, etc.
polygon: a plane figure consisting of three or more connected line
segments
octagon: a polygon with 8 sides
hexagon: a polygon with six sides
pentagon: a polygon with five sides
side: Side has two definitions. One definition is for a plane figure,
and one definition is for a solid figure.
• If you are referring to the side of a plane figure, it is the line
segments that go all around the figure. For example, there are 3
sides in a triangle, 8 in an octagon.
• The side of a solid figure is a plane figure. For example, there
are 6 sides of a box of cereal. All 6 sides are rectangles of various
sizes.
line segment: a section of a line bound by two endpoints
continued on page 6
Gourmet Curriculum Press, Inc.©
59 ( T )
Unit 2 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will identify, classify, and describe two- and threedimensional geometric solids including cones, cylinders, spheres triangular and
rectangular prisms, and cubes, based on attributes, using formal geometric language.
TEKS 3.6 (A)
Initial Instruction—Part II
Attributes of Geometric Figures
K
Teacher note: Students will use the information gathered in the Focus Activity homework
assignment “What’s in Your Pantry or Refrigerator?” to describe objects using geometric
vocabulary.
Group size: whole group
Materials: Instructional Strategy, page 8; “What’s in Your Pantry or Refrigerator?”
homework assignment (from Focus Activity); solid shapes or real-life objects that
represent solid shapes; large piece of butcher paper; marker
Before class: Divide the butcher paper into 5 sections, and label them “Solid Figure,”
“Number of Sides,” “Number of Edges,” “Number of Vertices,” and “Number of Faces” to
resemble the chart below; gather solid shapes.
Solid Figure
# of Sides
# of Edges
# of Vertices
# of Faces
Directions:
• Review geometric vocabulary.
• Explain how the students can use their homework assignment to practice using
geometric language.
• Distribute “What’s in Your Pantry or Refrigerator?” homework collected previously,
and follow the Instructional Strategy on the following page.
60
Gourmet Curriculum Press, Inc.©
3rd Grade
Geometry
Directions: Read each problem carefully. Decide which answer best completes the
question. Show your work.
Problem #1
Problem #4
A cone
F
G
H
J
Which of the following figures can
have five faces?
B square pyramid
Which of the following has a
curved surface?
C cube
D sphere
Problem #2
Which of the following ornaments
is shaped like a cone?
F
G
Problem #5
Which rug is an example of a
rectangle?
H
A
B
C
D
J
Problem #3
A can of soup is an example of
which type of shape?
A cone
B circle
C cube
D cylinder
SAMPLE 7
Gourmet Curriculum Press, Inc.©
61 ( T )
Table of Contents
Measurement
I.
Unit 1 - Lesson 1 (Length, Area, Weight/Mass & Capacity)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
II. Unit 1 - Lesson 2 (Length, Area, Weight/Mass & Capacity)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Find Perimeters
4. Optional Reading Activity
5. Guided Practice
Checking for Understanding
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
Pages
1
2
5-6
7-15
16-19
20
21-28
29-35
36
37
43-45
46-48
49-51
1
2
3-4
5-8
9-13
14-17
18-19
20-32
33-35
36-37
38-39
40-42
43-45
46-48
49-50
xv
SAMPLE8
Table of Contents
Measurement
III. Unit 1 - Lesson 3 (Length, Area, Weight/Mass & Capacity)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
IV. Unit 1 - Lesson 4 (Length, Area, Weight/Mass & Capacity)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
xvi
SAMPLE8
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
Pages
1
2
3
3-4
5-17
18-20
21-22
23-38
39-41
47-49
50
51-53
54-56
57-58
1
2-3
4
5-15
16-18
19-21
22-23
24
25-27
28-30
31-32
33-34
35-36
VI. Unit 1 - Lesson 6 (Length, Area, Weight/Mass & Capacity)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
1
2
3
4-12
13-14
15-16
17-19
20-24
25-26
27-31
32-34
35-37
39-41
SAMPLE8
Unit 2 – Lesson 2
Measurement
Student Expectation: Students will create a visual representation of capacity
measurements and practice measuring
Reteach
Measure Capacity with Concrete Models
“Gallon Guy”
C
Ap
Teacher note: In this Reteach, students will first show another representation of the
measurement tools they have learned by creating a “Gallon Guy.” Then they will practice
their measurement skills. If you think students may need additional practice measuring,
use the additional practice activity on page 29.
Group size: whole class
Materials: Instructional Strategy, pages 30-31; additional practice, page 32; Gallon Guy
parts, pages 33-34; scissors; glue sticks; colored construction paper; containers to measure;
colored water; measuring cups or approximate equivalencies (cup, pint, quart, gallon,
liter); crayons; markers; index cards
Before class: Copy pages 33-34 onto plain cardstock for each student.
Directions:
• Distribute 1 piece of construction paper to each student and one copy of pages 33-34.
• Students will cut out the pieces, keeping like pieces together.
• Then students will paste the Gallon Guy in the center of the construction paper
and draw a face on him.
• Use the Instructional Strategy to guide students in completing their Gallon Guys.
Questioning Technique
Instructional Strategy
Ask: How many quarts are in each gallon? (There are 4.)
• Direct the students to glue the 4 long rectangles as arms and legs to the gallon body,
and label each “quart.” Then they will color them all the same color. (See example on
page 28.)
Ask: How many pints are in each quart? (There are 2.)
• Direct the students to glue 2 smaller rectangles to each of the quart rectangles (8 in all),
and label each of these “pint.” Then they will color them all the same color.
Ask: How many cups are in each pint? (There are 2.)
• Direct the students to glue 2 ovals to each of the pint rectangles (16 in all), and label
each of these “cup.” Then they will color them all the same color.
• When students are finished, have them use their Gallon Guys to answer the following
questions.
SAMPLE8
Gourmet Curriculum Press, Inc.©
65
Unit 12 – Lesson 2
Algebraic Reasoning
Student Expectation: Students will create a visual representation of capacity
measurements and practice measuring
Reteach
Measure Capacity with Concrete Models
“Gallon Guy”
Questioning Technique
Instructional Strategy
Ask: How many pints are in a gallon? (8)
Ask: How is this shown in the picture? (Count the 8 pints. 4 quarts x 2 pints each = 8 pints)
Ask: How many cups are in a gallon? (16)
Ask: How is this shown in the picture? (Count the 16 cups. 2 cups x 2 pints x 4 quarts =
16 cups)
cups
cups pints
cups
pints
cups
quarts
ts
s pin
p
cu s
s
p
nt
i
u
c
p
ps
u
c
ps
u
c
ar
u
q
quarts
ts
Gallon Guy
qu
a
r ts
cups
pints cups
cups
pints
cups
pi
nt cu
s
ps
pi
c
u
nt
s cu ps
p
cu s
ps
Teacher note: To help the students understand how liters compare to the customary units,
tell them that liters are just a little more than a quart. They could remember this little
rhyme:
“Quarts can be exchanged for liters.
They’re almost the same size,
So it wouldn’t change anything
on our good-lookin’ Gallon Guys!!”
66
Gourmet Curriculum Press, Inc.©
3 Grade
rd
Meas
Measurement
Measurement
Measurement
urement
Measurement
M
easurement
Measurement
Measurement spans a lot of different areas. It includes the
attributes of length, area, weight/mass, capacity, temperature,
and time. These are the foundations for real-life mathematics,
and they are often used hand-in-hand with geometry. This
objective will help students apply their newly-acquired
measurement skills to real-life situations.
SAMPLE 8
Table of Contents
Measurement
,
I.
Unit 1 - Lesson 1 (Customerary & metric measurements) TEKS 3.7(A) Pages
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
II. Unit 1 - Lesson 2 (Length - perimeter TEKS 3.7(B)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
SAMPLE 8
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Find Perimeters
4. Optional Reading Activity
5. Guided Practice
Checking for Understanding
Cooperative Learning
Bonus Game
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
1
2
5-6
7-15
16-19
20
21-28
29-35
36
37
43-45
46-48
49-51
1
2
3-4
5-8
9-13
14-17
18-19
20-32
33-35
36-37
38-39
40-42
43-45
46-48
49-50
xiii
Table of Contents
Measurement
III. Unit 1 - Lesson 3 - Area TEKS 3.6(D)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
IV. Unit 1 - Lesson 4 Weight/Mass TEKS 3.7(D)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
xiv
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
Pages
1
2
3
3-4
5-17
18-20
21-22
23-38
39-41
47-49
50
51-53
54-56
57-58
1
2-3
4
5-15
16-18
19-21
22-23
24
25-27
28-30
31-32
33-34
35-36
SAMPLE 8
Table of Contents
Measurement
V. Unit 1 - Lesson 5 - Capacity TEKS 3.7(E)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
VI. Unit 1 - Lesson 6 - Volume & Capacity TEKS 3.7(D); (E)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
SAMPLE 8
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
Gourmet Curriculum Press, Inc.©
Pages
1
2-4
5
6-14
15
16-17
18-21
22-25
26-29
30-34
35-37
38-39
41-43
1
2
3
4-12
13-14
15-16
17-19
20-24
25-26
27-31
32-34
35-37
39-41
xv
Table of Contents
Measurement
VII.Unit 2 - Lesson 1 (Temperature ) optional A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
VIII.Unit 2 - Lesson 2 - Time Digital & analog TEKS 3.7 (C)
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Study the Skill
Focus Activity
Initial Instruction
1. Vocabulary
2. Explicit Instruction
3. Optional Reading Activity
4. Guided Practice
Checking for Understanding
Cooperative Learning
Enrichment
Reteach
Practice Application
Answer Keys
IX. End of Objective Material
A.
B.
C.
D.
E.
F.
SAMPLE 8
Objective 4 Supply List
Journal Entries
End of Objective Review Game
Final Test Objective 4
Answer Key
Bloom’s Taxonomy
Gourmet Curriculum Press, Inc.©
Pages
1
2-4
5
6-13
14-19
20-21
22-34
35-40
41-44
45-48
49-52
53-56
57-59
1
2-3
4-5
6-14
15-20
21-22
23-31
32
33-36
37-39
40-42
43-45
47-48
1
2-8
9-26
27-36
37-39
40-52
xv
Unit 1 – Lesson 3
Measurement
Student Expectation: Students will use inch and centimeter graph paper squares to
estimate the area of figures TEKS 3.6 (D)
Initial Instruction—Part III
Finding Area with Concrete/Pictorial Models
K
Teacher note: This standard asks students to use both physical and pictorial models to
find area. In this portion of the Initial Instruction, students will use inch and centimeter
graph paper to estimate the area of some figures. Through questioning, students will
extend using true-sized squares to a scale model with a square representing a larger area
(for example 1 square inch could represent 1 square mile). In the next section of the Initial
Instruction, pictorial models will be addressed.
Group size: no more than four students
Materials: Instructional Strategy, page 8; example, transparency page 9; shapes, pages 1011; inch and centimeter graph paper, pages 12-13; cardstock; scissors, tape or glue sticks;
pencils; colored pencils
Before class: Copy the shapes for each group onto cardstock. To save time, you may opt
to cut these out before class begins. Copy enough graph paper sheets so that each group
has 3 inch sheets and 3 centimeter sheets.
Teacher note: Save the copies of pages 12-13 for use in several other parts of this lesson.
Directions:
• Students will cut out the shapes from page 10. Instruct the students to cut very neatly
in the middle of the line and to watch the corners.
• Each group will start with the rectangle.
• Have the students take a sheet of graph paper that matches the units written on the
figure. For example, for the rectangle, use the centimeter paper. Students will trace the
figure onto the page twice. (Tell them to line up the figure with one of the squares so
that they don’t have too many fractional squares.)
• Students will then cut out one of the traced figures and glue it onto the shape so that
the lines for the graph paper can be seen. (Show the example on page 9. It is not one
of the problems from page 10 or 11.)
• Have the students shade in the other traced figure with a colored pencil. (Show the
example on page 9.)
• On BOTH of the figures, students should use a pencil to count the squares to find the
area. They should write their answers on the figure. Remind them to include “sq cm”
or “sq in.” (Show the example on page 9; the answer for their rectangle should be 40
square centimeters.)
• Direct the students to continue this process with the other 2 figures on page 10. When
all the groups are finished, continue with the questions on page 8 before moving on to
the shapes on page 11.
72
Gourmet Curriculum Press, Inc.©
SAMPLE 8
Unit 1 – Lesson 3
Measurement
Student Expectation: Students will use inch and centimeter graph paper squares to
estimate the area of figures; Students will decompose composite figures formed by
rectangles into non-overlapping rectangles to determine the area of the original figure
using the additive propert of area. TEKS 3.6 (D)
Initial Instruction—Part III—Example
Finding Area with Concrete/Pictorial Models
Example:
If we started with this figure:
cm
Cut out one set of square centimeters, glue them, and count:
1
2
3
4
5
6
7
8
9
10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
Trace one set of square centimeters, shade them, and count:
1
2
3
4
5
6
7
8
9
10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
Answer: area = 36 square centimeters
SAMPLE 8
Gourmet Curriculum Press, Inc.©
73 ( T )
Unit 1 – Lesson 3
Measurement
Students will decompose composite figures formed by rectangles into non-overlapping
rectangles to determine the area of the original figure using the additive propert of
area. TEKS 3.6 (D)
Checking for Understanding
Finding Area with Concrete/Pictorial Models
“Grab the Bag”
C
An
Teacher note: In this activity, the class will be divided into groups. Each group will
practice finding area using squares and counting squares already drawn in a picture.
Whole-class discussion will help the class to compare their answers and strategies.
Group size: Divide the class into 2 groups of 10. (If your class is larger than 20, then 3
groups can be used, but do not place more than 10 students in each group.)
Materials: activity diagram, page 24; area cards, pages 25-34 (Note that half of the pages
are “front sides” and half are “back sides;” the number in the lower left corner of each “front
side” indicates its matching “back side.” Copy matching sides together.); number cards,
pages 35-37; unit cards, pages 37-38; beanbag; measuring squares, pages 12-13 (or use saved
copies); 10-sided die or a bag with numbers 1-10 inside; answer key, page 57
Before class: Make a set of each of these for each group by copying them onto cardstock,
laminating them, and cutting out the cards/squares.
• Area Cards (pages 25-34)
• 40 inch squares (page 12)
• Number Cards (pages 35-37)
• 40 cm squares (page 13)
• Unit Cards (pages 37-38)
Directions:
• Place the beanbag in the center of the 2 groups.
• Distribute the cards and squares, as listed above, to each group.
• Each person in the group will receive one number card. If there are extras, some
students can have more than 1.
• Place the area cards (with the number side up) in numerical order in front of each
group. (See the activity diagram, page 24.)
• Place the unit cards right-side up (so you can see the words) halfway between the
group and the beanbag.
• Roll the die and call out the number.
• Each group will turn over its area card with the number called.
• Together, the students will determine the answer.
• When the group finds the answer, the student holding the number that matches the answer
will run to the unit cards, pick up the correct unit, and then grab the beanbag.
• The first group to grab the bag receives a point, as long as it has the correct answer
(including units).
• After all 10 rounds are complete, the group with the highest number of points wins.
74
Teacher note: Between each round, be sure to discuss with the groups HOW they arrived
at their answers. Give each group a chance to share and discuss the similarities and
differences in their descriptions. By doing this, students might modify their strategies to
help in the game.
Gourmet Curriculum Press, Inc.©
SAMPLE 8
Unit 1 – Lesson 3
Measurement
Students will decompose composite figures formed by rectangles into non-overlapping
rectangles to determine the area of the original figure using the additive propert of
area. TEKS 3.6 (D)
Initial Instruction—Guided Practice
Finding Area with Concrete/Pictorial Models
K
C
Teacher note: Students have just had explicit instruction in using manipulatives and
counting squares to find the area of objects. The following are practice problems and
questions to informally assess the students’ comprehension and abilities. It is the teacher’s
discretion to use or not use this section.
Group size: pairs
Materials: inch and centimeter graph paper, pages 12-13; transparency, page 22; copies of
the figures below; answer key, page 57
Before class: Make copies of pages 12-13 for each pair on cardstock and laminate (or
use saved copies). Students may place shapes over the squares to find area or cut out
the squares to place on top of shapes. It would be a good idea to cut out the squares in
advance if possible. The squares are often altered with elementary cutting skills. Make
copies of the bottom half of this page for each pair.
Directions:
• Instruct the students to find the area of each of the figures below using their cm or inch
squares (as indicated on each figure).
• Place transparency page 22 on the overhead, and have the students determine the area
of each of the figures. Be sure they pay attention to the key used for each.
Example #1
Measure me in
square inches.
Example #2
Measure me in
square centimeters.
SAMPLE 8
Gourmet Curriculum Press, Inc.©
75
Unit 1 – Lesson 3
Measurement
Students will decompose composite figures formed by rectangles into non-overlapping
rectangles to determine the area of the original figure using the additive propert of
area. TEKS 3.6 (D)
Checking for Understanding—Area Card Fronts
Finding Area with Concrete/Pictorial Models
“Grab the Bag”
Find the area of this triangle in square inches.
3
Joan created this
pinwheel with old
gum wrappers. What
is the area of it in
square centimeters?
4
76
Gourmet Curriculum Press, Inc.©
SAMPLE 8
Problem #4
This window has glass panes that
are 1 square foot each.
(
= 1 square foot)
What is the area of the glass in
this window?
F 4 square feet
H 12 square feet
F 8 square centimeters
G 9 square centimeters
H 10 square centimeters
12 square centimeters
Problem #7
16 square feet
Problem #5
Which of the following does not
have a shaded area of 12 square
meters?
A
What is the area of the shaded
figure drawn here on centimeter
square paper?
J
G 8 square feet
J
Problem #6
Grandma made a family quilt. Each
square is 1 square foot. What is the
area of the quilt?
B
A 27 square feet
B 24 square feet
C 18 square feet
C
(
SAMPLE 8
D
D 12 square feet
= 1 square meter)
Gourmet Curriculum Press, Inc.©
77
Unit 1 – Lesson 1
Personal Financial Literacy
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction
It’s off to Work We Go”
Teacher note: Students will perform their jobs for a week, and earn money daily. Students
will keep the money they earned in a money pouch in their notebook, and record their
earnings. At the end of the week, each student will count up the money he/she earned.
Materials: Initial Instruction pages, 80 - 81; Vocabulary, page 82; Basic Skills graphic
teaching page 83 (T); Job Descriptions table, page 84, one copy and teaching page; Job
Skills and Wages table; Personal Earnings table, one per student; Weekly Earnings,
transparency; Earnings Over Time table, one per student.
Group size: Students will be working individually
Before Class: Make several copies of play money (dollar bills), and cut them out pages
Directions for Teachers:
* Use the Instructional Strategy below to assign jobs, pay wages, and assess in
come over the period of one week.
* Create a Vocabulary Word Wall for Personal Finance Literacy.
* At the end of the Initial Instruction create a list of possible class employment
positions for which students will then earn money/
Directions for Students:
*Perform your job to earn your income.
*Use words from the Personal Finance Literacy Word Wall each day during your work in this unit.
*Record your earnings on the Weekly Earnings Chart
Questioning Technique
Instructional Strategy
Ask: What do people do with money? (save, spend, donate)
Ask: Do you get an allowance? Is it automatic or do you have to do jobs or
have good behavior to earn your money?
Ask: Do you get money from the Tooth Fairy for your teeth?
Ask: Have you sold lemonade or baked goods?
Ask: Do you get money for taking care of a pet? Cleaning up leaves?
Ask: How do adults make money? (They have jobs.)
Ask: Do all adults make the same amount of money? (No.)
78
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 1
Personal Financial Literacy
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction
It’s off to Work We Go”
Teacher note: Create class jobs with descriptions, and explain each job to the class.
Use this list as a guideline, and add jobs and change jobs as needed. It is important to
discuss what skills are critical for each job, and record that on the charts, pages 83 &
84. Assign jobs based on student interest and skills. Before jobs are assigned determine
the wages for each job, making sure that the job criteria and wages are commensurate.
Keep the salaries simple ($1, $2, $3, etc.). Record that on the charts as well.
Materials: Blank Job Description Tables, pages 85 & 86 (T)
Questioning Technique
Instructional Strategy
Ask: Why do some adults make more money than others? (Discuss the
concept of how some jobs pay more money, and what some high paying jobs
might be. Examples include software designer, dentist, and engineer. Discuss
how many hours someone works would affect how much he or she makes.
Part-time employees might make less per week than someone working fulltime or overtime.)
Ask: Why wold how many hours someone works would affect how much he
or she makes? (Part-time employees might make less per week than someone
working full-time or overtime.) If time allows ask students why they think
this might be a reality in the job market. Use the example of two people
working the same job, but one person is full-time and one person is parttime. Should they both be paid the same amount? Why or why not. Should
they both receive the same benefits, such as health-care, paid vacation?
Ask: Why do some jobs pay more than others? (Discuss how some jobs are physically
harder or require more education (college), some jobs require more skills, and some jobs
are in higher demand.)
Ask: What are some skills that employers might want? (Use the Basic Skills graphic to
discuss what skills employers want from their employees.)
Note: These skills are part of the Foundation Skills determined by the U.S. Department of
Labor report on the Secretary’s Commission on Achieving Necessary Skills (SCANS)
Say: As part of this math lesson, and our experience, you are each going to have jobs
in class, and you will earn money for the work that you do. Not everyone will make
the same amount of money, because not everyone is doing the same job with the same
skills. You will earn money each day, keep that money in your pouch in your notebook,
and record how much you earned each day. At the end of the week, you will count your
earnings, and we will share and discuss the results.
Gourmet Curriculum Press, Inc.©
79
Unit 1 – Lesson 1
Personal Financial Literacy
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction—Part I—Vocabulary
K
Definitions:
Employer – a person who provides another with a job for money
Employee – a person who works for another person or
company for money
Part-Time – working fewer hours than a usual working day
or week
Full-Time – working the standard number of hours, typically 40
hours per week
Wage – payment for work over an hourly or daily basis
Income – money earned over a period of time (money received from work, investments, or business)
Human capital – what people know and can do to earn
money (the knowledge, skills, creativity, motivation of people
used to produce work)
Labor – work one does to earn money (work that produces
goods or services for money)
80
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 1
Personal Financial Literacy
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction
It’s off to Work We Go” - Sample Job Description Charts
helps students with
problems, homework
Math Tutor
math
Reading and Language
Tutor
helps students with reading
homework
Science Tutor
helps students with science
homework
Spelling Tutor
helps students with spelling
homework
Social Studies Tutor
helps students with social
studies homework
Weekly Assignments
Secretary
keeps track of all the
assignments
Pencil Sharpeners Monitors
assist with pencil sharpening;
make sure pencil supply is
sharpened, empty sharpeners
daily
Playground Equipment
Monitor
reports missing or broken
equipment; selects equipment
to take out for recess; insures all
equipment taken out is returned
and accounted for
Classroom Equipment
Monitor
reports broken or missing
classroom equipment
Supplies Monitor
inventories classroom supplies;
reports when supplies are low;
replenishes at teacher’s direction
Gourmet Curriculum Press, Inc.©
81
Personal Financial Literacy
Unit 1 – Lesson 1
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction - continued
It’s off to Work We Go” Sample Job Description Charts
Calendar
changes calendar daily
Weatherman
reports on weather for the day
and the forecast for tomorrow;
makes appropriate clothing
suggestions for weather
Technician
sets up computer and audio/
visual equipment
Custodial Monitor
(classroom)
assists teacher with daily
attendance; runs office
errands
keeps track of all classroom
jobs; keeps job description
chart
monitors and assists class
with daily clean-up and
Banker
pays employees; exchanges
money
Attendance Clerk
Human Resources
Manager
82
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 1
Personal Financial Literacy
Student Expectation: The student is expected to explain the connection between
human capital/labor and income 3(9)(A)
Initial Instruction - continued
It’s off to Work We Go” Job Description Charts
Job Skills and Wages
Job
Paper Collector
Skills Needed
Organization, good
with people
Wage
(Daily Earnings)
$ 2.00
Board Cleaner
Gourmet Curriculum Press, Inc.©
83