TEXAS VERSION
TEKS Aligned—STAAR Ready
GRADE 6 SAMPLE
TEA
TEA­C
­CHER
HER EDITION
Published by
AnsMar Publishers, Inc.
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Thanks for requesting a sample of our new Texas Teacher Editions. We welcome the opportunity to
partner with you in building successful math students.
This booklet is a sample Texas Teacher Edition for Grade 6 (Table of Contents and first 10 lessons). You
can download Kindergarten through Grade 5 Texas Lesson Samples from our website:
www.excelmath.com/downloads/state_stdsTX.html
Here are some highlights of our new Texas Teacher Editions:
1. The Table of Contents will indicate Lessons that go further than TEKS concepts. There is a star
next to lessons that are “an advanced Excel Math concept that goes beyond TEKS for Grade 6.” With
this information, teachers can choose to teach the concept or skip it.
2. For each Lesson Plan (each day) we are changing the “Lesson Objective” to “TEKS Lesson
Objective” (see Lesson #1). On days where lessons are not directly related to the TEKS, we will offer
instruction for the teacher to alter what they do for the Lesson of the Day so they can still teach a
TEKS concept. The Objective on those days will look like this (from Lesson #21):
Objective
Students will recognize patterns.
TEKS Alternative
Activity #2 Ratios and Unit Rates (see page A3 in the back of this Teacher Edition) may be used
instead of the lesson part of the Student Lesson Sheet. Have your students complete the Guided
Practice and Homework portion of the Student Sheet.
-3. Within Guided Practice when a non TEKS concept is one of the practice problems we will indicate
it with the star again.
4. On Test Days (see Test #1) we indicate with a star any non TEKS concepts being assessed.
We are in the very early stages of creating these Texas Teacher Editions. When each one is released, we
will have an announcement on our website (focusing on grades K-5 first, and then grade 6). The student
sheets are now ready to ship.
In the meantime, you can find updates plus additional downloads on our website (manipulatives, Mental
Math, placement tests in English and Spanish, and lots more): www.excelmath.com/tools.html
Please give us a call at 1-866-866-7026 (between 8:30 - 4:00 Monday through Friday West Coast time)
if you have questions about these new Excel Math Texas Editions.
Cordially,
The Excel Math Team
Standards for Mathematical Practice
and Excel Math Grade 6
The Common Core State Standards for Mathematical Practice are integrated into
Excel Math lessons. Below are some examples of how to include these Practices into
the tasks and activities your students will complete throughout the year.
Mathematical Practices
1. Make sense of problems and persevere in solving them. Mathematically proficient
students solve real world problems through the application of algebraic and geometric concepts.
These problems involve ratio, rate, area and statistics. Students seek the meaning of a problem
and look for efficient ways to represent and solve it. They may check their thinking by asking
themselves, “Does this make sense?” “What is the most efficient way to solve this problem?” and
“Can I solve the problem a different way?” They check their answers using a different method.
2. Reason abstractly and quantitatively. Mathematically proficient students represent a wide
variety of real world contexts through the use of real numbers and variables in mathematical
expressions, equations and inequalities. Students contextualize to understand the meaning of
the number or variable as related to the problem and decontextualize to manipulate symbolic
representations by applying properties of operations.
3. Construct viable arguments and critique the reasoning of others. In Sixth Grade,
mathematically proficient students construct arguments using verbal or written explanations
accompanied by expressions, equations, inequalities, models, and graphs, tables, and other
data displays (i.e. dot plots, histograms, etc.). They critically evaluate their own thinking and
the thinking of others. Students ask questions such as, “How did you get that?” and ”Why is that
true?” They explain their thinking to others and respond to others’ reasoning and strategies.
4. Model with mathematics. In Sixth Grade, students model problems symbolically, tabularly,
graphically and contextually. They form expressions, equations or inequalities from real world
contexts and connect symbolic and graphical representations. Student use number lines
to represent inequalities and use measures of center and variability and data displays (e.g.
histograms) to compare data sets. They explain the connections between representations.
5. Use appropriate tools strategically. Mathematically proficient students consider available
tools when solving a problem and decide when certain tools might be helpful. For example, they
may represent figures on the coordinate plane to calculate area. Students might use physical
objects or drawings to construct nets and calculate the surface area of three-dimensional figures.
6. Attend to precision. Mathematically proficient Sixth Grade students use clear and precise
language in discussions. They use appropriate terminology when referring to rates, ratios,
geometric figures, data displays and components of expressions, equations or inequalities. For
example, when calculating the volume of a rectangular prism they use cubic units.
7. Look for and make use of structure. Mathematically proficient students carefully look for
patterns and structure. Students recognize patterns that exist in ratio tables recognizing both
the additive and multiplicative properties. Students compose and decompose two- and threedimensional figures to solve real world problems involving area and volume.
8. Look for and express regularity in repeated reasoning. Mathematically proficient
students use repeated reasoning to understand algorithms. They divide multi-digit numbers and
perform operations with multi-digit decimals. They make models to show a/b ÷ c/d = ad/bc.
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© 2014 AnsMar Publishers, Inc.
Lesson Page Reference
LESSON PAGE 1
CONCEPT
2
Recognizing numbers less than a million given in words or place value; adding, subtracting and multiplying
whole numbers or money amounts with regrouping; recognizing multiples; selecting the correct equation;
solving multi-step word problems using addition, subtraction and multiplication with regrouping; calculating
change using the least number of coins; recognizing money number words; recognizing addition and
subtraction fact families; optional: recognizing ordinal number words up to 100
2
4
Comparing two or more sets of data using bar or line graphs; interpreting information given in a histogram; recognizing the symbols < less than and > greater than; filling in missing numbers in sequences counting by numbers from 1 to 12; arranging 4 four-digit numbers in order from least to greatest and greatest to least; selecting the correct symbol for a number statement
3
6
Recognizing true and not true number statements; using trial and error to solve for unknowns in an
equation; solving algebraic equations with and without parentheses; changing a number statement from ≠
to =; learning the order of operations when solving an equation
4
8
Learning 7 days = 1 week; learning 1 year = 12 months; learning the number of days in each month;
optional: computing the date within the month; learning the abbreviations for days and months
5
10Defining numerator and denominator; determining the fractional part of a group of items when modeled or
given in words, sometimes with extraneous information and the word “not”; learning that the whole is the sum of its parts; adding and subtracting fractions and mixed numbers with like denominators
12
Test 1 - Assessment
6
14Recognizing multiplication and division fact families; learning division facts with dividends up through 81
and dividends that are multiples of 10 (to 90), 11 (to 99) or 12 (to 96); dividing a one-digit divisor into a
three-digit dividend using the standard algorithm with a two- or three-digit quotient with no regrouping or
remainders; solving multi-step word problems involving division; learning the terminology for multiplication
and division
7
16
Adding, subtracting and multiplying with multi-digit decimals using the standard algorithm; solving word
problems using deductive reasoning; determining if there is sufficient information to answer the question in a
word problem; determining what information is needed to answer the question in a word problem
8
18
Solving word problems by listing possibilities or by making a chart
9
20
Learning division facts with remainders with dividends up through 81; solving word problems involving division with remainders
10
22
Estimating measurements; measuring temperature; learning measurement equivalents for length, weight, volume: feet, inches, yards, centimeters, meters, kilometers, grams, kilograms, liters, milliliters, millimeters, quarts, gallons, ounces, pounds and tons; converting measurements using multiplication or division; making
tables of equivalent ratios; determining the measurement that is longer or shorter or heavier or lighter
24 Test 2
24
Create A Problem 2: Decoding Secret Messages
1126
Measuring line segments to the nearest half inch, quarter inch and half centimeter; comparing U.S. customary and metric units; making tables of equivalent ratios and finding missing values in the tables
12
28
Multiplying by a two-digit multiplier; multiplying multi-digit decimals using the standard algorithm
13
30
Finding the least common multiple of two whole numbers less than or equal to 12; learning 60 minutes
= 1 hour; telling time to the minute; recognizing a quarter past or before the hour and half past the hour;
calculating minutes before the hour; optional: calculating elapsed time (hours) involving AM and PM
14
32
Computing the area of the rectangle, doubling it, and comparing the two; learning the terminology of
parallel, intersecting and perpendicular lines, plane figure, polygon, quadrilateral, parallelogram, rectangle,
square, diagonal, rhombus and trapezoid
1534
Recognizing three-dimensional figures - sphere, cube, cone, cylinder, rectangular, square and
triangular pyramids and rectangular and triangular prisms; learning the terminology of flat and curved faces, bases, edges and vertices
36
Test 3
36
Create A Problem 3: Landscape Design
16
38
Dividing a one-digit divisor into a three-digit dividend with a two-digit quotient with regrouping and remainders
1740
Determining the lowest common multiple; learning division and multiplication facts with products with 11
(to 121) or 12 (to 144) as a factor
18
42
Understanding ratios; describing a ratio relationship between two quantities; determining equivalent fractions
using models, money, multiplication or division
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© 2014 AnsMar Publishers, Inc.
Lesson Page Reference
LESSON PAGE CONCEPT
19
44
Computing 1/2 to 1/9 of a group of items; optional recognizing odd and even numbers less than 1,000
2046
Rounding to the nearest ten, hundred or thousand; estimating the answers for addition, subtraction and
multiplication word problems using rounding to the nearest ten, hundred or thousand; estimating range for
an answer; rounding numbers so there is only one non-zero digit
48
Test 4
48
Create A Problem 4: Designing the Playground
21
50
TEKS Alternate: Activity #2 - Ratios in Word Problems; Opt: learning the terminology of pentagon, hexagon and
octagon; recognizing patterns; determining figures that do or do not belong in a set
22
52
Putting simple fractions in order from least to greatest and greatest to least; determining the fraction with
the greatest or least value in a set of fractions
23
54
TEKS Alternate: Activity #3 - Real & Whole Numbers on a Number Line; recognizing lines of symmetry; Opt:
Recognizing similar and congruent figures; recognizing flips, slides and turns; bilateral and rotational symmetry
24
56
Recognizing numbers up through trillions given in words or place value; recognizing numbers given in
expanded notation
25
58
Graphing coordinate points in all quadrants of the coordinate grid; learning the sum of the angles of
a rectangle; recognizing right, obtuse and acute angles; measuring and estimating angles; recognizing
equilateral, isosceles and scalene triangles; learning the sum of the angles of a triangle
60
Test 5
60
Create A Problem 5: Daily Activities
26
62
Dividing a two-digit divisor into a dividend less than 100 with remainders
2764
Converting an improper fraction to a mixed or whole number; determining the fraction with the greatest or
least value in a set of fractions
28
66
Adding and subtracting fractions with unlike denominators
29
68
Reading maps drawn to scale
3070
Calculating the area and perimeter of a rectangle; solving word problems involving area and perimeter
72
Test 6
72
Create A Problem 6: The Fruit Juice Stand
31
74
Dividing dollars by dollars
3276
Determining coordinate points
33
78
Recognizing the pattern in a sequence of figures or pattern of shading; solving for an unknown angle in a
triangle
34
80
Understanding ratios; describing a ratio relationship between two quantities; comparing probabilities
3582
Recognizing tenths and hundredths places; writing mixed numbers as decimal numbers; writing decimal
numbers as mixed numbers; recognizing decimal number words; adding and subtracting decimal
numbers
84
First Quarterly Test
36
86
Calculating the length of vertical and horizontal lines by subtracting x- and y-coordinates
3788
Learning the Distributive Property of Multiplication; learning the Associative Property of Multiplication and
Addition; learning the Commutative Property of Addition and Multiplication
38
90
Dividing a one-digit divisor into a four-digit dividend with a three-digit quotient; learning the Property of One
and the Zero Property
39
92
Adding and subtracting fractions in word problems
40
94
Recognizing multiplication without the “x” symbol; calculating answers to word problems using 2 to 1
and 5 to 1 ratios
96
Test 7
96
Create A Problem 7: A Whole Lotta Shaking Going On
41
98
Learning the equivalent for one year in days and in weeks; learning about leap year; calculating
elapsed time crossing months within a week
42
100
Determining the question given the information and the answer; estimating the most reasonable answer
43
102
Calculating elapsed time in minutes across the 12 on a clock
44
104
Converting fractions and decimal numbers to percents by setting up equivalent fractions
45
106Using Venn Diagrams to understand the union and intersection of sets 108
Test 8
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6 but may be required by some
states. Alternate TEKS Activities are provided in this Teacher Edition.
www.excelmath.com
© 2014 AnsMar Publishers, Inc.
i.35
Lesson Page Reference
CONCEPT
108
Create A Problem 8: Measuring Vision
46
110
Converting mixed numbers to decimal numbers by setting up equivalent fractions
47
112
Comparing fractions with unlike denominators in less than and greater than problems and in true and not true number statements by setting up equivalent fractions
48
114
Converting improper fractions as part of mixed numbers; recognizing division without the “÷” symbol
49116
Rounding money amounts and decimal numbers to the nearest dollar or whole number
50
118Determining factors, prime numbers, composite numbers, prime factors and greatest common factors
120
Test 9
120
Create A Problem 9: Measuring the Heat in Spicy Food
51
122
Multiplying decimal numbers
52
124
Dividing decimal numbers by whole numbers; converting percents to decimal numbers
53
126
Comparing decimal numbers in less than and greater than problems
54
128
TEKS Alternate: Activity #1 - Percent Problems; Opt: recognizing Roman numerals: I, V, X, L, C, D and M
55
130Calculating averages
132
Test 10
132
Create A Problem 10: Measuring Carats
56
134
Determining the greatest common factor and least common factor
57
136
Simplifying fractions; solving equations involving fractions
58
138
Estimating answers to problems involving numbers with up to nine digits
59
140
Calculating the volume of a rectangular prism with one or more layers of cubes using the formula L x W x H
60
142
Recognizing parts of a circle; calculating diameter and radius; associating the 360 degrees in a circle with one-
quarter, one-half, three-quarter and full turns
144
Test 11
144
Create A Problem 11: Diagramming a Class Survey
61
146
Recognizing the thousandths place; rounding decimal numbers to the nearest tenth or hundredth; solving
equations involving decimals
62
148
Dividing a two-digit divisor into a three-digit dividend with a two-digit quotient; simplifying fraction answers
63
150Comparing positive and negative numbers
64
152
Determining numbers that are multiples of one number and factors of another
65
154Calculating mean, median and mode; using stem and leaf plots
156
Test 12
156
Create A Problem 12: Rainfall Report
66
158Calculating equivalent ratios
67
160
Determining percent in word problems
68
162
Determining if coordinate points are on a given line
69
164
Using trial and error and charting strategies to solve word problems
70
166Defining dependent and independent variable, central tendency, statistics and outlier; recognizing factors that
influence data collection; creating a scatter plot and a box plot
168
Second Quarterly Test
71
170
Computing the percent of a whole number, money amount or decimal number
72
172Calculating cost per unit
73
174
Filling in missing numbers in a sequence of decimal numbers
74
176
Putting decimal numbers in order from least to greatest and greatest to least; evaluating decimal numbers in
true and not true number statements
75
178
Calculating the perimeter and area of an irregular figure
180
Test 13
180
Create A Problem 13: Rock Concert
76
182
Calculating area and perimeter given coordinates on a coordinate grid
77
184
Calculating using exponents; calculating square roots
78
186
Selecting an equivalent fraction; simplifying improper fractions as part of a mixed number answer
79
188
Solving word problems involving decimals
80
190Recognizing complementary, straight and supplementary angles
LESSON PAGE = This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6 but may be required by some
states. Alternate TEKS Activities are provided in this Teacher Edition.
www.excelmath.com
i.36
© 2014 AnsMar Publishers, Inc.
Lesson Page Reference
LESSON PAGE CONCEPT
192
Test 14
192
Create A Problem 14: Road Trip
81
194
Calculating decimal answers in division problems when zeroes need to be added to the right of the dividend
82
196
Dividing using short division
83
198
Converting mixed numbers to improper fractions
84
200
Filling in missing numbers in sequences counting by varying amounts
85
202
Multiplying fractions and whole numbers by fractions
204
Test 15
204
Create A Problem 15: The Last Frontier
86206
Estimating to the nearest dollar or whole number
87
208
Comparing fractions in word problems
88
210
TEKS Alternate: Activity #8 - Graphing Coordinate & Drawing Polygons on a Plane; Opt: recognizing angles
89
212
Calculating distance, time, rate and speed in word problems
90
214
Selecting the fraction, percent or decimal number that best represents a shaded region
216
Test 16
216
Create A Problem 16: The Great Race
91
218
Solving equations with embedded parentheses
92
220
TEKS Alt: Activity #4 - Area & Perimeter of Triangles; Opt: calculating elapsed time more than one week
93
222
Reducing improper fraction answers to their lowest terms
94
224
Solving problems using data displayed as percent pie graphs
95
226
Recognizing decimal places to the right of the thousandths; multiplying decimals when zeroes need to be
added to the product
228
Test 17
228
Create A Problem 17: Gloria’s World Tour
96
230
Solving word problems by working backwards
97
232
Writing probability as a fraction, decimal, percent or proportion (ratio)
98
234
Selecting the most reasonable answer involving percents
99
236
Writing probabilities as lowest-terms fractions
100238
Calculating the surface area of a rectangular prism; determining the equation that creates a pattern
240
Test 18
240
Create A Problem 18: The Long Jump Competition
101
242 TEKS Alternate Activity #5 - Area & Perimeter of Polygons; Opt: determining reciprocals
102
244
Multiplying and dividing decimal numbers by powers of ten
103
246
Dividing a three-digit divisor into a three-digit dividend with a one-digit quotient
104
248
Multiplying mixed numbers
105
250
Solving word problems involving percent, including the word “not”
252
Third Quarterly Test
106
254
Subtracting fractions with like denominators with regrouping
107
256
Simplifying division problems using powers of ten
108
258
Estimating using rounding to one-digit accuracy; calculating volume in word problems
109
260
Determining negative numbers using coordinate points
110
262
Solving word problems involving sales tax, sale price, interest and profit
264
Test 19
264
Create A Problem 19: Guess the Shape
111
266
Converting decimal numbers to percents and percents to decimal numbers
112
268
Using multiplication and division to simplify fraction multiplication problems; simplifying fractions before multiplying
113
270
Converting decimal numbers to lowest-terms fractions or mixed numbers
114
272
Determining the equation that represents a problem and the equation that solves it
115
274
Identifying the equation that represents a line on a coordinate graph; learning slope and intercept
276
Test 20
276
Create A Problem 20: Planting Trees = This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6 but may be required by some
states. Alternate TEKS Activities are provided in this Teacher Edition.
www.excelmath.com
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© 2014 AnsMar Publishers, Inc.
Lesson Page Reference
LESSON PAGE CONCEPT
116
278
Determining percent of a whole number
117
280
Solving word problems involving the multiplication of fractions and mixed numbers
118282
Dividing fractions
119
284
Arranging fractions, decimal numbers and mixed numbers on a number line
120
286
Calculating averages involving decimals and fractions
288
Test 21
288
Create A Problem 21: Planting More Trees
121290
Calculating the area of a parallelogram
122
292
Multiplying a three-digit number by a three-digit number
123
294
Rounding mixed numbers
124296
Calculating the area of a triangle
125
298
TEKS Alternate: Activity #6 - Area & Perimeter of Trapezoids; Opt: calculating circumference and area of a circle; π (pi)
300
Test 22
300
Create A Problem 22: Paying Taxes I
126
302
Converting measurements using multiplication or division with fractional or decimal remainders
127
304
Calculating percents in word problems
128
306
Converting fractions to decimal numbers using division; recognizing the symbol for a repeating decimal
129
308
Converting fractions to percents
130
310
Understanding absolute value using number lines; adding positive and negative integers
312
Test 23
312
Create A Problem 23: Paying Taxes II
131
314
TEKS Alt: Activity #9 - Constructing Cubes to Find Volume Using Exponents; Opt: adding positive and negative integers
132
316
Dividing a two-digit divisor into a three-digit dividend with a one-digit quotient
133
318
Calculating expected numbers based on probabilities
134
320
Using rounding to estimate quotients
135
322
Determining percents that are greater than 100% and less than 1%
324
Test 24
324
Create A Problem 24: Climbing Mt. Whitney
136
326
Dividing a three-digit divisor into a four-digit dividend with a two-digit quotient
137
328
Adding and multiplying measurements, then simplifying units
138
330
Dividing a decimal number by a decimal number
139332
Calculating the volume of a triangular prism or cylinder (optional)
140
334
Reviewing rounding quotients; calculating percents in word problems, rounding to the nearest whole percent
336
Fourth Quarterly Test
141
338
Subtracting measurements by exchanging units
142
340
Dividing mixed numbers
143
342
Subtracting positive and negative integers
144
344
Subtracting positive and negative integers
145
346
Determining the fourth vertex of a parallelogram on a coordinate graph
348
Year-End Test 1
146
350
Subtracting mixed numbers and fractions with unlike denominators with regrouping
147
352
Dividing a three-digit divisor into a four-digit dividend with a one-digit quotient
148
354
TEKS Alternate: Activity #7 - Calculating Surface Area & Ratios; Opt: solving for an unknown with similar polygons
149
356
Determining number patterns
150
358
TEKS Alternate: Activity #17 - Calculating Unit Rate, Speed, Range and Velocity; Opt: calculating the probability of two
separate events as a sum and two consecutive events as a product; calculating using factorials and permutations
360
Year-End Test 2
151
362
Using ration reasoning; comparing the value of products using different currencies
152
364
Calculating and comparing cost per unit
153
366
Solving word problems involving division of fractions and mixed numbers
154
368
Solving unit rate problems; using ratio and rate reasoning; estimating answers to division word problems
155
370
Multiplying and dividing positive and negative integers
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6. Alternate TEKS Activities are
provided in this Teacher Edition.
www.excelmath.com
i.38
© 2014 AnsMar Publishers, Inc.
Texas Edition
6th Grade Lesson Plans
#1-10 and Answer Keys
www.excelmath.com
1
© 2014 AnsMar Publishers, Inc.
Lesson 1
TEKS Objective
own equation first and then look for that
equation among the choices. Explain that
the order for addition and multiplication is
not important, but the order is important
for subtraction and division. Give your
students the following word problem:
“Jackson had $5.11. He earned $4.50 and
then spent $7.99 on a computer game. How
much money does he have now?” ($1.62)
Students will add, subtract, multiply and
divide integers fluently.
Students will recognize numbers less than a
million given in words or place value.
Students will multiply and divide positive
rational numbers fluently.
For problems #16 – #18, the students
should start with the largest possible coin.
If adding another coin takes them over
the given amount, they should drop down
to the next smaller value coin. As they
add coins, they should write an addition
problem to verify their choices.
Students will recognize ordinal numbers up
to 100.
Preparation
For each student: Ones and Tens Pieces,
Hundreds Pieces, Hundreds Exchange Board
(masters on M13 – M14 and M16)
Ordinal Numbers Option
Lesson Plan
Read through the ordinal numbers section.
Explain that ordinal numbers (first, second,
third, etc.) indicate position, not value.
Write the number 253,874 on the board.
Point out that the value of the thousands
place is 3 times one thousand (3 x 1,000).
The words ten and hundred are repeated in
the two places to the left of the thousands
place. This pattern will repeat itself in larger
numbers. Do #1 and #2 with the students.
In each, point out the importance of each
zero as a placeholder.
Stretch
Starting with this lesson, there will be a
problem of the day or brainteaser called a
STRETCH. Write the problem on the board
in the morning for bell work. The students
will have all day to come up with a solution.
Reward those who have the answer by
the end of the day when you provide the
solution. Sometimes there may be other
answers in addition to the ones we provide.
Review the addition, subtraction and
multiplication problems in #4 – #9.
Read the definition of multiple with the
students. For problems#10 – #11, the
students are to select the set that only
contains multiples of the given number. The
other three choices will contain at least one
number that is not a multiple of the given
number.
Stretch 1
Three consecutive numbers that add to 6
are 1, 2 and 3. (1 + 2 + 3 = 6) What three
consecutive numbers add to 345?
Answer: 114, 115 and 116
(114 + 115 + 116 = 345)
Go over the word problems in #12 – #15.
For #12, the students should write their
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.
2
Lesson 1
Name
Date
Recognizing numbers less than a million given in words or place value; recognizing
ordinal number words up to 100; adding, subtracting and multiplying whole
numbers or money amounts with regrouping; recognizing multiples; selecting the
correct equation; solving multi-step word problems; calculating change using the least
number of coins; recognizing money number words; recognizing addition and
subtraction fact families
12
Write each number.
2 hundred thousands, 7 tens, 8
ones, 9 thousands and 3 hundreds
1
six hundred fifty-one thousand,
eight hundred thirty
2
209, 378
6 5 1 , 83 0
Ordinal numbers are used to indicate where an item is located in relation to others
in the same set.
3
14
Felipe was waiting in line at the movie theater. He counted the number of people
ahead of him in the line. He was the fifty-third person in line. How many people
were ahead of him?
5 2 p eo p l e
284
4,3 6 7
92
+ 63
4
5
6
5,0 0 0
- 1,5 3 5
3, 465
4 , 806
7
8
9,805
- 3,452
942
x 5
681
x 8
469
x 7
6 ,3 5 3
4 ,7 1 0
5 ,4 4 8
3 , 28 3
Which set shows multiples of 12?
11
16
(6, 12, 14, 17)
(7, 10, 13, 16)
(2, 3, 4, 6)
(12, 20, 30, 44)
(9, 12, 15, 18)
(3, 11, 14, 18)
CheckAnswer
368
- 48
320
57
+ 320
377
Marcia did 7 pull-ups on Friday, 8 on
Saturday and 3 on Sunday. Vicky did
7 fewer pull-ups than Marcia. How
many pull-ups did Vicky do?
18 - 7 = 11
11 p ull- ups
Orange soda is sold in packs of
six. Which set shows possible
numbers of sodas that could be
bought?
3. (6, 12, 15, 18)
5. (15, 21, 27, 33)
27 s t ick s
15
A picture frame costs 51¢. Amber
gave the clerk a dollar. How much
was her change?
Eddie has 8 nickels, 6 dimes and
3 quarters. How much money
does he have?
$ .40
. 60
+ .75
$ 1. 75
$ . 49
Using the fewest coins,
how many dimes are
there in 23¢?
2
17
Using the fewest coins,
how many nickels are
there in 43¢?
10¢
10¢
+ 3¢
23¢
1
18
$ 1 .7 5
Using the fewest coins,
how many quarters are
there in 58¢?
25¢
10¢
5¢
+ 3¢
43¢
25¢
25¢
5¢
+ 3¢
58¢
2
© Copyright 2007-2014 AnsMar Publishers, Inc.
$3 0 .7 0
B 748
460
- 60
400
9,6 5 2
- 3,2 4 1
6,411
5,7 8 6
- 2,3 5 8
3,428
245
+103
348
400
+ 348
748
D
Roscoe had $3.74. He spent
$2.78 and he earned $3.85. How
much money does he have now?
$3 .7 4
$3 .8 5
- 2 .7 8
+ .9 6
$ .9 6
$4 .8 1
6 x 11 = 6 6
$3.8 7
x
6
$2 3 .2 2
$ 30.70
4. 81
23. 22
+ 33. 94
$ 92.67
$4 0.0 3
- 6.0 9
$3 3 .9 4
$4 .8 1
9,850
11
6 ,4 1 1
+ 3 ,4 2 8
9 ,8 5 0
E 2,758
Which fact does not
belong in this set?
1. 8 + 4 = 12
2. 4 + 8 = 12
3. 12 - 4 = 8
397
38
104
+ 2,1 9 2
2 ,7 3 1
2 0 nickels
$1.00 = _____
3 quarters
75¢ = _____
4
2, 731
20
+
3
2, 758
4. 8 - 4 = 4
F 154
12 x 7 = 8 4
C $92.67
thirty dollars and seventy cents
CheckAnswer
A 377
4. (12, 18, 24, 36)
39
- 12
27
Name
To check your work, add the answers to your problems and compare the
result to the CheckAnswer that is provided. If the two numbers are equal,
your answers are correct and you may go on to the next problem. If the
sum of your answers does not equal the CheckAnswer, then go back and
check your work. If you are unable to find your mistake, ask for help.
4
84
+ 66
154
two hundred seventeen thousand,
eight
one hundred thousand, fifty-nine
nineteen hundred
6. (4, 10, 16, 22)
www.excelmath.com
9. 5 x 4 = 20
6001
www.excelmath.com
7
8
+ 3
18
7. 5 - 4 =
Which set shows multiples of 3?
(12, 24, 36, 48)
Guided Practice 1
Alek threw 26 sticks to his dog on
Monday and 13 on Tuesday. Twelve
of the sticks got lost in the bushes, so
the dog couldn't bring them back. How
many sticks did his dog bring back?
Change can be given in several different combinations of coins.
For example, 15¢ can be 3 nickels or 1 dime and 1 nickel.
If you want to use the fewest coins, it's 1 dime and 1 nickel.
(6, 12, 18, 24)
12
3
+42
57
8. 5 ÷ 4 =
9
13
26
+ 13
39
6. 4 + 5 =
$ 1. 00
- .51
$ . 49
A multiple is the result of multiplying two numbers. Some of the multiples of
2 are 2, 4, 6, 8 and 10. Some of the multiples of 5 are 5, 10, 15, 20 and 25.
10
Matilda would like to plant 4 different
herbs in each of her 5 gardens. Which
equation shows how many herbs she
will need?
6002
G 318,967
2 1 7 ,0 0 8
1 0 0 ,0 5 9
217, 008
100, 059
+
1,900
318, 967
1 ,9 0 0
© Copyright 2007-2014 AnsMar Publishers, Inc.
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6. The stars are not marked on the
Student Lesson Sheets.
3
Lesson 2
TEKS Objective
Students will represent numeric data
graphically, including histograms, bar
graphs and line graphs.
the numbers: two dots next to the larger
number and one dot next to the smaller
number. Next, connect the one dot to each
of the two dots.
Students will order a set of rational
numbers arising from mathematical and
real-world contexts and will recognize the
symbols “<” less than and “>” greater than.
You will see a sideways “V”. The bottom
point of the “V” points to the smaller
(in value) of the numbers. The number
statement is “2,801 is greater than 2,534.”
Students will fill in missing numbers in
sequences counting by numbers from 1 to
12.
Have the students make “Vs” with their
thumbs and pointer fingers. Have them
turn their “Vs” sideways. Note that the left
“V” shows less than (your fingers look like
an “L”). The right “V” shows greater than.
Students will arrange 4 four-digit numbers
in order from least to greatest and greatest
to least.
Write on the board a series of numbers that
increases or decreases by 12. Ask the class
in what direction the sequence is counting
(+ or –), by what number the sequence
is counting and how they know. (Find
the difference between each number.) Then
ask them to determine what the missing
number in the sequence will be.
Preparation
No special preparation is required.
Lesson Plan
Read through the explanation and do
#1 – #4 together. Explain that when
multiple sets of data appear on the same
graph, a legend is shown below the graph
indicating the information each line or bar
is representing.
Have a student give you 3 four-digit
numbers less than 10,000. Write them on
the board in random order. Ask a student
to come forward and rewrite the numbers
in order from least to greatest and have
the class explain how to tell if the order is
correct. (The values in the thousands place are
compared, then the hundreds and so on, down
to the ones place.) Have students put more
numbers in order, this time from greatest
to least.
The graph on the bottom right side of the
lesson is a histogram. Histograms are used
to group data using intervals. (As opposed
to bar graphs, which group data according
to the amount in each category.) To build
a histogram, find the lowest value and the
highest value. Divide the values between
them into equal groups. Each of the values
is then placed into one of the segments.
Stretch 2
Kim, Brian and Lee have 42 cats. Lee has
twice as many as Kim. Brian has half as
many as Kim. How many cats do they each
have?
i The following concept is found on Guided
Practice D and E.
Write “2,801” and “2,534” on the board.
Ask a student to put notations between
Answer: Kim has 12 cats, Lee has 24 cats
and Brian has 6 cats.
4
Lesson 2
Name
Date
Comparing two or more sets of data using bar or line graphs; interpreting information
given in a histogram; recognizing the symbols < less than and > greater than; filling
in missing numbers in sequences counting by numbers from 1 to 12; arranging 4 fourdigit numbers in order from least to greatest and greatest to least
A histogram is a type of graph used when you want to group the data.
Our example shows the amount of time it took students to complete a math test.
We put the information into a tally chart. You will need to know the least amount of
time a student took and the greatest amount of time. This is the range of the data.
Next, decide how to divide the range into equal parts. We used 5-minute intervals.
Circle or pie graphs are used primarily to organize data. Picture graphs
use symbols and pictures to compare data. Bar graphs also compare
data. Line graphs are used to show change over time.
Part-time Employees Work Days
1
20
How many more days
did Gail work in January
than Sean?
Intervals
0 - 5 minutes
6 - 10 minutes
11 - 15 minutes
16 - 20 minutes
21 - 25 minutes
20
- 10
10 more days
10
15
10
5
2
Jan
Feb
Mar
Apr
May
How many days did
Paul and Sean work
in May?
Paul Gail Sean
High Temperatures
During the First Week in June
Temperature
(ºC)
26
25
24
23
22
21
20
20 days
3
4
1
2
3
2000
2001
2002
4
Days
5
6
7
15
+ 5
20
How much warmer was it on the
third day of June in 2002
than in 2000?
A
7 2 , _____
6 5 , 5 8 , 5 1 , 44 , 37)
(_____
26
- 22
4
536
38 1
72
65
+ 18
53 6
Select the number from the
given set to fill in the blank.
(3,4 3 4 ; 3 , 3 4 3 ; 3 , 4 3 3 ; 3,334)
>
3 , 3 34
________
one hundred two thousand,
fifteen
102,015
Taking Photographs
Glen
Each
1
0-5
6-10 11-15 16-20 21-25
Minutes
© Copyright 2007-2014 AnsMar Publishers, Inc.
9,3 6 1
- 4,1 9 5
5,166
3,334
2,300
102,015
+651,429
759,078
2,30 0
5 ten thousands, 2 tens,
1 thousand, 6 hundred
thousands, 9 ones and
4 hundreds
$ 4 0 .6 0
ten dollars and
eighty cents
$ 1 0 .8 0
2 4 a pple s
4
+ 7
11
How many took fewer than four
photographs?
2 - Ruthie and Glen
F 17
11
2
+ 4
17
Ronnie would like to give
each of his ten friends a
$5.00 gift certificate.
Which equation shows
how much money he
will need?
6. 10 + $5 =
How many more photos does Glen
need to take to catch up with Barry?
represents 2 photos
4 more photos
6-2=4
7. 10 - $5 =
8. 10 x $5 = $ 5 0
9. 10 ÷ $5 =
6004
5
$40.60
10.80
78.40
+ 30.87
$160.67
$6 7.0 5
- 3 6.1 8
$30.87
$ 9 .8 0
x
8
$78.40
Brian picked 21 apples on Monday
and 15 on Tuesday. Twelve of the
apples were bad, so he threw them
away. How many apples does he
have left?
21
36
+ 15
- 12
36
24
6 5 1 ,42 9
How many photographs did Carly
and Lupe take?
3,893
5,166
2,552
+1,743
13,354
C $160.67
forty dollars and
sixty cents
249
x 7
1,743
D 759,078
twenty-three hundred
11 photographs
www.excelmath.com
2
B 13,354
638
x 4
2,55 2
18 ahead of him.
are _____
Ruthie
3
Write 3 statements about the information in this graph.
How could the information about taking a test help the teacher of this class?
417
649
1,3 0 9
+ 1,5 1 8
3 ,89 3
Rod is nineteenth in line. There
Lupe
4
Name
381 )
( 41 3 , 4 0 5 , 3 9 7 , 3 8 9 , _____
Carly
5
6003
Guided Practice 2
Barry
6
0
www.excelmath.com
3,343
Time Needed to Complete the Math Test
How much cooler was it on the
second day of June in 2000
26
than in 2001?
- 24
2
2° cooler
4° warmer
Number of Students
Next, transfer the information from the tally chart to the histogram.
Number of Students
Days
25
Draw the correct symbol ( < or > )
between the pair of numbers.
1 ,6 11
>
1 ,1 6 1
6.
7.
>
<
E 35
24
6
+ 5
35
5
2 quarters = ______
dimes
Dakila feeds her goats
six pounds of grain
every day. How many
pounds of grain does
Dakila feed her goats
each week?
6
x 7
42
4 2 po unds
Using the fewest
coins, how many
quarters are there
in 33¢?
25¢
5¢
+ 3¢
33¢
G 51
8
42
+ 1
51
1
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 3
TEKS Objective
9 on a team. So far you have 3. How many
more do you need to complete the team?
Write: 3 + __ = 9. Explain that this equation
represents the same question you have
asked them but in numerical form. Fill in
the 6. Do #7 – #9 together.
Students will write one-variable, one-step
equations and inequalities to represent
constraints or conditions within problems.
Students will model and solve one-variable,
one-step equations and inequalities that
represent problems.
Replace the letters with the given values
and solve problems #10 – #11.
Students will recognize true and not true
number statements.
The number statement in #12 is not an
equation. Because the right side is greater
than the left side, select a number on the
right to move to the left and write a new
number statement with an “=” symbol.
Students will determine if the given values
make one-variable, one-step equations or
inequalities true.
Explain that we use parentheses to change
the order (or sequence) of what is done.
Read through the section on the order of
operations and do #13 – #15 together.
Preparation
No special preparation is required.
Lesson Plan
Write on the board: 4 + 5 = 2 + 7. This is an
equation because the value on the left is
the same as the value on the right. Ask the
class if the above equation is true.
i Problems #2 – #3 and #7 – #9 do not
appear on the Student Lesson Sheets. Please
read them aloud from the next page.
Problems in which students choose the correct
symbol are not located on the lesson itself but
appear on Guided Practice D.
For problems #1 – #3 on the Student Lesson
Sheet, the students are to combine any
numbers they can before evaluating the
statement. If they have trouble, they should
cover the comparison symbol and decide
which symbol belongs.
Students should be able to find the value of an
unknown by performing the same operation on
both sides of an equation.
Write on the board: N + 2 = N x 3. They
already know that N represents a number.
Now they will “solve” for N using trial and
error. They should start with 0 and work up
until they find a value for N that makes a
true statement. Do #4 – #6 together.
Stretch 3
What number is as much greater than 105
as it is less than 177?
Answer: 141
Write “9” on the board with an equal
symbol to the left. Explain that you need
6
Lesson 3
Name
Date
Recognizing true and not true number statements; using trial and error to solve for
unknowns in an equation; solving algebraic equations; changing a number statement
from ≠ to =; learning the order of operations when solving an equation; selecting the
correct symbol for a number statement
For each of these problems, replace the letter or the blank with the number that will
make the equation true.
7
2
10
9
2 x 5 < 9 x 1 NT
3
13
12
4 + 9 > 6 + 6
0
1
2
N x 2 = 6 - N
N = 2
0
6
0
X x 5 = X + 0
X = 0
0
3
17
14
First, combine numbers within parentheses.
Second, multiply or divide as you come to them going left to right.
Third, add or subtract as you come to them going left to right.
3
9 + B = B x 4
B = 3
Therefore, the proper order for 3 x 4 - 2 is (3 x 4) - 2, which equals 10.
0
1
2
3
13
14
6
2 + (3 x 2) = N + 5
8 = N+5
A 417
208
200
+ 9
417
Select the correct
symbol.
<
3+6
3. =
Frank has four sweatshirts.
Al has nine sweatshirts.
Which equation could
be used to find out how
many more sweatshirts
Al has than Frank?
7. 4 x 9 =
8. 9 - 4 = 5
9. 4 + 9 =
www.excelmath.com
5. >
A=8
7. ninety-second
6. 9 ÷ 4 =
4. <
7+3
B = 42
34
B-A=
6,3 2 7
- 2,4 4 8
3,879
7,3 0 5
- 4,4 2 8
2,877
$ .5 7
2 8.4 9
6.8 7
+ 1 9.3 6
$5 5 .2 9
$8 7.0 6
- 4 5.3 9
$ 41.6 7
$1. 97
x
8
$ 15.7 6
11 - 2 = 9
9 scarves
6. ninety-first
7
8
1
2 + (8 - 1) = (2 x 4) + ___
15 - Y = 0
9 = 8 + 1
Y = 15
© Copyright 2007-2014 AnsMar Publishers, Inc.
Name
Mandi has 3 scarves. She bought 8 new ones.
When she got home she discovered that two of
her new scarves were torn, so she returned
them. How many scarves does she have now?
5. ninetieth
15
7
1 5 - Y = 0 x (3 + 4)
6005
208 , 2 0 4 , _____
200 , 196 )
( 2 1 2 , _____
There are 90 people
ahead of Barbara in
line. She is ____ in
line.
14
Fortunately, mathematicians have developed rules for solving equations involving
multiple operations. These rules help make sure everyone gets the same result.
www.excelmath.com
Guided Practice 3
L - K= 6
L=9
3+3+6+2=6+8
N = 3
3 + 8 = 11
K=3
3+6+2 ≠ 6+8+3
This statement is true, so N equals 2.
5
M ÷ N= 4
If you had the equation 3 x 4 - 2 = , would you first multiply the 3 and the 4 or first
subtract the 2 from the 4?
(3 x 4) - 2 = 10
3 x (4 - 2) = 6
but
not true
not true
For each problem, find the value for the unknown (letter) that results in a true
statement.
4
11
12
T
N x 4 = 6 + N
0 x 4 = 6 + 0
1 x 4 = 6 + 1
2 x 4 = 6 + 2
N=2
In this inequality, which number can be moved to change the ≠ to = ?
Determine the number that needs to move so the ≠ can change to =. Circle
the number and write the new number sentence.
To discover the value of N, start with N = 0 and see if it results in a true equation. If
it isn't true, try N = 1 and so on until you find a value for N that will make a true
statement.
N = 0
N = 1
N = 2
7 = 9 - 2
11
M=8
Put "T" next to each true statement and "NT" next to each one that is not true.
20
3 + 4 = __ - 2
10 - 4 = 6
10
An equation is a number statement with an equal symbol. If a number statement is true,
the value on the right side will equal the value on the left side. If both sides are not
equal, the number statement is NOT true. It is an inequality. You must replace the equal
sign with a not equal, greater than or less than symbol for the statement to be true.
21
7
9
__ - 4 = 9 - 3
For these problems, letters are used to represent numbers. To find the answers,
replace the letters with the numbers they represent.
The not equal symbol ( ≠ ) means " is not equal to ".
7 x 3 ≠ 4 x 5 T
6
8
R = 5
The equal symbol ( = ) means " is equal to ".
1
3
15 ÷ R = 9 - 6
D 44
6
4
+ 34
44
B 159.97
$4 1 .6 7
5 5 .2 9
1 5 .7 6
+ 4 7 .2 5
$1 5 9 .9 7
1 0 3 ,7 4 3
four hundred sixty thousand, two
hundred eighteen
4 6 0 ,2 1 8
15. (3, 8, 13, 18)
G 6,781
8
3,879
2,877
+
17
6,781
E 769,021
103,743
460,218
+205,060
769,021
3 x 4 = 12
17. (10, 20, 30, 40)
12
x 4
48
4 8 tic kets
6006
7
13
13
0
1
2
3
9+4+2≠7+3+1
9+4=7+3+1+2
C 10
2
3
+ 5
10
352
x 9
3 ,1 6 8
876
x 7
6 ,1 3 2
5 mo re c ats
Oksana has drum lessons 6
hours and volleyball practice
5 hours a week. How many
hours does Oksana play the
drums and practice volleyball
in seven weeks?
6 + 5 = 11
F 9,377
3,168
6,132
+
77
9,377
11
x 7
77
7 7 ho u rs
Miguel went to the fair 3
days in a row. He rode
the ferris wheel 4 times
each day. He needed 4
tickets per ride. How many
tickets did Miguel use?
16. (2, 5, 15, 30)
11
7 - 2 = 5
5 thousands, 2 hundred thousands
and 6 tens
2 0 5 ,0 6 0
Film is sold five rolls
to a package. Which
set shows possible
numbers of rolls that
might be purchased?
15
N x 6 = 15 + N N = 3
Ann has 2 dogs, 7 cats and 3 birds. How many
more cats than dogs does she have?
$5.25
x
9
$4 7 .2 5
1 hundred thousand, 4 tens, 3 ones,
3 thousands and 7 hundreds
Which number can
be moved to change
the ≠ to = ?
Rachel caught 5 fish on
Friday, 6 on Saturday and
3 on Sunday. Emily caught
8 fewer fish than Rachel.
How many fish did Emily
catch?
5
6
+ 3
14
H 150
8 x 12 = 9 6
48
6
+ 96
150
14 - 8 = 6
6 fish
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 4
TEKS Objective
Days/Months Abbreviations Option
Students will learn 7 days = 1 week and 1
year = 12 months.
Read through the next calendar section
with the class. One simple rhyme that
might help students remember the number
of days in each month is:
Review with the class the abbreviations for
days and months.
Students will compute the date within the
month. (This is a review of previous TEKS
concepts).
Students will learn the number of days in
each month.
Thirty days hath September,
April, June, and November;
All the rest have thirty-one
Excepting February alone:
Which has but twenty-eight, it’s fine,
‘Til leap year gives it twenty-nine.
Students will learn the abbreviations for
days and months.
Preparation
No special preparation is required.
Stretch 4
Lesson Plan
Brian, Peggy and Blaine collect U.S. and
foreign stamps.
Have students suggest 5 different activities
for which the duration can be measured in
minutes, hours, days or weeks. For example:
1. It usually takes 1 _______ to do my daily
homework.
2. I will probably spend 180 _______ in
school this year.
3. It usually takes about 6 _______ to fly
across the United States.
4. It might take 1 _______ to paint the
inside and the outside of the house.
5. If I added up all the hours that I have
slept this month, it would probably add up to between 1 and 2 ______.
Brian has 9 U.S. stamps.
Blaine has 13 stamps in all.
Peggy has 3 times as many U.S. stamps as
Blaine has U.S. stamps.
Blaine has half as many foreign stamps as
Brian.
They have a total of 63 stamps, 37 of which
are U.S. stamps.
How many stamps of each kind do they
have?
Answer:
Next, point to a day on the calendar and
ask one of the students to tell you what the
date is. Ask what the date will be in 3 days,
what day of the week it was 4 days ago, etc.
U.S.
Ask how they could figure out the answers
if they did not have a calendar to look at.
Do problems #1 – #2 with the class.
Foreign Totals
Brian
9
12
Peggy
21
8
Blaine
7
6
13
Totals
37
26
63
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.
8
Lesson 4
Name
Date
Computing the date within the month; learning the abbreviations for days and months;
learning 7 days = 1 week and 1 year = 12 months; learning the number of days in
each month
Today is Wed, Jul 8. Two weeks
1
2
24 .
from this Friday will be Jul _____
W Th F
10 + 14 = 24
8
9 10
Dear Parents,
You can help your child by getting involved with homework. You may
not always have time to help, but just showing an interest may really
motivate your child.
Today is Tues, May 19.
Sunday .
May 10 was on ________
S
10
19 - 7 = 12
M
T
11 12
The problems on the back of this Lesson Sheet were done in class.
The children check their work by adding the answers of two or more
problems, then comparing the result to the CheckAnswer that we
provide above and to the right of the problem.
A 392
Here are the abbreviations for the days and months:
Sunday (Sun) Monday (Mon) Tuesday (Tues) Wednesday (Wed) Thursday (Thur)
Friday (Fri) Saturday (Sat)
January (Jan) February (Feb) March (Mar) April (Apr) May (May) June (Jun) July (Jul)
August (Aug) September (Sept) October (Oct) November (Nov) December (Dec)
Sometimes we find students will add the answers incorrectly rather than
ask for help. If parents and teachers work together, we can help students
learn the value of asking for help now, rather than being satisfied
with a wrong answer.
The calendar we use is called the Gregorian calender (after Pope Gregory). It was
introduced in 1582. You might look up the Julian calendar, which was used before
1582. It was named after Julius Caesar. See how it differs from the Gregorian calendar.
Homework is available four nights a week and will be located on the
Lesson Sheet where this letter appears starting with Lesson 6. Whenever
you have the time, please check to see that the answers on your child's
homework are added correctly and the calculations are shown.
Nov
Dec
Aug
Oct
Jun
Jul
Apr
May
Feb
Mar
Jan
Sept
Here is one way to determine how many days are in each of the 12 months in a year.
With your assistance, I look forward to a successful year in mathematics.
Please contact me if you need any clarification of our math program.
Fist of
left hand
Fist of
left hand
Sincerely,
Make a fist with your left hand. With the back of your left hand facing you, list
the months of the year starting with January on the knuckle of your little finger.
Continue through July using the space between each knuckle and the knuckle itself.
Start again with August at the same place you used for January. The months that
land up high on a knuckle have 31 days, while the others down between the knuckles
have 30 days (except February). February has 28 or 29 days, depending on whether
it is a leap year or not. Determining leap year is discussed in Lesson 41.
Guided Practice 4
28
A 38
25. =
27
>
4 x 7
27
7
+ 4
38
3 x 9
26. <
27. >
9 - 2=r
9 - 2 = 7
r= 7
5 + N=9
5 + 4 = 9
N= 4
If DVDs are sold in
sets of four, which
set shows possible
numbers of DVDs
that could be bought?
D 7,449
49
867
5,1 3 8
+ 1,3 8 6
7 ,44 0
8
7 ,44 0
+
1
7 ,44 9
N x 7 = 7 ÷ N
9. (14, 18, 22, 26)
N = 1
500
Berries
400
300
200
100
W
Days
Kelly Dawn Tim
T
two hundred thousand, nine hundred
eighty-seven
200,987
0
1
three dollars and
eighty-seven cents
$3.87
$9.12
x
8
$72 .96
How many berries were 35 0
picked on Friday?
30 0
+2 5 0
90 0
900 berries
Picking Berries
T
2 thousands, 1 hundred, 7 hundred
thousands, 6 tens, 3 ten thousands
and 9 ones
732,169
F
How many fewer berries
did Dawn pick on Tuesday
than on Wednesday? 2 5 0
-150
100 berries
100
B 937,756
732,169
200,987
+
4 ,6 0 0
937,756
Sopea takes a weekly 9-mile kayak trip down
the river. How far does she kayak in 8 weeks?
4,600
forty-six hundred
7. (2, 4, 6, 8)
8. (12, 20, 24, 28)
© Copyright 2007-2014 AnsMar Publishers, Inc.
Name
Select the correct symbol.
www.excelmath.com
_________________________________________________
Parent's signature
6007
www.excelmath.com
M
I have read this letter and I will do my best to help at home.
9 x 8 = 72
7 2 mi le s
6
2 + (3 x 2) = Z + 5
8 = 3 + 5
Z= 3
14 nickels
7 dimes = ______
Put the numbers in order
sixteen dollars and E $128.55
ninety-eight cents
from least to greatest.
$ 3.87
(4
,8
1
4
; 4 ,4 8 1 ; 4 ,1 4 8 ; 4 ,8 4 1 )
16.98
72.96
$16.98
4 , 1 4 8 ________
4 , 4 8 1 ________
4,814
4,841
________
________
+ 34.74
$
1
2
8
.
5
5
$ 3 .8 6
4,148
Which number is first? _________
x
9
5,0 0 5
$34.74
- 3,2 2 6
9 x 12 = 1 0 8
1,779
G 1,150
900
100
+ 150
1,150
It is 3:15. Jonah can go out
and play after he helps his
mother for 20 minutes.
Which equation shows how
many minutes after 3 it will
be when Jonah has finished
helping his mother?
6. 60 - 20 =
7. 60 - 15 =
Which person picked more berries each day than
the day before? Kelly
Dawn
Tim
50.
100.
150.
8. 20 - 15 =
9. 15 + 20 = 3 5
6008
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.
9
Pamela swims 2 miles
and runs 5 miles a day.
She also drives 4 miles
to work each day. How
much farther does she
run than swim after 2
days?
5 - 2 = 3
3 + 3 = 6
C 89
72
3
+ 14
89
F 6,035
4,148
1,779
+ 108
6,035
H 103
12 - 2
10 = ____
13 + 4 = 17
____
J=7
JxK=
9
6
12
13
+ 63
103
K=9
63
6 miles farther
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 5
TEKS Objective
Group students in threes and have them
cut out the fraction pieces. The fraction
pieces are labeled in three different ways.
The students should understand that they
can describe fractions in three ways. Each
“whole” is the same size so the fractions
can be compared.
Students will solve real-world and
mathematical problems by writing and
solving equations of the form x + p = q and
px = q, and will add and subtract fractions
and mixed numbers with like denominators.
Students will determine if the given values
make one-variable, one-step equations or
inequalities true.
Ask the class how your paper labeled “One
Half” compares to theirs. (Yours is larger
because the whole it came from was larger.)
Ask them how both pieces can be labeled
“One Half” even though they are different
sizes or have perhaps been cut in different
ways—horizontally, vertically, diagonally,
etc. (Fractional parts are related to the whole
of which they are a part.)
Students will extend representations for
division to include fraction notation such as
a/b represents the same number as a ÷ b
where b ≠ 0.
Students will define numerator and
denominator and will determine the
fractional part of a group of items when
modeled or given in words.
Have the students cut out their circle
fraction pieces. Ask them if the “onefourths” bars can be combined with the
“one-fourth” pieces of the circle. (No. The
“wholes” are not the same, so the parts of the
wholes would not be the same.)
Preparation
For each student: scissors, Circle Fraction
Pieces, Fraction Pieces I and II (masters on
M18, M19 and M21)
Explain that if they add thirds, their
answers will be in thirds. Some students
will want to add the denominators and
write their answers in sixths. Manipulating
the pieces should discourage this, however.
Keep the pieces available for the students.
For the class: a piece of paper cut in half
and labeled “One Half”
Lesson Plan
Fractions describe a portion of a group.
The number under the line (denominator)
represents the total number of parts in
the group. The number above the line
(numerator) indicates the part of the total
group to which you are referring.
Stretch 5
Write these three number statements on
the board:
AB ÷ C = D, ( A + A ) x C = D and
C - (A + A) = A.
Ask 3 boys and 2 girls to come forward.
Ask the class how many total students have
come forward. Then ask them how many
boys they count. Ask, “What fraction would
represent the boy’s portion of the group?”
Repeat this with several groups of students.
The number statements have been written
in code. Each letter represents a digit 0 – 9.
What are the three number statements in
numerical form?
Answer: 18 ÷ 3 = 6, (1 + 1) x 3 = 6 and
3 - (1 + 1) = 1
10
Lesson 5
Name
Date
Defining numerator and denominator; determining the fractional part of a group of
items when modeled or given in words; learning that the whole is the sum of its parts;
adding and subtracting fractions and mixed numbers with like denominators
You can think of fractional parts as pieces. They can be added or subtracted.
7
The bottom portion of a fraction refers to the total number of parts in the group
and is called the denominator. The top portion of the fraction is the part of the
total group that you are referring to and is called the numerator.
1
4
1
4
For each problem, fill in the numerator and the denominator and then select the
correct fraction from the choices.
1
2
2
are shaded.
6
2
4
4
6
9
of the figures
are circles.
5
2
6
2
3
2
5
3
5
7
is written seven thirteenths.
13
Nine children are playing.
3 of them are boys. How
9
many girls are playing?
4
6
3 x 4 = 12
12
13
14
11
7. 5 + 9 > 3 + 8
11
10
8. 9 + 2 > 6 + 4
36
36
9. 4 x 9 ≠ 6 x 6
32 = Y x 8
Y = 4
3 x 5 = 15
15
14
3
2
=
6
11
6
4
8
-
4
=
8
0
8
1
When adding or subtracting mixed numbers, whole numbers can only be added to
or subtracted from whole numbers. Fractions can only be added to or subtracted
from fractions.
16
17
1
3
1
6
+
3
2
9
3
3
4 x 2 = 8
8 pieces
A 44
96 = 12 x P
96 = 12 x 8
P= 8
7
15 - A = 0 x (3 + 4)
15 - 15 = 0
A = 15
N =3
5+3+1+2=4+7
Boxes of Cookies Sold
Number of Students
6
5
0
1
2
3
How many students sold
between 11 and 20 boxes
of cookies?
6 + 5 = 11
1 1 s tu de nt s
How many students sold
at least 16 boxes of cookies?
4
3
5 + 1 = 6
2
1
11-15 16-20
Boxes
21-25
6
7
8
8
+15
44
C 34
10 = 90
9 x ____
11
6-10
15
7
3
4
+
=
10
10
10
3 is a whole number. 4 is a fraction. 3 4 is a mixed number.
Four strips of ribbon are cut into
halves. How many pieces will
there be?
2 + 2 + 2 + 2 = 8
N x 4=9 + N
Which number can be moved to change
13
the ≠ to = ? 9
5+1+3 ≠ 4+2+7
www.excelmath.com
-
-
2
4
2
4
0 = 0
4
18
19
1
6
4
+
6
5
2
6
2
20
7
9
3
3
9
4
5
9
8
1
3
1
7
+
3
2
8
3
1
21
3
5
2
5
1
6
5
6
© Copyright 2007-2014 AnsMar Publishers, Inc.
Name
How many fifths are
there in 3 wholes?
0-5
5
6
6009
Which statements are true?
0
2 fifths
1
12 fourths
6. 8 + 4 ≠ 7 + 6
3 tenths
+ 4 tenths
7 tenths
A mixed number is a number that is made up of a whole number and a fraction.
www.excelmath.com
Guided Practice 5
12
4 fifths
- 2 fifths
many of her apples are not red?
8 apples are not red
How many fourths are
there in 3 wholes?
4 + 4 + 4 = 12
11
4 eighths
- 3 eighths
1 eighth
0
Draw pictures and use addition or multiplication to compute the answers.
5
10
4 sevenths
+ 2 sevenths
6 sevenths
Notice that the answer for #15 is not 0 . The denominator (8) is the number of
pieces into which the whole has been divided. It does not change.
fifteenths of them are red. How
6 girls
5 sixths - 2 sixths = 3 sixths
1
4
Corina has 15 apples. Seven
15 - 7 = 8
9-3=6
1
4
Fill in the missing number.
13
When writing fractions in words,
3
is written three fifths.
5
3
2
8
3 fourths - 2 fourths = 1 fourth
15
4
2
10
+ 3
34
Today is Sunday, January 25. Three weeks
1 2 months
1 year = _____
3 1 days
______
2
12
31
+ 99
144
11 x 9 = 9 9
5
14
3
2
are red,
are silver,
are gold,
14
14
1
is black and 3 are white.
14
14
Dana bought 14 cans of paint.
Siri waited an hour to get
tickets for a concert. Dani
stood in line three times as
long as Siri. Which equation
shows how long Dani stood
in line?
How many of her paint cans were
2
gold? _______
11
6
+ 3
20
B 144
23
-21
2
F S S
23 24 25
11
not silver? _______
E 20
Days in March?
2
ago last Friday was January _____.
3
white? ____
9
not red? ____
Melody paid for dinner with
a ten-dollar bill. Her change
was two one-dollar bills,
three quarters and two
dimes. How much was
her dinner?
$2.00
.75
+ .20
$2.95
6 s tu de nt s
How many students sold
fewer than 6 boxes of cookies?
3 s tu de nt s
$ 1 0 .0 0
- 2.95
$7.05
$7.05
6010
11
6. 3 x 4 =
8. 3 + 4 =
7. 3 x 1 = 3
9. 2 x 4 =
Barney had $1.32. His
father gave him a dime
and he spent a quarter.
How much money does
Barney have now?
$1.32
+ .10
$1.42
$1.42
- .25
$1.17
D 32
11
3
2
9
+ 7
32
F $107.29
$ 9 .3 3
x
7
$65.31
$7.05
1.17
65.31
+ 33.76
$107.29
$ 8 .4 4
x
4
$33.76
$1.17
© Copyright 2007-2014 AnsMar Publishers, Inc.
Test 1 - Assessment
Test 1
Use tally marks on the right side of the
chart to record how many students missed
a particular question. There is no need
to review the entire test, but you could
go over problems missed by a number of
students.
This test is an assessment test covering
the concepts on Lessons 1 – 30. You can
download the TEKS correlations from our
website: www.excelmath.com/tools.html
If the class as a whole scores an average of
90% or better, feel free to jump ahead to
Lesson 31. If they score below 90%, copy
the Score Distribution and Error Analysis
charts provided on pages i.20 - i.22 in the
front of this Teacher Edition and online:
www.excelmath.com/tools.html
The tables below indicate which questions
reflect which objectives, and where that
content is taught in this curriculum. Use this
guide if you want to have students review
one or two specific lessons. If the class is
weak in several areas, we recommend you
continue through Lessons 6 – 30.
Record each student’s identification
number on a line, indicating the number
of problems he missed. This distribution of
test results will help you analyze their work
and show parents how their child did in
comparison to the rest of the class without
revealing names of students who scored
higher or lower than their child.
Feel free to skip the starred problem if
your students have not learned rotational
symmetry.
Q#
Q# Lesson# Concept
1
2
Lesson#
Concept
1 Addition: 4 digits with regrouping
21
1 Subtraction: 4 digits with regrouping
22
28 Addition of fractions
6 1-digit divisor into a 3-digit dividend
3
12 Multiplication: 3 digits x 2 digits
23
16 1-digit divisor into a 3-digit dividend
4
18 Equivalent fractions
24
26 2-digit divisor into a 2-digit dividend
5
14 2-D figures: rhombus
25
25 Angle estimation
6
10 Measurement equivalents
26
7
25 Sum of the angles in a rectangle
27
3 Equations with parentheses
5 Fractional parts of groups of items
8
1 Number words less than one million
28
9
48 Simplification of improper fractions
29
23 Lines of symmetry
21 2-D figures: pentagon
30
20 Rounding to one non-zero digit
31
14 2-D figures: parallelogram
32
11 U.S. customary and metric units
33
17 Lowest common multiples
10
11
12
13
14
15
16
1 Number words less than one million
10 Measurement equivalents
2 Sequences: counting from 1 to 12
34
25 Equilateral triangles
6 Multi-step word problems
19 1/2 to 1/9 of a group of items
20 Rounding to the nearest hundred
3 True and not true number statements
35
25 Obtuse angles
36
24 Numbers to trillions
22 Fractions: greatest and least value
17
9 Multi-step word problems with division
37
18
7 Deductive reasoning
38
23 Rotational symmetry
1 Multi-step word problems
39
30 Area of a rectangle
40
8 Listing possibilities
19
20
24 Expanded notation
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.
12
= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.
13
2
9
6
3
24 =
5
Mrs. Harper has three sons and two
daughters. She bought $9 CDs for
each of her children. How much did
she spend?
9 c a no es
$45
13
4
7 5
16
6
3
5 vertices.
_____
A pentagon has
360°
a rectangle is _______.
21 p e ts
One eighth of Art's 24
pets are dogs. How
many of his pets are
not dogs?
Ana
Jill
4 8 6 ,9 5 1 ,0 3 7
Write this number in expanded notation.
Betsy
6011
+ (7 x 1)
© Copyright 2007-2014 AnsMar Publishers, Inc.
(5 x 10,000) + (1 x 1,000) + (3 x 10)
+ (6 x 1,000,000) + (9 x 100,000) +
(4 x 100,000,000) + (8 x 10,000,000)
20
=
x 3
The sum of the angles of
1
2
x 3
Betsy, Ana and Jill each sang at a concert.
Betsy sang longer than Ana. Jill sang
longer than Betsy. Who sang the least?
8 p eo p le
18
10
7
4
Date
4 35 , 4 2 7 , 4 1 9 , 4 11 )
( 4 4 3 , _____
Four groups of 20 people
want to take boat tours. If
there are ten boats, how
many people will be on
each boat?
Thirty-five people want to go on a
canoe trip. Each canoe will hold 4
people. How many canoes will be
needed for the whole group to go?
a scalene
an equilateral
an isosceles
This is ________
triangle.
15
9 lb _____
1
145 oz = _____
oz
o ne h u ndr ed t h o us a nd , f i ve
100,005
723
x 58
4 1,9 3 4
3
#
7 3 inches
6 ft 1 in = _____
6,5 0 2
- 4,1 7 9
2,323
Name
Write the words for this number.
6 7 0 ,0 1 4
7 ten thousands, 4
ones, 1 ten and 6
hundred thousands
4
______
sides.
A rhombus has
89
1,0 9 5
179
+ 1,3 8 6
2 ,7 4 9
www.excelmath.com
19
17
14
12
11
8
5
1
Test 1 Assessment
C
80°
A
20°
50°
Select the
best estimate
for ∠B.
4
15 km
3
2
5
N= 8
no
yes
8
)
miles
6012
40
38
a right
an acute
an obtuse
trillions
billions
millions
represents _______ .
The underlined portion
4 7 9 , 1 0 5 , 3 5 7 ,9 8 8
24
What is the lowest common
multiple of 8 and 12?
20,000
15,456 ___________
Round this number so
there is only one non-zero
digit.
20 f if th s
does not
does
This figure ______ have
rotational symmetry.
36
3 r3
32 99
How many fifths are
there in four wholes?
24
© Copyright 2007-2014 AnsMar Publishers, Inc.
6 c o nc er ts
Brock and Buzz have been to 10
concerts. Buzz attended 2 fewer
than Brock. How many concerts
did Brock see?
This is
________
angle.
feet
yards
33
30
27
6 9 r2
4 2 7 8
8 kilometers ≈ 5 _______
Does this
figure show
a line of
symmetry?
, 6 , 1 , 2 , 1 , 1
90 sq km
area = ____________
6
km
( 11
35
32
23
(6 - 2) x 6 = N x (1 2 ÷ 4)
Circle the denominator of the fraction
in the set with the least value.
6x4 > 3x7
8÷2 < 9-3
9+7 ≠ 4x4
Which statements
are true?
Circle the parallelogram.
21, 900
2 1 ,8 6 9 _________
29
26
9 1
7 6 3 7
Name
22
Round to the nearest
hundred.
B
+ 2
1
4
11
5
12
2
3
3
www.excelmath.com
39
37
34
31
28
25
21
Test 1 Assessment
Lesson 6
TEKS Objective
can divide the twelve tens into two equal
groups, and if so, how many will be in each
group? (yes, six tens)
Students will recognize multiplication and
division fact families.
Are there any tens left over? (no)
Students will multiply and divide positive
rational numbers fluently.
Subtract the 12 tens that they have divided
and repeat the process with the 4 ones. Ask
if the number 124 is now divided into two
equal groups. (yes)
Students will divide a one-digit divisor
into a three-digit dividend with a two- or
three-digit quotient with no regrouping or
remainders.
Ask the class how they know. Is anything
left over? (no)
Students will solve multi-step word
problems involving division.
Explain that when the dividend is a dollar
amount, the decimal in the quotient will be
directly above where it is in the dividend.
Students will learn the terminology for
multiplication and division.
Go through problems #3 – #7 together,
checking each answer with multiplication
and, if time permits, with repeated
subtraction using a calculator.
Preparation
For each student: Number Chart, Ones and
Tens Pieces, Hundreds Pieces, Hundreds
Exchange Board (masters on M10, M13, M14
and M16), optional calculator
Do #8 together and review the terminology
for multiplication and division problems.
Give your students the answers to the
starred problems if they have not been
taught these concepts (so they can
complete the CheckAnswers).
Lesson Plan
In problems #1 – #2, provide one
multiplication fact and ask students to fill
in the other multiplication fact and the two
division facts that are in the same family.
i Problems #1 – #2 do not appear on the
Lesson Sheets. Please read them aloud.
Write the following problem on the board:
2
124
Stretch 6
Shirley ran 15 km in January.
She ran 25 km in February.
She ran 35 km in March.
As the students go through the following
process with the pieces, write on the board
what they are representing.
If she continues at this same pace, how
many kilometers will she run in July?
Ask the students if they can divide the
one hundred into two equal groups. (Yes.
Exchange the one hundred for ten tens.)
Answer: 75 km
On the board, draw a line under the “1”
and “2”. Next, ask the students if they
14
Lesson 6
Name
Date
Homework
Recognizing multiplication and division fact families; learning division facts with
dividends up through 81 and dividends that are multiples of 10 (to 90), 11 (to 99) or
12 (to 96); dividing a one-digit divisor into a three-digit dividend with no regrouping or
remainders; solving multi-step word problems involving division
4 hundred thousands, 1 ten, 3
thousands, 7 ones and 9 hundreds
403,917
For each multiplication fact that is given, write the other multiplication and division
facts that are in the same family.
1
12
x 3
36
3
x 12
36
12
36
3
12
2
3
36
8
x 6
48
8
6 48
6
x 8
48
4
4
2 8
-8
0
-
x
8
4 3
8 6
5
5
8
8
0 6
- 6
0
8 0
4 0 0
6
7
-4 0
8 1
5 6 7
-5 6
0 0
443
2
886
x
0 7
- 7
0
80
5
400
x
81
7
567
3
9
$ .6
2 $1.2
-1 2
0
-
9
9
0
$3.13
x
3
$9.39
3
6
6
6
0
multiplicand
x multiplier
product
$ .63
x
2
$1.26
2 + 4 = 6
divisor
5 cookie s
67
- 4
63
quotient + remainder
dividend
A 26
8
8
1
7
16 piece s
Which fact does
not belong?
-
2
8
=
6
8
+
3
7
=
4
2. 6 ÷ 2 = 3
3. 2 x 6 = 1 2
4. 2 x 3 = 6
16
6
+ 4
26
D 11
3
1
+ 7
11
7
numerator = _____
Dan organized a 10 km run.
He had 348 entries one
week before the event. In
the last week, 7 canceled
and 20 entered late. How
many people ran in the
race?
341
+ 20
361
3 6 1 pe o pl e
6,6 0 1
- 3,2 5 7
3,344
4,0 0 1
- 2,3 1 8
1,683
63
+ 8
71
D 5,098
71
1, 683
+3, 344
5, 098
71º F
© Copyright 2007-2014 AnsMar Publishers, Inc.
B 126
Select the correct symbol.
3 + 24 = 27
=
3+(6x4)
>
26.
9 x 3 = 27
9 x ( 2 + 1)
=
<
27.
28.
5
7 + (5 - 0) = R x 4
12 = 3 x 4
R= 3
7
Using the fewest coins,
how many quarters are
there in 42¢?
2 5¢
1 0¢
5¢
+ 2¢
1
4 2¢
1. 3 x 2 = 6
www.excelmath.com
6 + 6 = 12
12
6, 750
+2, 388
9, 150
Name
2 x 8 = 16
348
- 7
341
398
x 6
2,388
6013
Guided Practice 6
7
9
C 9,150
750
x 9
6,750
This morning the temperature was 67º F.
By lunchtime it had dropped 4º but then
the sun came out and it has now gone
up 8º. What is the temperature now?
(factor)
(factor)
www.excelmath.com
Two pies are cut
into eighths. How
many pieces are
there?
8, 523
1, 864
+ 3, 792
14, 179
474
x 8
3,792
12 kites
Parts of a division problem
15 ÷ 3 = 5
8,1 0 0
- 6,2 3 6
1,864
Chloe has 2 kites with hearts on
them and 4 with birds. Kylie has
the same number of kites as
Chloe. How many kites do they
have in all?
Parts of a multiplication problem
Ten chocolate and five
oatmeal cookies were
divided equally among 3
children. How many
cookies did each child get?
10 + 5 = 15
403, 917
217, 008
+
14
620, 939
B 14,179
919
37
859
+ 6,7 0 8
8,523
7
$3.1
3 $9.3
-9
0 3
- 3
0
-
217,008
A 620,939
14 people ahead of her.
Erin is fifteenth in line. There are _____
6
8 48
Check each answer with multiplication.
3
two hundred seventeen
thousand, eight
Today is Friday, May 21. May 15
Satu r day.
was on a _________
S S M T W T F
15 16 17 18 19 20 21
1. Monday
2. Sunday
3. Saturday
27
3
+ 96
126
Which statements
are true?
14
16
7. 5 + 9 < 8 + 8
14
13
24
24
8. 7 + 7 > 4 + 9
361
3
+ 30
394
E 26
2
7
8
+ 9
26
Miguel has 18 peanuts.
He would like to divide
them equally among 3
friends. Which equation
shows how many peanuts
each friend will get?
6. 18 - 3 =
7. 18 + 3 =
8. 18 ÷ 3 = 6
30 days
Days in September? ______
9. 18 x 3 =
6014
15
6.
5
12
12
7
7.
4
7
8.
6
15
+ 6
27
7
12
72 ÷ 12 = 6
15
product ____
9. 4 x 6 = 2 x 12
G 394
are shaded.
12
5 x 3 = 15
8 x 12 = 9 6
Today is Monday,
December 13.
December 20 will be
Mond a y.
on a _______
13
+ 7
20
1. Friday
2. Monday
3. Sunday
C 27
5
6
7
F
-
4
7
= 0
4
7
+
1
7
=
5
7
5
7
1
+
7
3
7
-
2
7
=
1
7
6
7
Deon swims six
laps twice a day.
How many laps
does Deon swim
every week?
0
H 129
B ÷ 6 = 5
B = 30
8
84
30
+ 7
129
6 x 2 = 12
7 x 12 = 84
7 days
1 week = _____
8 4 la ps
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 7
TEKS Objective
“not enough information” or “enough
information” accordingly. If possible, they
should write an equation with the solution
if they have enough information.
Students will add, subtract, multiply and
divide integers fluently.
Students will determine if there is sufficient
information to answer the question in a
word problem.
Read problems #5 – #6 with the students
and have them determine whether or not
each choice will provide the information
that is needed to solve the problem.
Students will solve word problems using
deductive reasoning and will determine
what information is needed to answer the
question in a word problem.
After they have chosen the correct answer,
show them the equation they would use to
solve the problem.
Preparation
When these problems appear on their
Lesson Sheets, the students should try to
write the equation that is used to solve
the problem. This demonstrates that they
understand the concept. You may want
to write the equation as a class if some
students are having difficulty with the
concept.
No special preparation is required.
Lesson Plan
Read through problem #1 on the Student
Lesson Sheet with the class. The second
sentence states that Eduardo is older than
Eric. So draw a vertical line over Eduardo
that is longer than the line over Eric.
Then give the class the following word
problem: “Jonah bought 3 books at $6.95
each and 4 shirts at $12.35 each. How much
did he spend?” (Answer: $70.25)
3 x $6.95 = $20.85
4 x $12.35 = $49.40
$20.85 + $49.40 = $70.25
In the third sentence, we learn that Hugo is
younger than Eric. Therefore, the line over
Hugo should be shorter than the line over
Eric. Hugo’s line is the shortest, so Hugo is
the youngest.
Read through #2 with the class. It requires
two steps. In order to calculate how late Tia
was, we need to calculate how late Will was
(sentence #4). From sentence #2 we know
that Don was 13 minutes late, and from
sentence #3 we know that Will arrived five
minutes earlier than Don. Therefore, Will
arrived eight minutes late (13 - 5 = 8). From
this answer, we calculate that Tia arrived 11
minutes late because we read in sentence
#4 that she was three minutes later than
Will ( 8 + 3 = 11).
Remind the class to show their work as they
solve the Guided Practice and Homework
word problems.
Stretch 7
Todd, Chris and Rod have 30 birds.
Rod has five times as many as Todd.
Todd has one fourth the number that Chris
has. How many birds do they each have?
Answer: Todd - 3, Rod - 15, Chris - 12
Read problems #3 – #4 with the students
and ask them what information they need
to answer the questions. Have them select
16
Lesson 7
Name
Date
Homework
Solving word problems using deductive reasoning; determining if there is sufficient
information to answer the question in a word problem; determining what information is
needed to answer the question in a word problem
1
Eric, Eduardo and Hugo are
brothers. Eduardo is older than
Eric. Hugo is younger than Eric.
Who is the youngest?
Eric
3
Hugo
2
Eduardo
Lawrence has 2 aunts and an uncle.
Raquel has aunts and uncles. How
many more uncles does Raquel have
than Lawrence?
4
A. enough information
B. not enough information
5
Tia, Will and Don were late to school.
Don arrived 13 minutes late.
Will was 5 minutes earlier than Don.
Tia was 3 minutes later than Will.
How many minutes late was Tia?
13 (D on ) - 5 e a r lier = 8 (Will)
8 (W ill) + 3 la t e r = 11 (Tia)
1 1 minutes
Hugo had 16 shells. Leona had 25
shells. They gave 8 shells to Hilda.
How many shells do Hugo and
Leona have now?
Oliver and Bob were playing basketball.
Oliver made five baskets. Bob made
four more baskets than Oliver. How
many baskets did Bob make?
5 (O liv er ) + 4 = 9 (Bo b )
16
+ 25
41
a. the amount of paint she used
b. time it took to paint each picture
c. number of pictures Sherry painted
6
Tristan has two
flower gardens in
his yard. In one garden
he has 24 flowers. What
information is needed to find out how
many flowers are in the other garden?
a. how much he paid for the flowers
b. the total number of flowers
Guided Practice 7
819
x 7
5,73 3
6,75 0
2,02 8
+ 5,73 3
1 4 ,51 1
Rob has 5 hats and
three fifths are pink.
How many of his
hats are not pink?
B 6
D 10 8
10
4
10
7
5
10
+3
5
10
1
3
10
-1
6 9
10
-4
2
9
10
7
5 10
1
3 10
+2
8
10 10
Richard can buy caps
in packages of three.
Which set shows the
number of caps he
could buy?
8÷2=4
8
dividend ____
5 x 11 = 5 5
7. (12, 18, 21, 27)
8. (1, 3, 9, 15)
9. (4, 7, 10, 13)
2
3
+ 1
6
3
7, 061
+ 4, 867
11, 931
7,0 3 6
- 2,1 6 9
4,867
D 6,721
1,3 9 5
1,1 8 9
687
+ 1,4 9 7
4,768
15
4, 768
+ 1, 938
6, 721
8,5 0 0
- 6,5 6 2
1,938
V = 66
How many halves are
there in 3 wholes?
Which fact does
not belong?
C 23
6
6
+ 11
23
4. 18 ÷ 3 = 6
5. 3 x 6 = 1 8
3 x 2 = 6
6. 6 x 6 = 3 6
6 h a lv e s
4 fifths
- 3 fifths
1 fi ft h
2 hat s
4 6
10
C 11,931
1,9 6 7
1,5 4 6
853
+ 2,6 9 5
7,061
© Copyright 2007-2014 AnsMar Publishers, Inc.
2 fourths
+ 1 fourth
3 fo urt h s
5 - 3 = 2
2 3
10
33 s hells
Name
A 14,511
338
x 6
2,028
B 6,974
33
173
+ 6, 768
6, 974
846
x 8
6,768
6015
www.excelmath.com
$34.44
41. 13
+ 22. 80
$98.37
173 , 184, 195)
(151, 162, _____
Andrew tried to catch 20
waves when he went surfing.
He fell 3 times and missed the
wave twice. How many waves
did he ride?
20
2 + 3 = 5
- 5
15
15 waves
c. how many flowers are roses
(Sherry's pictures) - 5 =
number of pictures
(Total number of flowers) - 24 =
her friend painted
number of flowers in the other garden
750
x 9
6,7 5 0
41
- 8
33
A $98.37
$2.85
x
8
$22.80
Willie had 15 bags of cement. He
used 8 for a patio and 4 for a
sidewalk. How many bags of
cement does he have left? 15
- 12
8 + 4 = 12
3
3 b ags left
A. enough information
B. not enough information
Sherry painted 5 more pictures than
her friend did. What information is
needed to find out the number of
pictures her friend painted?
$4.57
x
9
$41.13
$4 7.2 3
- 1 2.7 9
$34.44
9
11
7. 6 x 3 = 1 8
11
denominator = _______
F 123
E 76
7
8
55
+ 6
76
W = 11
6
6 1
3 1 8 3
-1 8
0 3
-3
0
61
41
+ 21
123
2 1
7 1 4 7
-1 4
0 7
-7
0
4 1
6 2 4 6
-2 4
0 6
-6
0
V÷W=
Today is Friday, December 15. December
Rosalee cooked twentyWednes day .
27 will be on a ___________
nine hamburgers. She
15
ate one and gave two to
+ 7
1. Monday
each of her guests. There
22
2. Wednesday
were none left over. How
3. Friday
many guests did she have?
F S S M T W
29
2 2 23 24 25 26 27
28 ÷ 2 = 14
- 1
28
3 1 days
Days in January? ______
1 4 guest s
www.excelmath.com
G 47
14
2
+ 31
47
Christa wrote three
letters a day for six
days. Which equation
shows how many total
letters she wrote?
6. 6 x 3 = 1 8
7. 3 + 6 = 9
8. 6 ÷ 3 = 1 8
9. 6 - 3 = 3
6016
17
For each of her six dogs,
Mora bought 7 chew
toys, two bowls and
a leash. How many
items did Mora buy?
7 + 2 + 1 = 10
10 x 6 = 60
H 80
64 ÷ 8 = 8
6
9
a x (18 ÷ 3) = 4 x (3 x 3)
a x 6 = 36
a= 6
6
60
8
+ 6
80
6 0 i t e ms
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 8
TEKS Objective
of plants in each row. The students should
first determine by what number each row
is counting. (The top row is counting by 1,
and the bottom row is counting by 6.) They
can then fill in the missing number. Do #3
together.
Students will give examples of ratios
as multiplicative comparisons of two
quantities describing the same attribute.
Students will write one-variable, one-step
equations and inequalities to represent
constraints or conditions within problems.
Use the Guided Practice portion of your
math lesson to ask students to “explain
their thinking.” Texas Knowledge and Skills
(TEKS) stress the importance of “students
making sense of mathematics by describing
their thinking.”
Students will understand that solving
an equation or inequality is a process of
answering a question: which values from a
specified set, if any, make the equation or
inequality true?
Asking students to explain their work will
help you to determine the students’ depth
of understanding and will give you a chance
to clear up any misconceptions.
Preparation
No special preparation is required.
Lesson Plan
Stretch 8
When solving a problem, it is sometimes
useful to list all the possible solutions. This
strategy works best when there is only a
small number of possible solutions.
Write on the board:
CxC=C
DxA=B
Read the example on the Lesson Sheet. The
first sentence identifies the first parameter:
the two numbers in the solution must add
to 8. Therefore, list all the combinations of
two numbers that add to 8. The solution
will be one of these choices.
D+A=H
ExE=F
K + G = CD
The number statements are written in code.
Each letter represents a digit 0 – 9. What
are the number statements in numerical
form?
The second parameter is that one of the
numbers will be 2 more than the other. The
students should look at the choices and pick
the one that has a number 2 more than the
other. 5 + 3 fits both parameters.
Answers:
1x1=1
2x4=8
2+4=6
3x3=9
5 + 7 = 12
Go through problems #1 – #2 on the
Student Lesson Sheets using the above
process.
The two rows in the chart in #3 are related.
The top row shows the number of rows of
plants. The bottom row shows the number
18
Lesson 8
Name
Date
Homework
Solving word problems by listing possibilities or by making a chart
Maurice and Donnie have 8 marbles. Maurice has 2 more marbles than Donnie.
How many marbles does Donnie have?
16.
<
These are possible answers because each pair of numbers adds to 8, which is the
total number of marbles. The second sentence says that Maurice's number is 2 more
than Donnie's. Which pair of numbers has one number that is 2 more than the other?
(0 + 9 )
(1 + 8 )
(3 + 6 )
(4 + 5 )
( 0+6)
( 1+5)
( 2+4)
( 3+3)
4 book s
17
30
4,443
+ 4,865
9,355
695
x
7
4,865
B $181.48
$ .4 9
2 5.6 0
1.8 7
+ 1 3.9 8
$41.94
$30.06
Micah and Ruben have 6 belts. Micah
has 4 more than Ruben. How many
belts does Ruben have?
( 2+7)
17.
>
thirty dollars and six cents
Go through both steps in order to solve each of these problems.
2
6,9 1 1
- 2,4 6 8
4,443
3,388
30 days
Days in June? ______
Answer: ( 5 + 3 ). Maurice has 5 marbles and Donnie has 3 marbles.
April and Ivy read 9 books over
their summer break. April read
1 less book than Ivy. How many
books did April read?
>
3,883
Make a list of the possible answers: ( 8 + 0 ) , ( 7 + 1 ) , ( 6 + 2 ) , ( 5 + 3 ) and ( 4 + 4 ).
1
A 9,355
Draw the correct symbol ( < or > )
between the pair of numbers.
fifty dollars and seventy-six
cents
$30.06
50.76
41.94
+ 58.72
$181.48
$7.34
x
8
$58.72
$50.76
1 b elt
C 859,474
Put the numbers in order from greatest to least.
(3,773; 3,373; 3,337; 3,737)
3
While visiting a park, Gary noticed that in one area the gardener designed the flowers
with 12 plants in the second row, 18 in the third, 24 in the fourth and 30 in the fifth. If
this pattern continues, how many plants will be in the sixth row?
3,373
Which number is third? _________
One way to solve the problem is to create a chart and look for
patterns.
rows of plants
2
number of plants
in each row
3
4
5
6
12 18 24 30 36
36 pla nts
6. 5 x 9 = 4 5
4
8
+
6
7
-
1
8
=
4
7
=
7. 45 ÷ 5 = 9
8. 9 x 5 = 4 5
9. 45 ÷ 15 = 3
5
8
2
9
8
+ 7
24
7
Vanessa had 52 pennies.
She gave 14 of them to a
friend and then found 6
more. How many pennies
does she have now?
52
- 14
38
38
+ 6
44
D 20
1
of the figures
are circles.
7
7. 2
7
8. 7
1
10 nickels
50¢ = ______
Brooke, Derrick and Andres
ran in a race. Brooke finished
between Derrick and Andres.
Derrick wasn't first. In what
order did they finish the race?
B
D
12. Andres, Brooke, Derrick
13. Derrick, Andres, Brooke
14. Andres, Derrick, Brooke
www.excelmath.com
100,059
5,200
© Copyright 2007-2014 AnsMar Publishers, Inc.
5
x 4
20
4
multiplier ____
6 0
7 4 2 0
-4 2
0 0
6
10
+ 4
20
9
10
9
numerator = ____
9
15
12
6 x 3 = 18
(3x4)+7 >
6x(2+1)
<
37.
12
3+6+2+1=7+5
12 + 7 = 19
36.
N= 4
=
38.
3 x 9 = 27
Miguel ate 3 carrots and
5 grapes. He also ate
some cherries. How many
more cherries than carrots
did he eat?
We are not told how
many cherries he ate.
0
1
2
3
4
3
8
C 79
4 x (7 - 4) = (2 x 4) + K
12 = 8 + 4
K= 4
12 x 6 = 7 2
36
4
+ 27
67
4
72
+ 3
79
Today is Wednesday, January 14. January
M o nda y .
5 was on a ___________
14
- 7
1. Friday
7
2. Wednesday
M T W
3. Monday
5 6 7
F 6 4
8
E 67
N x 4 = 12 + N
Three boards are each cut into ninths.
How many pieces are there?
enough
information
7.
44
9
+ 3
56
Which number can
be moved to change
the ≠ to = ?
Select the correct symbol.
>
B 56
6+2+1≠7+5+3
4 4 p e nni e s
A
one hundred thousand, fifty-nine
Name
A 24
Which fact does
not belong?
1
7
750,842
6017
Guided Practice 8
6.
5 ten thousands, 4 tens, 8 hundreds, 2
ones and 7 hundred thousands
fifty-two hundred
www.excelmath.com
3,373
750,842
100,059
+ 5,200
859,474
3,773 ________
3,737 ________
3,373
3,337
________
________
2
2
8
1
8
3 3
8
+1
4
3
8
- 1
3
8
7
8
-
3
3 3
8
6
8
1
8
3
+
6
1
8
4
8
2 7 pi e c e s
G 80
12
60
+ 8
80
Katy, Jess and Elton went
to a show. Elton was 13
minutes late. Jess was 5
minutes earlier than Elton.
Katy was 3 minutes later
than Jess. How many
minutes late was Katy?
E 13 - 5 = 8 J
not enough
information
8.
J 8 + 3 = 11 K
1 1 mi nut e s
6018
19
Brielle bought 89 lb of
ice. She used 41 lb for
snow cones and divided
the rest evenly between
6 coolers. How many lb
will be in each cooler?
89
- 41
48
48 ÷ 6 = 8
8 lb
H 94
36 ÷ 9 = 4
7
6 4 2
-4 2
0
-
1
6
11
8
4
+ 71
94
6
6
0
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 9
TEKS Objective
Students will add, subtract, multiply and
divide integers fluently.
to the value of the dividend without going
over it. They should then try to mentally
subtract to determine the remainder.
Students will learn division facts with
remainders with dividends up through 81.
Read through the division word problems
in #6 – #9 and do them together.
Students will solve word problems involving
division with remainders.
Stretch 9
Nine people are in a room.
If they each shake hands one time with
every other person, how many handshakes
will there be?
Preparation
For each student: two copies of One to Ten
Number Pieces (master on M15)
Answer: 36 handshakes
For the class: items to model the word
problems
Write the answer on the board so students
can model it:
Lesson Plan
8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36
Write, “How many 2s are there in 7?”
Have the students take out a “7” strip and
the “2” strips. Ask them to cover up the “7”
strip with as many “2” strips as they can
without going over the edges of the “7”. If
there is any space left over, see how many
ones it will take to finish covering the “7”.
Ask how many groups of 2 went into 7.
(3) Ask the class if 3 groups of two remind
them of anything else they have learned. (6
is a multiple of 2; it is the largest multiple of 2
that goes into 7 without going over 7.)
Remind the students that just as
multiplication is a faster way of adding,
division is a faster way of subtracting.
For problems #1 – #5 on the Student Lesson
Sheets, students should determine the
number that when multiplied by the divisor
results in the value that comes the closest
20
Lesson 9
Name
Date
Homework
Learning division facts with remainders with dividends up through 81; solving word
problems involving division with remainders
Divide 7 into 2 equal groups.
2
7
3
7
-6
1
2
The "r" stands
for remainder.
3 r1
6
Divide 7 by 2. 3 x 2 is the closest multiple. Put the 3 over the 7. Multiply
2 times 3, and subtract 6 from 7. There is 1 left over. When you try to divide
7 into 2 equal groups, you get 3 in each group with a remainder of 1.
2
6 r5
7 47
8
3
4 r3
35
Erasers are sold 5 to a
box. Violet wants to buy
erasers for 17 students.
How many boxes will
she have to buy?
8 r1
3 25
7
3r2
5 17
-15
2
4 boxes
6 hundreds, 3 ten
thousands, 1 one
and 2 hundred
thousands
4
5
8 r2
6 50
9 r6
8 78
9
Hiroko bought 30 pears for
3r6
her 8 friends. After dividing
8 30
them equally, how many
pears did each friend get?
-24
How many pears were left
6
over?
3 pears each
6 left over
Guided Practice 9
A 86
26
27
9
+ 24
86
26. 15 ÷ 3 < 9 - 3
27. 8 ÷ 8 > 2 x 0
Which fact does
not belong?
341,002
4
8
7
8
3
8
0
1
+ 8
6
8
-
1
8
3 x 4 = 12
5. 72 ÷ 8 = 9
12 thirds
6. 6 x 12 = 72
2
24 months = _____
years
0
+
6
8
5
8
1
8
6
8
Hector, Jamal and Edgar
met at the gym after
school. Hector arrived
last. Jamal didn't arrive
first. Who arrived first?
Leigh wants to share
her 16 books equally
with Joseph. Which
equation shows how
many books Joseph
will get?
E
1
J
2
Hector
13.
Jamal
14.
6. 16 - 2 =
7. 16 ÷ 2 = 8
8. 2 + 16 =
9. 2 ÷ 16 =
3
B 20
5
12
+ 3
20
tenths
Fill in the missing number for the
buttons needed for each jacket.
17
24
jackets
1
2
3
4
buttons
5
10
15
20
24
denominator = _______
10 ÷ 2 = 5
Edgar
15.
72
2,444
+
2
2,518
24 ÷ 12 = 2
D 2,189
2 = 14 - a
2 = 14 - 12
a = 12
240
x 9
2,160
17
2,160
+
12
2,189
© Copyright 2007-2014 AnsMar Publishers, Inc.
7. 72 ÷ 6 = 12
8 tenths - 5 tenths =
D
3
8
H
3
C 2,518
6 11
x 4
2,444
Rusty got up to bat 32 times. He
struck out 6 times and walked 9
times. The rest of his at-bats were
hits. How many hits did he get?
32
- 15
6 + 9 = 15
17
17 hits
How many thirds are
there in 4 wholes?
4. 12 x 6 = 72
12 x 2 = 24
5
8
2,375
3,789
+
21
6,185
Name
25. 9 + 9 ≠ 3 x 6
99 ÷ 11 = 9
14
+ 7
21
M
7
A 6,185
three hundred forty-one B 675,640
thousand, two
230,601
104,037
+ 341,002
675,640
7 2 h ou r s
Grace divided 26 toy cars equally
among 7 boys. How many cars did
each boy get? How many cars were
left over?
3 r5
7 26
-21
5
3 cars each
5 cars left over
S
6
6019
Which statements are true?
www.excelmath.com
S
5
104,037
Aaron gives tennis lessons
three hours per day, four times
a week. How many hours of
lessons does he give in six
weeks?
12
3 x 4 = 12 x 6
72
Naomi has 25 flowers. A vase
will hold 4 flowers. How many
vases does she need?
6 r 1
4 25
-24
1
7 vases
www.excelmath.com
-
F
4
1 hundred thousand,
3 tens, 7 ones and
4 thousands
230,601
Sometimes a problem requires two answers.
8
21 .
from this Monday will be June _____
What multiple of 2 ( 2, 4, 6, 8, ...) comes closest to 7 without going over?
For each of these problems try to mentally subtract to find the remainder.
1
Today is Friday, June 4. Two weeks
5,2 8 5
- 1,4 9 6
3,789
5,6 5 4
- 3,2 7 9
2,375
Milo and Kari ate 7
lollipops. Kari ate 3
more than Milo. How
many lollipops did
Kari eat?
( 0+7) ( 1+6 )
( 2+5) ( 3+4 )
5 lolli p o p s
7 ninths - 3 ninths =
4
ninths
4 sixths + 1 sixth =
5
sixths
Alyssa has 12 books. That is 3 fewer books than
Hershel. Debra has 5 more than Hershel. How
many books does Debra have?
H 15
A 12
+ 5
+ 3
20 books
D 20
H 15
4
5
+ 20
29
F $2.14
E 54
20
24
+ 10
54
C 29
$1.0 3
3 $3.0 9
- 3
0 0 9
-9
0
$ .7
7 $4.9
-4 9
0
-
1
7
$ .4 0
9 $3.6 0
-3 6
0 0
7
7
0
$1.03
.71
+ .40
$2.14
10
dividend ____
G 27
15
7
+ 5
27
Isabella plays soccer. She usually
scores two goals in each game
she plays. What information do
you need to estimate how many
goals she scored last season?
(number of games) x 2 = total goals
6. number of minutes she played
7. number of goals the others scored
8. number of games she played
6020
21
3 1 days
Days in July? ______
25 ÷ B = 5
25 ÷ 5 = 5
B= 5
8
24
H 50
8
31
5
+ 6
50
p x (2 x 4) = 2 x (4 x 6)
6 x 8 = 48
p= 6
© Copyright 2007-2014 AnsMar Publishers, Inc.
Lesson 10
TEKS Objective
Use a ruler and a yardstick to demonstrate
the equivalents in the lesson.
Students will give examples of ratios
as multiplicative comparisons of two
quantities and will make tables of
equivalent ratios, relating quantities with
whole number measurements and finding
missing values.
Using the ruler, measure the length of a
table in the room. Write on the board the
table’s length in feet and inches. Next,
tell the class that you want to lay a piece
of tape across the table, but the tape can
only be measured in inches. Ask them how
they would determine how many inches of
tape you would need. (Some of the students
will multiply the number of feet times 12 and
others will add. Either way is acceptable.)
Students will convert units within a
measurement system, including the use of
proportions and unit rates.
Students will measure temperature and will
determine if a measurement is longer or
shorter or heavier or lighter.
As a class, make a conversion table for
problems #3 – #4 showing the number of
inches to feet and feet to yards. Do the first
few together. See Lesson 40 if you want to
introduce ratios at this time:
Preparation
For the class: Standard and Metric
Measurements (master on M12), a ruler
and a yardstick, measuring cups, quart
and gallon bottles, scales that register in
pounds and ounces, thermometers, etc.
Lesson Plan
Measure distances around the classroom in
inches, feet, yards, centimeters and meters.
Depending on the distance measured, ask
the students which unit they would most
likely use to measure that distance and why.
Inches Feet
Feet
121
Yards
31
18 1.5
4.5
24
6
1.5
Go through problems #1 – #4 on the
Student Lesson Sheets together. For
problems #5 – #8, the students need to
determine how the measurements compare
to each other. Do these problems together.
Use several items as examples. For each
item, give the students three possible
choices for that item’s weight or length. Do
not give choices that are close. Remember,
you are only working on gross estimating.
Stretch 10
John, Jim, Gino and Bert have 32 baseball
cards. Jim has 1 more card than Gino.
Jim has one third the number that Bert has.
John has twice the number that Gino has.
How many cards do Bert, John, Jim and
Gino each have?
Explain that a temperature in Fahrenheit
can be converted to Celsius by subtracting
32 from the Fahrenheit temperature,
multiplying the result by 5, and then
dividing that result by 9. A temperature in
Celsius can be converted to Fahrenheit by
multiplying the Celsius temperature by 9,
dividing the result by 5, and then adding 32
to that result.
Answer: Bert-15, Jim-5, Gino-4, John-8
22
Lesson 10
Name
Date
8
Estimating measurements; measuring temperature; learning measurement equivalents
for length, weight and volume; converting measurements using multiplication or division;
determining the measurement that is longer or shorter or heavier or lighter
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
7
6
5
4
3
2
1
7
8
1
2
3
4
5
6
7
8
1
2
3
A pencil might be measured
in grams, a bird in ounces, a
person in pounds or kilograms
and an elephant in tons.
5
10
15
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
The prefix "kilo" means a thousand.
1000 grams (g) = 1 kilogram (kg)
8
6
7
5
6
4
5
3
25
30
35
40
45
1000 meters = 1 kilometer (km)
The prefix "milli" means "one-thousandth of".
Grams, kilograms, ounces,
pounds and tons are all
measures used for weight.
20
The height of a small child
might be measured in
1. miles.
2. kilometers.
3. inches.
4
2
3
1
2
Inches, feet, yards, miles, centimeters, meters and kilometers are
all units of length or distance.
A door might be measured in centimeters or inches, the width of a room
in feet, yards or meters, and the length of a road in miles or kilometers.
2
The weight of a sparrow
might be measured in
6. grams.
7. gallons.
8. kilometers.
1
1
1
1000 milliliters (ml) = 1 liter (l)
1000 millimeters (mm) = 1 meter (m)
Other standard measurement equivalents are:
1 yard (yd) = 3 feet (ft) 1 foot (ft) = 12 inches (in)
100 centimeters (cm) = 1 meter (m)
50
12 items = 1 dozen 1 gallon (gal) = 4 quarts (qt)
1 pound (lb) = 16 ounces (oz) 1 ton = 2,000 pounds (lb)
Sometimes converting a measurement requires 2 or 3 steps.
3
Cups, pints, quarts, gallons, milliliters and liters are units of volume.
A thimble filled with water might be measured in milliliters. If you fill
the gas tank of a car, it might be measured in gallons or liters.
Milk is sold by the pint, quart or gallon.
12
x 2
24
70
65
5
72 F.
The temperature is _____°
22 C.
In Celsius, it is _____°
Guided Practice 10
6 r6
8 54
-48
6
5 r8
9 53
-45
8
12 + 7 = 19
29 - 19 = 10
1 0 st a t e s
6
shorter?
7
longer?
12 x 4 = 4 8
3 1
8 2 4 8
-2 4
0 8
-8
0
Fish in 4 Lakes
500
Boyd wants to put his A 25 r14
18 books into boxes.
Each box will hold five
10
books. How many
6 r6
boxes will he need?
5 r8
+ 4
3 r3
2 5 r1 4
5 18
-15
3
9 0
6 5 4 0
-5 4
0 0
9
7 6 3
-6 3
0
-
How many trout are in all
four lakes?
1 ,05 0 tr ou t
300
How many more trout
than bass are there in
Lake Windy?
200
100
Lake
Soar
lighter?
a. 3 miles
a. 46 ounces
a. 3 kilograms
b. 2 feet = 24 inches
b. 56 feet
b. 4 pounds
b. 26 grams
© Copyright 2007-2014 AnsMar Publishers, Inc.
Today is Monday, January 7. January
Tue s da y .
22 will be on a ___________
7
+14
1. Monday
21
2. Tuesday
M
T
3. Wednesday
21 22
3
Lake Lake
Windy Mudd
Trout Bass Carp
7
7
0
40 0
20 0
40 0
+ 50
1 ,05 0
35 0 mor e tr ou t
What is the total number of
fish in Lake Mudd?
6 0 0 f is h
1
7
400
- 50
350
50
300
+ 25 0
600
8
48
31
90
+ 91
268
E 2,000
1,050
350
+ 600
2,000
9
7
8
3
3
8
7
5
8
4
6
8
+
1
2
8
-
2
4
8
-
Celia can buy stickers
six to a page. Which set
shows the number of
stickers she could buy?
7 . (6 , 1 2 , 1 5 , 1 8 )
8 . (3 , 9 , 1 5 , 2 1 )
4
1
8
=
4
5
8
=
5
1
8
12
6.
12
3
Reilly collected 348 rocks
over 6 days. 276 were
granite and the rest were
quartz. If he collected the
same number of quartz
rocks every day, how
many did he collect each
A
R
F
day?
348
oldest
youngest
- 276
72
Ricky Fran Abby
72 ÷ 6 = 12
6022
23
6.
7.
D 22 7
8
6
Ricky is older than
Fran but younger
than Abby. Who is
the youngest?
5.
2
5
9
+ 30
46
3 0 days
Days in November? ______
5
=
B 46
9 . (1 2 , 2 4 , 3 0 , 3 6 )
3 x (4 - 1) = (2 x 2) + B
9 = 4 + 5
B= 5
4 boxes
400
Lake
Roam
8
heavier?
a. 22 inches
C 268
96 ÷ 12 = 8
9
+ 2
11
Name
Kyla visited 29 states on
her 3-month trip. She visited
12 states in April and another
7 in May. How many states
did she visit in June?
Fish
3
x 3
9
6021
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www.excelmath.com
1 1 feet
3 yards 2 feet = ____
24
+ 3
27
For each problem, draw a circle around the letter representing the correct
answer. Sometimes you will need to convert one of the choices.
Temperature is measured using a thermometer.
Degrees Fahrenheit (F) or Celsius (C) are the
terms used to describe how hot or cold it is.
The symbol ° represents the word "degrees".
75
4
27 inches
2 feet 3 inches = _____
1 2 qua rt z ro c k s
7.
are shaded.
12
6
8.
6
12
Brock and Buzz
have been to 10
concerts. Buzz
attended 2 fewer
than Brock. How
many concerts did
Brock see?
8
5 1
8
4 5
8
+ 5 1
8
22 7
8
F 24
6
12
+ 6
24
( 1 + 9 ) ( 2 + 8)
( 3 + 7 ) ( 4 + 6)
(5 + 5)
6 c o nc e rt s
© Copyright 2007-2014 AnsMar Publishers, Inc.
Manipulatives
Table of Contents
Introduction
Coins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M2
The manipulatives below are used in lessons
throughout the year but are not necessarily
included in this book. Each lesson plan will
specify the required manipulative for that day’s
lesson.
One and Two Dollar Bills . . . . . . . . . . . . . . . . . . M3
Five, Ten and Twenty Dollar Bills . . . . . . . . . . . . M4
Random Pictures I . . . . . . . . . . . . . . . . . . . . . . . . M5
Random Pictures II . . . . . . . . . . . . . . . . . . . . . . . M6
Analog Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . M7
In place of items we suggest, you may want
to substitute items you already have in your
classroom.
Rulers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M8
Percent Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . M9
Number Chart . . . . . . . . . . . . . . . . . . . . . . . . . . M10
Many of the manipulatives are used repeatedly,
so it might be helpful to store them in small
plastic bags, one for each student.
1.Numeration blocks for ones, tens, hundreds
2.Play money: pennies, nickels, dimes,
quarters, half dollars and one-dollar bills
3.Analog clock with moveable hands
4. Balance scale
5.Inch ruler
6.Centimeter ruler
7.Yardstick
8. Meter stick/wheel
9. Scale that measures ounces and grams
10. Scale that measures pounds and kilograms
11.Containers for cup, pint, liter, quart, half
gallon and gallon
12.Fractional pieces
13.Advertisements or labels from products
that show length, weight, volume and
area (carpet sizes, food quantities, etc.)
14.Three-dimensional figures: spheres, cones,
cylinders, cubes, rectangular prisms,
rectangular pyramids, square pyramids,
triangular prisms and triangular pyramids
15. Number line chart that includes positive and negative numbers
16. Coordinate grid with four quadrants
Positive and Negative Cubes . . . . . . . . . . . . . . M11
Standard and Metric Measurements . . . . . . . . M12
Ones and Tens Pieces . . . . . . . . . . . . . . . . . . . . M13
Hundreds Pieces . . . . . . . . . . . . . . . . . . . . . . . . M14
One to Ten Number Pieces . . . . . . . . . . . . . . . . M15
Hundreds Exchange Board . . . . . . . . . . . . . . . . M16
One Whole, Tenths and Hundredths . . . . . . . . M17
Fraction Pieces I . . . . . . . . . . . . . . . . . . . . . . . . M18
Fraction Pieces II . . . . . . . . . . . . . . . . . . . . . . . . M19
Fraction Pieces III . . . . . . . . . . . . . . . . . . . . . . . M20
Circle Fraction Pieces . . . . . . . . . . . . . . . . . . . . M21
Area of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . M22
Area of a Parallelogram . . . . . . . . . . . . . . . . . . M23
Area of a Triangle . . . . . . . . . . . . . . . . . . . . . . . M24
Area of an Irregular Figure . . . . . . . . . . . . . . . . M25
Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M26
Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M27
Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M28
Rectangular Prism . . . . . . . . . . . . . . . . . . . . . . . M29
Rectangular Pyramid . . . . . . . . . . . . . . . . . . . . . M30
Triangular Prism . . . . . . . . . . . . . . . . . . . . . . . . M31
Triangular Pyramid . . . . . . . . . . . . . . . . . . . . . . M32
For additional manipulatives, visit us online:
www.excelmath.com/downloads/manipulatives.html
M1
Ones and Tens Pieces
Cut these two bars into ones pieces.
Do not cut up the other eight bars. Use them for tens pieces.
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M13
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Hundreds Pieces
Permission granted to copy this page
M14
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