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TABLE SETS
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Mathematics Achievement Academy Kindergarten – Grade 1: Day 1
Academic Vocabulary
Anchor Chart
Learning Progression
Magnitude
Numerical Fluency • Counting• Inclusion of Set: Cardinality and
Conservation• One-to-One Correspondence• Part-Whole Relationship
(Composing/Decomposing)• Relative Magnitude• Representations of Number• Subitizing (Perceptual and Conceptual)• Unitizing
Pre-Assessment
Quick Images
Rekenrek
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Sample Learning Progression of Whole Number Concept Cards
Cut along the dotted lines. Relative Magnitude Magnitude of a number describes its distance from zero. Relative magnitude is the comparative distance or size of two or more numbers. Understanding the relative magnitude of numbers allows students to reason about the relationships between numbers. Children may express the relationships using comparative language or symbols.
One-to-One Correspondence It is matching two groups so each member of one group is matched up with an object from the second group and vice versa. It is also the ability to count objects so that each object counted is matched with one number word. It is imperative not to have the objects always in the same arrangements.
Part-Whole Relationships Seeing part-whole relationships reflects the ability to compose and decompose numbers by looking at the whole and the parts that make up that whole. This is one of the most important concepts in number sense.
Subitizing (Perceptual) It is the ability to name the number of objects in a set without counting the objects based on the arrangement of objects. It is perceptual understanding of magnitude rather than counting to determine the magnitude or value on a number line.
Cardinality The last number stated is the number of objects in the set. It is the ability to count a set of objects. When asked how many objects are in the set, a child can say the number of objects without recounting the objects.
Conservation It consists of having the child count the objects, tell how many objects there are, and tell how many objects are present without having to recount the objects when the objects are rearranged.
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Subitizing (Conceptual) It is the ability to subitize the subgroups of a set and combine them to compose a whole.
Unitizing It is the ability to understand that items can be grouped to make a larger unit. For example, 10 ones can be grouped to make 1 ten. This also includes the understanding that the number 4 has a different value based on its place value location, such as 4 and 40.
4 tens 16 ones
40 + 10 + 6
30, 40, 50, 60, . . . 57, 56, 55, 54, . . . 45, 46, 47, 48, . . .
89 < 92
5
5 10 15 20 2 5
7
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
18 One Less One More
17 19
546 Less Than Greater Than
521 643
12 Less Than Equal To More Than
102 Less Than Greater Than
72 108
13 19 13 is less than 19.
19 is more than 13.35
30 + 5
2 hundreds 14 tens 16 ones 200 + 100 + 40 + 10 + 6
45 54 45 is less than 54.
I know because the digits in the tens places have values of 40 and 50. I know 40 is less than 50, so 45 is less than 54.
8 is more than 6.
6 is less than 8.
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
1,113
One thousand one hundred thirteen
1,000 + 100 + 10 + 3
676 632 676 > 632
The value of the digits in the hundreds place is the same. The value of the digit in the tens place in 676 is 70. The value of the digit in the tens place in 632 is 30. I know that 676 is greater than 632.
Hierarchical Inclusion
1 1 2 1 2 3 Hierarchical inclusion means when we construct a set of two, the value of one is included. When we construct a set of three, the value of two is included which also includes the value of one.
5 and 2 is 7. 3 and 3 is 6.
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
TEKS: Kindergarten Student Expectations Cards Copy on pink paper. Cut along the bold dotted lines. One set of cards is provided.
K(2)(A) Number and operations. The student is expected to count forward and backward to at least 20 with and without objects.
K(2)(B) Number and operations. The student is expected to read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.
K(2)(C) Number and operations. The student is expected to count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.
K(2)(D) Number and operations. The student is expected to recognize instantly the quantity of a small group of objects in organized and random arrangements.
K(2)(E) Number and operations. The student is expected to generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20.
K(2)(F) Number and operations. The student is expected to generate a number that is one more than or one less than another number up to at least 20.
K(2)(G) Number and operations. The student is expected to compare sets of objects up to at least 20 in each set using comparative language.
K(2)(H) Number and operations. The student is expected to use comparative language to describe two numbers up to 20 presented as written numerals.
K(2)(I) Number and operations. The student is expected to compose and decompose numbers up to 10 with objects and pictures.
K(5) Algebraic reasoning. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
TEKS: Grade 1 Student Expectations Cards Copy on green paper. Cut along the dotted lines. One set of cards is provided.
1(2)(A) Number and operations. The student is expected to recognize instantly the quantity of structured arrangements.
1(2)(B) Number and operations. The student is expected to use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.
1(2)(C) Number and operations. The student is expected to use objects, pictures, and expanded and standard forms to represent numbers up to 120.
1(2)(D) Number and operations. The student is expected to generate a number that is greater than or less than a given whole number up to 120.
1(2)(E) Number and operations. The student is expected to use place value to compare whole numbers up to 120 using comparative language.
1(2)(F) Number and operations. The student is expected to order whole numbers up to 120 using place value and open number lines.
1(2)(G) Number and operations. The student is expected to represent the comparison of two numbers to 100 using the symbols >, <, or =.
1(5)(A) Algebraic reasoning. The student is expected to recite numbers forward and backward from any given number between 1 and 120.
1(5)(B) Algebraic reasoning. The student is expected to skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set.
Sample Learning Progression: Whole Number Concepts Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
TEKS: Grade 2 Student Expectations Cards Copy on yellow paper.
Cut along the bold dotted lines. One set of cards is provided.
2(2)(A) Number and operations. The student is expected to use
concrete and pictorial models to compose and decompose numbers up
to 1,200 in more than one way as a sum of so many thousands,
hundreds, tens, and ones.
2(2)(B) Number and operations. The student is expected to use
standard, word, and expanded forms to represent numbers up to 1,200.
2(2)(C) Number and operations. The student is expected to generate
a number that is greater than or less than a given whole number up to
1,200.
2(2)(E) Number and operations.
The student is expected to locate the position of a given whole number on
an open number line.
2(2)(F) Number and operations.
The student is expected to name the whole number that corresponds to a
specific point on a number line.
2(2)(D) Number and operations.
The student is expected to use place value to compare and order whole
numbers up to 1,200 using comparative language, numbers, and
symbols (>, <, or =).
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rapid Assessments: Teacher
Rapid Assessment 1 Provide students with counters. 1. Prompt students to create a set of 5.2. Prompt students to create a set of 14.
Rapid Assessment 2 1. Create a set of 8 counters in a random arrangement. Ask students, “How
many counters are in this set?”2. Create a set of 12 counters in a random arrangement. Ask students,
“How many counters are in this set?”
Rapid Assessment 3 1. Ask students to count orally by tens to 100.2. Ask students to count orally by ones from 25 to 50.
Rapid Assessment 1: Student Responses Student A created a set with: □ 5 counters□ _____ counters
Student B created a set with: □ 5 counters□ _____ counters
Student C created a set with: □ 5 counters□ _____ counters
Student A created a set with: □ 14 counters□ _____ counters
Student B created a set with: □ 14 counters□ _____ counters
Student C created a set with: □ 14 counters□ _____ counters
Rapid Assessment 2: Student Responses Student A □ Correct□ Another Number: ___□ No response
Student B □ Correct□ Another Number: ___□ No response
Student C □ Correct□ Another Number: ___□ No response
Student A □ Correct□ Another Number: ___□ No response
Student B □ Correct□ Another Number: ___□ No response
Student C □ Correct□ Another Number: ___□ No response
Rapid Assessment 3: Student Responses Student A □ Counts by tens without
errors□ Counts by tens with
errors
Student B □ Counts by tens without
errors□ Counts by tens with
errors
Student C □ Counts by tens without
errors□ Counts by tens with
errorsStudent A □ Counts by ones without
errors□ Counts by ones with
errors
Student B □ Counts by ones without
errors□ Counts by ones with
errors
Student C □ Counts by ones without
errors□ Counts by ones with
errors
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rapid Assessments: Observer
Rapid Assessment 1: Student Strategies Student A: □ Counted counters one at
a time.□ Pushed aside counters or
pointed to counters.□ Other:
Student B: □ Counted counters one at
a time.□ Pushed aside counters or
pointed to counters.□ Other:
Student C: □ Counted counters one at
a time.□ Pushed aside counters or
pointed to counters.□ Other:
Rapid Assessment 2: Student Strategies Student A: □ Counted objects by
touching each one onceand only once – but didnot say numbers outloud.
□ Touched objects and saidcounting numbers outloud for each one.
□ Said number wordsaloud but did not useone-to-onecorrespondence toaccurately count theobjects in the set.
□ Counted one or moreobjects more than once.
□ Rearranged objects intoa different formation andthen counted each objectonly once.
□ Said counting numbersaloud without touchingobjects.
□ None observed.
Student B: □ Counted objects by
touching each one onceand only once – but didnot say numbers outloud.
□ Touched objects and saidcounting numbers outloud for each one.
□ Said number wordsaloud but did not useone-to-onecorrespondence toaccurately count theobjects in the set.
□ Counted one or moreobjects more than once.
□ Rearranged objects intoa different formation andthen counted each objectonly once.
□ Said counting numbersaloud without touchingobjects.
□ None observed.
Student C: □ Counted objects by
touching each one onceand only once – but didnot say numbers outloud.
□ Touched objects and saidcounting numbers outloud for each one.
□ Said number wordsaloud but did not useone-to-onecorrespondence toaccurately count theobjects in the set.
□ Counted one or moreobjects more than once.
□ Rearranged objects intoa different formation andthen counted each objectonly once.
□ Said counting numbersaloud without touchingobjects.
□ None observed.
Rapid Assessment 3: Student Observation Student A: □ Skipped numbers.□ Paused at each multiple
of 10.
Student B: □ Skipped numbers.□ Paused at each multiple
of 10.
Student C: □ Skipped numbers.□ Paused at each multiple
of 10.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rapid Assessment: Student A
Rapid Assessment 1 Count one object at a time and count aloud to create the sets.
Rapid Assessment 2 Touch each counter in the arrangement and say the counting number aloud as you touch each one.
Rapid Assessment 3 Count by tens correctly but pause between each multiple of ten. Count by ones correctly but pause at each multiple of 10 (i.e., 25, 26, 27, 28, 29, [pause] 30).
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rapid Assessment: Student B
Rapid Assessment 1 Push aside counters or point to counters to create the sets.
Rapid Assessment 2 Move the counters into a line then and correctly count the set of counters aloud.
Rapid Assessment 3 Count by tens correctly. Count by ones correctly.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Rapid Assessment: Student C
Rapid Assessment 1 Create the set incorrectly in an arbitrary way.
Rapid Assessment 2 Point to the counters as you count out loud. Count incorrectly by repeating a number in the sequence (i.e., 6, 7, 7, 8, 9, 10, 11, 12).
Rapid Assessment 3 Count by tens incorrectly by skipping numbers. Count by ones but start with 1, not 25. When you get to the teen numbers, forget the order of some of the numbers.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Progress Monitoring Card: Developing Whole Number Concepts
Student Name:
Counting
Count
and r
epre
sent
arr
angem
ents
of
obje
cts
up t
o 1
0.
Count
and r
epre
sent
arr
angem
ents
of
obje
cts
beyond 1
0.
Count
forw
ard
and b
ackw
ard
with o
r w
ithout
obje
cts
.
Recite n
um
bers
up t
o 1
00 u
sin
g m
ultip
les o
f 10.
Recite n
um
bers
up t
o 1
00 b
y o
nes.
Recite n
um
bers
forw
ard
and b
ackw
ard
up t
o 1
20.
Skip
-count
by t
ens t
o d
ete
rmin
e t
he t
ota
l num
ber
of
obje
cts
.
Skip
-count
by fiv
es t
o d
ete
rmin
e t
he t
ota
l num
ber
of
obje
cts
.
Skip
-count
by t
wos t
o d
ete
rmin
e t
he t
ota
l num
ber
of
obje
cts
.
Conserv
e n
um
bers
.
Instructional Sequence: Use Counting to Compare Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Five Frame Cards Two sets of cards are provided.
Instructional Sequence: Use Counting to Compare Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Ten Frame and Double Ten Frame Cards
Instructional Sequence: Use Counting to Compare Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Instructional Sequence: Use Counting to Compare Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparing Numbers Cards
Cut along dotted lines.
4
is more than
8 15
is more than
18 is the same number as is the same number as
is less than is less than
6
is more than
6 13
is more than
12 is the same number as is the same number as
is less than is less than
10
is more than
10 13
is more than
16 is the same number as is the same number as
is less than is less than
11
is more than
1 7
is more than
2 is the same number as is the same number as
is less than is less than
19
is more than
19 18
is more than
8 is the same number as is the same number as
is less than is less than
_____
is more than
_____ _____
is more than
_____ is the same number as is the same number as
is less than is less than
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Using Anchor Charts Concept Process Repertoire
A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons
A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies
A record of multiple options to develop and emphasize flexibility, persistence, and strategic thinking
Example
Example
Example
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Using Anchor Charts Concept Process Repertoire
A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons
A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies
A record of multiple options to develop and emphasize flexibility, persistence, and strategic thinking
Example
Example
Example
Generate Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set A – Kindergarten Two sets of cards are provided. Cut along dotted lines.
3 5 6 8
9 10 12 14
15 16 17 18
3 5 6 8
9 10 12 14
15 16 17 18
Generate Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set A – Grade 1 Two sets of cards are provided. Cut along dotted lines.
17 27 34 49
51 60 72 86
93 100 108 112
17 27 34 49
51 60 72 86
93 100 108 112
Generate Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set B – Kindergarten Two sets of cards are provided. Cut along dotted lines.
2 4 6 7
8 10 11 12
13 15 17 19
2 4 6 7
8 10 11 12
13 15 17 19
Generate Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Number Cards: Set B – Grade 1 Two sets of cards are provided. Cut along dotted lines.
18 25 34 42
50 66 79 81
93 99 103 110
18 25 34 42
50 66 79 81
93 99 103 110
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparing Numbers Using a Beaded Number Line
Cut along dotted lines.
38
is greater than >
45 61
is greater than >
68 is equal to =
is equal to =
is less than <
is less than <
25
is greater than >
52 75
is greater than >
75 is equal to =
is equal to =
is less than <
is less than <
87
is greater than >
84 24
is greater than >
20 is equal to =
is equal to =
is less than <
is less than <
85
is greater than >
35 15
is greater than >
15 is equal to =
is equal to =
is less than <
is less than <
_____
is greater than >
_____ _____
is greater than >
_____ is equal to =
is equal to =
is less than <
is less than <
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Supporting the Needs of Diverse Learners: Elements of Instructional Design
ConceptsMental Strategies, Procedures, and
Algorithms Applications
Manipulatives
Gestures/movement
Anchor charts
Pictures/visuals
Concrete to abstract
Pre‐teach academicvocabulary
Visuals of strategies
Multiple strategiespresented
Chunk information intoshort steps
Connections acrossrepresentations madeexplicit in student activities
Gestures to connect tocontent
Model correct speech andmathematical language
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Supporting the Needs of Diverse Learners: Elements of Instructional Design
ConceptsMental Strategies, Procedures, and
Algorithms Applications
Manipulatives
Gestures/movement
Anchor charts
Pictures/visuals
Concrete to abstract
Pre‐teach academicvocabulary
Visuals of strategies
Multiple strategiespresented
Chunk information intoshort steps
Connections acrossrepresentations madeexplicit in student activities
Gestures to connect tocontent
Model correct speech andmathematical language
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Speech/Language Impairments Characteristics
Expressive Language Disorder
Difficulty using oral language ortalking
Lacks variation in intonation or volumeof speech
Difficulty with imaginative play Impaired social language Difficulty describing, defining,
explaining, and retelling events Limited vocabulary often prompting
non-specific words (i.e., stuff) Difficulty with writing, spelling,
composing sentences, and answeringall but the most straightforwardquestions
Function words such as “the” and “is”and grammatical markers may beomitted
Receptive Language Disorder
Difficulty understanding oral languageor listening
Difficulty processing and retainingauditory information
Difficulty following verbal instructionsand directions
Difficulty answering questions outsidebasic question forms
Difficulty with verbal reasoning Difficulty filtering out background
noise Difficulty taking turns when talking in
conversation Difficulty maintaining learning and
conversation topics due to languagelimitations
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Speech/Language Impairments Characteristics
Expressive Language Disorder
Difficulty using oral language ortalking
Lacks variation in intonation or volumeof speech
Difficulty with imaginative play Impaired social language Difficulty describing, defining,
explaining, and retelling events Limited vocabulary often prompting
non-specific words (i.e. stuff) Difficulty with writing, spelling,
composing sentences, and answeringall but the most straightforwardquestions
Function words such as “the” and “is”and grammatical markers may beomitted
Receptive Language Disorder
Difficulty understanding oral languageor listening
Difficulty processing and retainingauditory information
Difficulty following verbal instructionsand directions
Difficulty answering questions outsidebasic question forms
Difficulty with verbal reasoning Difficulty filtering out background
noise Difficulty taking turns when talking in
conversation Difficulty maintaining learning and
conversation due to languagelimitation
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Strategies for Learning and Teaching for Students with SLI
Teach words and concepts using objects.
Progress activities from concrete to abstract.
Use a slower speech rate, if necessary, as this facilitates the processing of information.
Repeat information, language, sentences, phrases, and words more frequently.
Use consistent gestures when helping a student understand the meaning of a word that symbolizes an object or an action.Build consistency with the gestures within the grade-level team and department.
Use pictures or photographs to reinforce and review vocabulary that has been taught.
Add pictures within the story context for position and action words or use objects to model the story problem.
Give simple directions in sentence form to provide experiences in understanding sentences. Give directions in chunks of oneor two steps at a time.
Support the development of a peer buddy to help provide modeling for the student.
Allow the student to work at his/her own pace.
Develop procedures for how the student asks for help.
Model speech, and avoid overcorrecting.
Be patient with the student’s speech; rushing the student could result in frustration.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Strategies for Learning and Teaching for Students with SLI
Teach words and concepts using objects.
Progress activities from concrete to abstract.
Use a slower speech rate, if necessary, as this facilitates the processing of information.
Repeat information, language, sentences, phrases, and words more frequently.
Use consistent gestures when helping a student understand the meaning of a word that symbolizes an object or an action.Build consistency with the gestures within the grade-level team and department.
Use pictures or photographs to reinforce and review vocabulary that has been taught.
Add pictures within the story context for position and action words or use objects to model the story problem.
Give simple directions in sentence form to provide experiences in understanding sentences. Give directions in chunks of oneor two steps at a time.
Support the development of a peer buddy to help provide modeling for the student.
Allow the student to work at his/her own pace.
Develop procedures for how the student asks for help.
Model speech, and avoid overcorrecting.
Be patient with the student’s speech; rushing the student could result in frustration.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Exit Slip: Day 1
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Whole Number Learning Progression ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Counting ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Comparing Numbers ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Student Tools ⃝ ⃝ ⃝ ⃝
Support for Students with Speech and
Language Impairments ⃝ ⃝ ⃝ ⃝
Anchor Charts ⃝ ⃝ ⃝ ⃝
Rapid Assessments ⃝ ⃝ ⃝ ⃝
Additional Comments:
Exit Slip: Day 1
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Whole Number Learning Progression ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Counting ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Comparing Numbers ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Student Tools ⃝ ⃝ ⃝ ⃝
Support for Students with Speech and
Language Impairments ⃝ ⃝ ⃝ ⃝
Anchor Charts ⃝ ⃝ ⃝ ⃝
Rapid Assessments ⃝ ⃝ ⃝ ⃝
Additional Comments:
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Mathematics Achievement Academy Kindergarten – Grade 1: Day 2
Academic Vocabulary Addition and Subtraction Problem Types
• Comparison• Joining• Part-Part-Whole• Separating
Anchor Chart Repertoire Chart
Balanced Pre-Assessment
Foundational-Bridging-Target Knowledge and Skills
Learning Progression
Numerical Fluency • Part-Whole Relationship (Composing/Decomposing)• Relative Magnitude• Subitizing (Perceptual and Conceptual)• Unitizing
Open Number Line
Quick Images
Representations of Number • Expanded Form• Standard Form
Running Record
Unknown
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Guiding Questions for Balanced Pre-Assessment Toolkit Card What are the broad and deep ideas that students must master to be successful in
mathematics this year?
What are the concepts and procedures from the previous grade level that students shouldhave mastered?
What are the foundational knowledge and skillsthat students may use to build toward mastery?
What are the bridging knowledge and skills thatstudents may use to connect foundationalunderstandings to target understandings?
What are the target knowledge and skills inmathematics that students must master?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Guiding Questions for Balanced Pre-Assessment Toolkit Card What are the broad and deep ideas that students must master to be successful in
mathematics this year?
What are the concepts and procedures from the previous grade level that students shouldhave mastered?
What are the foundational knowledge and skillsthat students may use to build toward mastery?
What are the bridging knowledge and skills thatstudents may use to connect foundationalunderstandings to target understandings?
What are the target knowledge and skills inmathematics that students must master?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Activity Role Cards Copy on colored paper. Cut along dotted lines.
Teacher: • Follow the steps found on the teacher page in the
participant journal.• When prompted, video record students as they
work to solve word problems and as they explainhow they solved the problem.
Facilitator: Distribute materials and assist the teacher as needed.
Time keeper: Keep track of the allotted time and participate as a student in the activity.
Student: Participate in the activity as a kindergarten or grade 1 student by using the lesson materials as guided by the teacher.
Student: Participate in the activity as a kindergarten or grade 1 student by using the lesson materials as guided by the teacher.
Student: Participate in the activity as a kindergarten or grade 1 student by using the lesson materials as guided by the teacher.
Student: Participate in the activity as a kindergarten or grade 1 student by using the lesson materials as guided by the teacher.
Representing Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Tens Cards Copy on green paper. Cut along dotted lines.
0 tens 0 tens 0 tens 1 ten 1 ten 1 ten 2 tens 2 tens 2 tens 3 tens 3 tens 3 tens 4 tens 4 tens 4 tens 5 tens 5 tens 5 tens 6 tens 6 tens 6 tens 7 tens 7 tens 7 tens 8 tens 8 tens 8 tens 9 tens 9 tens 9 tens
Representing Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Ones Cards Copy on yellow paper. Cut along dotted lines.
0 ones 0 ones 0 ones 1 one 1 one 1 one 2 ones 2 ones 2 ones 3 ones 3 ones 3 ones 4 ones 4 ones 4 ones 5 ones 5 ones 5 ones 6 ones 6 ones 6 ones 7 ones 7 ones 7 ones 8 ones 8 ones 8 ones 9 ones 9 ones 9 ones
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Standard Form Cards Cut along dotted lines.
79 25 48 54 61 33 86 52 17 99 108 120 116 110 101 112
Representing Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Expanded Form: Hundreds Cards Copy on blue paper. Cut along dotted lines.
1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0
Representing Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Expanded Form: Tens Cards Copy on yellow paper. Cut along dotted lines.
1 0 1 0 2 0 2 0 3 0 3 0 4 0 4 0 5 0 5 0 6 0 6 0 7 0 7 0 8 0 8 0 9 0 9 0 0 0 0 0
Expanded Form: Ones Cards
Copy on green paper.
Cut along dotted lines.
1 2 1 2
3 4 3 4
5 6 5 6
7 8 7 8
9 0 9 0
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
More or Less Cards Cut along dotted lines.
More Less
More Less
More Less
More Less
More Less
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparison Language Cards
Cut along dotted lines.
is more than is less than is the same number as
is greater than is less than is equal to
is more than is less than is the same number as
is greater than is less than is equal to
is more than is less than is the same number as
is greater than is less than is equal to
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparing Numbers Cards Cut along dotted lines.
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparison Symbol and Word Cards Cut along dotted lines.
> is greater
than
< is less than
= is equal
to
> is greater
than
< is less than
= is equal
to
> is greater
than
< is less than
= is equal
to
> is greater
than
< is less than
= is equal
to
> is greater
than
< is less than
= is equal
to
> is greater
than
< is less than
= is equal
to
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Numbers to Compare Cards Cut along dotted lines.
120 111 103 100 118
92 70 81 42 25
18 67 56 70 92
24 52 65 76 29
120 111 103 100 118
92 70 81 42 25
18 67 56 70 92
24 52 65 76 29
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Place Value Puzzle Cut along dotted lines.
114 > ___04 118 < 1___0 2___ = 27
72 > ___8 4 < ___ 84 = ___4
91 > 9___ 90 < 10___ 32 = 3___
120 > 1___2 6___ < 98 ___05 = 105
___0 > 87 ___5 < 60 ___7 > 13
100 > ___3 ___0 < 95 84 > ___9
___ > 7 52 < ___6 11___ < 118
70 > ___2 17 < ___1 4___ > 39
Sample Learning Progression: Addition and Subtraction Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
TEKS: Kindergarten Student Expectations Cards Copy on pink paper. Cut along the bold dotted lines. Three sets of cards are provided. K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.
K(3)(B) Number and operations. The student is expected to solve word problems using objects and drawings to find sums up to 10 and differences within 10.
K(3)(C) Number and operations. The student is expected to explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences.
K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.
K(3)(B) Number and operations. The student is expected to solve word problems using objects and drawings to find sums up to 10 and differences within 10.
K(3)(C) Number and operations. The student is expected to explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences.
K(3)(A) Number and operations. The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.
K(3)(B) Number and operations. The student is expected to solve word problems using objects and drawings to find sums up to 10 and differences within 10.
K(3)(C) Number and operations. The student is expected to explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences.
Sample Learning Progression: Addition and Subtraction Kindergarten - Grade 1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
TEKS: Grade 1 Student Expectations Cards Copy on green paper. Cut along the dotted lines. One set of cards is provided. 1(3)(B) Number and operations. The student is expected to use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3.
1(3)(C) Number and operations. The student is expected to compose 10 with two or more addends with and without concrete objects.
1(3)(D) Number and operations. The student is expected to apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.
1(3)(E) Number and operations. The student is expected to explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences.
1(3)(F) Number and operations. The student is expected to generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.
1(5)(D) Algebraic reasoning. The student is expected to represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.
1(5)(E) Algebraic reasoning. The student is expected to understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).
1(5)(F) Algebraic reasoning. The student is expected to determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.
1(5)(G) Algebraic reasoning. The student is expected to apply properties of operations to add and subtract two or three numbers.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Learning Progression Kindergarten: Addition and Subtraction of Whole Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Learning Progression Grade 1: Addition and Subtraction of Whole Numbers
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Question Mark Cards
Cut along dotted lines. Twelve cards are provided.
? ? ?
? ? ?
? ? ?
? ? ?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Comparison Mat Cut along the dotted lines and glue or tape the three pieces together where indicated.
Glue or tape Glue or tape Glue or tape
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Types of Addition and Subtraction Word Problems Joining and Separating Problems
• An action or change that occurs over time is involved.• An initial quantity (start) is increased/decreased by a particular quantity
(change) to get a final quantity (result).• The start, change, or result may be unknown.
Part-Part-Whole Problems • An action is NOT involved.• A change over time is NOT involved.• A relationship between a whole quantity and two (or more) parts make up the whole quantity.• A part or the whole may be unknown.
whole
part part
Comparison Problems
• An action is NOT involved.• A change over time is NOT represented.• A comparison of two distinct sets is involved.• One set is labeled the referent, and the other is
labeled the compared set.• The difference, the larger quantity, or the smaller
quantity may be unknown. • The referent, the compared set, or the difference
may be unknown.
larger quantity
smaller quantity difference
Result
Change
Start
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Types of Addition and Subtraction Word Problems Joining and Separating Problems
• An action or change that occurs over time is involved.• An initial quantity (start) is increased/decreased by a particular quantity
(change) to get a final quantity (result).• The start, change, or result may be unknown.
Part-Part-Whole Problems • An action is NOT involved.• A change over time is NOT involved.• A relationship between a whole quantity and two (or more) parts make up the whole quantity.• A part or the whole may be unknown.
whole
part part
Comparison Problems • An action is NOT involved.• A change over time is NOT represented.• A comparison of two distinct sets is involved.• One set is labeled the referent, and the other is
labeled the compared set.• The difference, the larger quantity, or the smaller
quantity may be unknown.• The referent, the compared set, or the difference
may be unknown.
larger quantity
smaller quantity difference
Result
Change
Start
Addition and Subtraction Problem Types
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Joining Problems Start Unknown
David had some baseball cards. Kayla gave him 3 baseball cards. Now he has 12 baseball cards. How many baseball cards did David have at the start?
Change Unknown David had 5 baseball cards. Then Kayla gave him some baseball cards. Now he has 10 baseball cards. How many baseball cards did Kayla give David?
Result Unknown* David had 6 baseball cards. Kayla gave him 2 baseball cards. How many baseball cards does David have now?
Separating Problems Start Unknown
David had some baseball cards. He gave 4 baseball cards to Kayla. Now he has 8 baseball cards. How many baseball cards did David have at the start?
Change Unknown David had 14 baseball cards. He gave some baseball cards to Kayla. Now he has 9 baseball cards. How many baseball cards did David give to Kayla?
Result Unknown* David had 10 baseball cards. He gave 1 baseball card to Kayla. How many baseball cards does David have now?
Part-Part-Whole Problems Part Unknown
David has 13 baseball cards. He has 7 new baseball cards. The rest are old baseball cards. How many old baseball cards does David have?
Whole Unknown* David has 4 old baseball cards and 6 new baseball cards. How many baseball cards does David have altogether?
Comparison Problems Difference Unknown
David has 12 baseball cards. Kayla has 9 baseball cards. How many more baseball cards does David have than Kayla?
Larger Unknown Kayla has 5 baseball cards. David has 8 more than Kayla. How many baseball cards does David have?
Smaller Unknown David has 14 baseball cards. He has 7 more baseball cards than Kayla. How many baseball cards does Kayla have?
* Kindergarten
Addition and Subtraction Problem Types
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Joining Problems Start Unknown
David had some baseball cards. Kayla gave him 3 baseball cards. Now he has 12 baseball cards. How many baseball cards did David have at the start?
Change Unknown David had 5 baseball cards. Then Kayla gave him some baseball cards. Now he has 10 baseball cards. How many baseball cards did Kayla give David?
Result Unknown* David had 6 baseball cards. Kayla gave him 2 baseball cards. How many baseball cards does David have now?
Separating Problems Start Unknown
David had some baseball cards. He gave 4 baseball cards to Kayla. Now he has 8 baseball cards. How many baseball cards did David have at the start?
Change Unknown David had 14 baseball cards. He gave some baseball cards to Kayla. Now he has 9 baseball cards. How many baseball cards did David give to Kayla?
Result Unknown* David had 10 baseball cards. He gave 1 baseball card to Kayla. How many baseball cards does David have now?
Part-Part-Whole Problems Part Unknown
David has 13 baseball cards. He has 7 new baseball cards. The rest are old baseball cards. How many old baseball cards does David have?
Whole Unknown* David has 4 old baseball cards and 6 new baseball cards. How many baseball cards does David have altogether?
Comparison Problems Difference Unknown
David has 12 baseball cards. Kayla has 9 baseball cards. How many more baseball cards does David have than Kayla?
Larger Unknown Kayla has 5 baseball cards. David has 8 more than Kayla. How many baseball cards does David have?
Smaller Unknown David has 14 baseball cards. He has 7 more baseball cards than Kayla. How many baseball cards does Kayla have?
* Kindergarten
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Accommodations for English Language Learners
Visuals for vocabulary Peer interaction
Use of anchor charts Gestures for memorization of academicconcepts
Use of graphic organizers Use of sentence stems/frames
Use of manipulatives Pre-teach academic vocabulary
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Accommodations for English Language Learners
Visuals for vocabulary Peer interaction
Use of anchor charts Gestures for memorization of academicconcepts
Use of graphic organizers Use of sentence stems/frames
Use of manipulatives Pre-teach academic vocabulary
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Supporting Students with Diverse Needs
Text to Speech (TTS) www.naturalreaders.com
Super Tools for Teachers www.esc4.net/UDL
UDL Tech Toolkit http://udltechtoolkit.wikispaces.com
Institute of Education Sciences (IES) What Works In Math? http://ies.ed.gov/ncee/wwc/MathHome.aspx
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Supporting Students with Diverse Needs
Text to Speech (TTS) www.naturalreaders.com
Super Tools for Teachers www.esc4.net/UDL
UDL Tech Toolkit http://udltechtoolkit.wikispaces.com/
Institute of Education Sciences (IES) What Works In Math? http://ies.ed.gov/ncee/wwc/MathHome.aspx
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Exit Slip: Day 2
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Whole Number Concepts:
Subitizing ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Representing, Comparing, and Ordering ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Composing and Decomposing Numbers ⃝ ⃝ ⃝ ⃝
Addition and Subtraction
Learning Progression ⃝ ⃝ ⃝ ⃝
Support for Students who are English
Language Learners ⃝ ⃝ ⃝ ⃝
Pre-Assessment ⃝ ⃝ ⃝ ⃝
Problem Types ⃝ ⃝ ⃝ ⃝
Additional Comments:
Exit Slip: Day 2
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Whole Number Concepts:
Subitizing ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Representing, Comparing, and Ordering ⃝ ⃝ ⃝ ⃝
Whole Number Concepts:
Composing and Decomposing Numbers ⃝ ⃝ ⃝ ⃝
Addition and Subtraction
Learning Progression ⃝ ⃝ ⃝ ⃝
Support for Students who are English
Language Learners ⃝ ⃝ ⃝ ⃝
Pre-Assessment ⃝ ⃝ ⃝ ⃝
Problem Types ⃝ ⃝ ⃝ ⃝
Additional Comments:
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Mathematics Achievement Academy Kindergarten – Grade 1: Day 3
Academic Vocabulary Anchor Chart
• Concept
Feedback • Intervention• Process• Task
Fractions • Partition
Learning Progression • Addend• Associative Property• Commutative Property• Difference• Equation• Expression• Minuend• Subtrahend• Sum
Practice • Blocked• Interleaved• Skill
Fact Cards
Cut along the dotted lines. Two sets of cards provided.
+8 8 8 3+ 10 5+
10 3+ 3 3+ 8 5+
8 1+ 7 7+ 9 10+
2 10+ +2 2 8 4+
+8 8 8 3+ 10 5+
10 3+ 3 3+ 8 5+
8 1+ 7 7+ 9 10+
2 10+ +2 2 8 4+
Fact Building for Addition and Subtraction
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
+ 1 or –1 + 2 or –2
+ or – 0 Ten Facts Decompose, Then
Make 10 Doubles and Near
Doubles
Students build on their understanding of counting by exploring addition facts with an addend of 1 or 2 and subtraction facts with a
subtrahend of 1 or 2.
Students explore addition facts with an addend of zero and subtraction facts with a subtrahend of zero.
Students explore addition facts with two addends that result in a sum of 10.
Students explore addition facts with an addend of 7, 8, or 9 and a second addend that is decomposed to make
10 with 7, 8, or 9.
Students explore facts with the same addends, doubles, facts with addends of only a difference of one, and near
doubles.
7 + 1 = 8 5 – 1 = 4
2 + 0 = 2 5 – 0 = 5
1 + 9 = 10 3 + 7 = 10
9 + 6 9 + 1 + 5
10 + 5 = 15
8 + 8 = 16 8 + 9 = 17
Think Addition Down Through 10 Take From 10
Students explore subtraction facts
by thinking about the relationship between the quantity in the subtrahend and a quantity that
composes to make the quantity of the minuend.
Students explore subtraction facts by decomposing the subtrahend in order to find a difference of 10. They then subtract the remaining
quantity from 10.
Students explore subtraction facts by decomposing the minuend into a 10 and the remaining quantity. The subtrahend is subtracted from
10, and the remaining quantities are composed to determine the difference.
12 5
5 12
15 8
15 5 3
10 3 7
15 8
10 5 8
10 8 5
2 5 7
Fact Building for Addition and Subtraction
+ 1 or –1
+ 2 or –2 + or – 0 Ten Facts
Decompose, Then
Make 10
Doubles and Near
Doubles
Students build on their understanding of
counting by exploring addition facts with an addend of 1 or 2 and subtraction facts with a subtrahend of 1 or 2.
Students explore addition facts with
an addend of zero and subtraction facts with a subtrahend of zero.
Students explore addition facts with
two addends that result in a sum of 10.
Students explore addition facts with
an addend of 7, 8, or 9 and a second addend that is decomposed to make 10 with 7, 8, or 9.
Students explore facts with the same
addends, doubles, facts with addends of only a difference of one, and near doubles.
7 + 1 = 8 5 – 1 = 4
2 + 0 = 2 5 – 0 = 5
1 + 9 = 10 3 + 7 = 10
9 + 6 9 + 1 + 5
10 + 5 = 15
8 + 8 = 16 8 + 9 = 17
Think Addition Down Through 10 Take From 10
Students explore subtraction facts
by thinking about the relationship between the quantity in the subtrahend and a quantity that composes to make the quantity of the minuend.
Students explore subtraction facts by decomposing the subtrahend in order to find a difference of 10. They then subtract the remaining quantity from 10.
Students explore subtraction facts by decomposing the minuend into a 10 and the remaining quantity. The subtrahend is subtracted from 10, and the remaining quantities are
composed to determine the difference.
12 5
5 12
15 8
15 5 3
10 3 7
15 8
10 5 8
10 8 5
2 5 7
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Fact Cards
8 1 6 4 3 0
7 4 18 9 2 0
6 7 5 2 7 5
16 9 4 5 5 3
8 3 4 4 8 2
3 2 3 7 6 1
9 4 8 7 7 7
19 10 13 6 5 5
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Expression Cards 1-10
Cut along the dotted lines.
3 6+2 4+
2 1+
1 2+ 5 5+5 3+ 2 6+1 1+
0 2+
6 1+ 3 4+
4+10+12+2
6 4+ 0 5+
+1 01+3
+4 5+3 3
Expression Cards 10-20
Cut along the dotted lines.
7 3+ 2 8+ 2 9+
8 3+ 6 6+ 9 3+
12 3+ 10 5+ 9 9+
10 8+ 9 7+ 8 8+
7 7+ 9 5+ 4 4 4+ +
4 3 3+ + 7 7 4+ + 5 5 6+ +
2 6 3+ + 10 2 2+ + 7 3 5+ +
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Meaningful Practice
Skill Practice
Primary focus on buildingprocedural fluency
Repetitive practice for aspecific skill
Promotes automaticity Increases ability to perform
math tasks quickly Allows brain to focus on
more challenging problem-solving steps
Blocked Practice
Narrow focus on specificcontent Skills and processes are the
same/similar for everyproblem
One given process ispracticed
Promotes learning of new skillor process Knowledge of content and
strategies are introducedjust prior to practice
The rigor of practice isreduced because choice ofstrategy or process is notrequired between problems
Interleaved Practice
Wide focus on broad content Skills and processes are
different across theproblems
Focuses on interpretingsituations and determiningthe process
Promotes decision making andproblem solving Knowledge of content and
strategies are from newlyintroduced as well asprevious learning
The rigor of practice isincreased because studentsmust choose the strategy orprocess
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Meaningful Practice
Skill Practice
Primary focus on buildingprocedural fluency
Repetitive practice for aspecific skill
Promotes automaticity Increases ability to perform
math tasks quickly Allows brain to focus on
more challenging problem-solving steps
Blocked Practice
Narrow focus on specificcontent Skills and processes are the
same/similar for everyproblem
One given process ispracticed
Promotes learning of new skillor process Knowledge of content and
strategies are introducedjust prior to practice
The rigor of practice isreduced because choice ofstrategy or process isreduced between problems
Interleaved Practice
Wide focus on broad content Skills and processes are
different across theproblems
Focuses on interpretingsituations and determiningthe process
Promotes decision making andproblem solving Knowledge of content and
strategies are from newlyintroduced as well asprevious learning
The rigor of practice isincreased because studentsmust choose the strategy orprocess
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Sample Learning Progression Grade 1: Fraction Concepts
Developing Fraction Concepts
Grade 1: Fraction Concepts
Data Collection
Identify examples and non-examples of halves and fourths
Readiness For
Grade 2
Pre-Assessment
Partition two-dimensional figures into two and four fair shares or equal parts and describe the
parts using words
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Sample Learning Progression Grade 1: Fraction Concepts
Developing Fraction Concepts
Grade 1: Fraction Concepts
Data Collection
Identify examples and non-examples of halves and fourths
Readiness For
Grade 2
Pre-Assessment
Partition two-dimensional figures into two and four fair shares or equal parts and describe the
parts using words
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Example and Non-Example Cards Cut along the dotted lines.
Card A Card B
Card C Card D
Card E Card F
Card G Card H
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Workstation 1: Example and Non-Example Sorting Cards Cut along the dotted lines.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Task Feedback
• You have all the questions about _____ correct.
• Question _____ is incorrect. You forgot to _____.
• Your solution to question _____ is correct.
• When you _____, the _____ was done incorrectly.
• Although you got the answer correct, you _____ incorrectly.
• The answer to question _____ is incorrect because it looks like you are confusing
_____ with _____.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Task Feedback
• You have all the questions about _____ correct.
• Question _____ is incorrect. You forgot to _____.
• Your solution to question _____ is correct.
• When you _____, the _____ was done incorrectly.
• Although you got the answer correct, you _____ incorrectly.
• The answer to question _____ is incorrect because it looks like you are confusing
_____ with _____.
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Process Feedback
• I see that you are _____, and that is working for you.
• How would the thinking you used for question _____ help you understand question
_____?
• Have you thought of using _____ to solve the problem?
• I see that you used _____ to _____. Have you thought about using _____?
• How would the process we learned when we _____ help you _____?
• You chose to use a _____ to answer the question. How could _____ have helped you?
• Think back to when you used _____ to solve the problem. How can that help
you solve _____?
• How would the process you used for question _____ help you find your mistake
in question _____?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Process Feedback
• I see that you are _____, and that is working for you.
• How would the thinking you used for question _____ help you understand question
_____?
• Have you thought of using _____ to solve the problem?
• I see that you used _____ to _____. Have you thought about using _____?
• How would the process we learned when we _____ help you _____?
• You chose to use a _____ to answer the question. How could _____ have helped you?
• Think back to when you used _____ to solve the problem. How can that help
you solve _____?
• How would the process you used for question _____ help you find your mistake
in question _____?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Intervention Feedback
• Remember when we learned about ____? This can help you solve the problem because
_____.
• Using _____ did not always _____. How could you use _____ to solve the problem?
• Doing all of the thinking in your head did not help you solve the problem. Try showing your
thinking by _____.
• Remember when we learned about _____? Try using that process first.
• Your method required you to _____. How could you use _____ to solve the problem?
• Remember to _____ before choosing _____.
• How could you _____ when you _____?
• The _____ appeared useful in solving the problem. How could you use this idea to _____?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Effective Feedback: Intervention Feedback
• Remember when we learned about ____? This can help you solve the problem because
_____.
• Using _____ did not always _____. How could you use _____ to solve the problem?
• Doing all of the thinking in your head did not help you solve the problem. Try showing your
thinking by _____.
• Remember when we learned about _____? Try using that process first.
• Your method required you to _____. How could you use _____ to solve the problem?
• Remember to _____ before choosing _____.
• How could you _____ when you _____?
• The _____ appeared useful in solving the problem. How could you use this idea to _____?
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Curriculum and Instruction for Gifted/Talented Students
Districts meet the needs of gifted/talented students by modifying the __________, __________, and
_________ of the curriculum and instruction ordinarily provided by the school.
• WHAT• TEKS• Instructional Materials
• HOW• Instructional Activities• Instructional Grouping
• EVIDENCE• Student Demonstration
of Mastery
Content Process Product Examples:
Next grade-level TEKS Higher magnitude of
numbers
Examples: G/T small groups Separate G/T stations
Examples: Video Written report Performance task
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Curriculum and Instruction for Gifted/Talented Students Districts meet the needs of gifted/talented students by modifying the __________, __________, and
_________ of the curriculum and instruction ordinarily provided by the school.
• WHAT• TEKS• Instructional Materials
• HOW• Instructional Activities• Instructional Grouping
• EVIDENCE• Student Demonstration
of Mastery
Content Process Product Examples:
Next grade-level TEKS Higher magnitude of
numbers
Examples: G/T small groups Separate G/T stations
Examples: Video Written report Performance task
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1
Exit Slip: Day 3
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Addition and Subtraction:
Representing Problem Situations ⃝ ⃝ ⃝ ⃝
Addition and Subtraction:
Generating and Solving Problem Situations ⃝ ⃝ ⃝ ⃝
Addition and Subtraction Facts ⃝ ⃝ ⃝ ⃝
Properties of Operations, The Equal Sign,
Determining the Unknown ⃝ ⃝ ⃝ ⃝
Learning Progression: Fractions
and Fraction Concepts ⃝ ⃝ ⃝ ⃝
Support for Students who are
Gifted/Talented ⃝ ⃝ ⃝ ⃝
Meaningful Practice ⃝ ⃝ ⃝ ⃝
Types of Feedback ⃝ ⃝ ⃝ ⃝
Additional Comments:
Exit Slip: Day 3
Rate your level of proficiency and comfort for the content addressed.
Developing
Proficiency
Approaching
Proficiency
Meeting
Proficiency
Mastering
with
Proficiency
Addition and Subtraction:
Representing Problem Situations ⃝ ⃝ ⃝ ⃝
Addition and Subtraction:
Generating and Solving Problem Situations ⃝ ⃝ ⃝ ⃝
Addition and Subtraction Facts ⃝ ⃝ ⃝ ⃝
Properties of Operations, The Equal Sign,
Determining the Unknown ⃝ ⃝ ⃝ ⃝
Learning Progression: Fractions
and Fraction Concepts ⃝ ⃝ ⃝ ⃝
Support for Students who are
Gifted/Talented ⃝ ⃝ ⃝ ⃝
Meaningful Practice ⃝ ⃝ ⃝ ⃝
Types of Feedback ⃝ ⃝ ⃝ ⃝
Additional Comments:
©2017 Texas Education Agency. All Rights Reserved 2017 Mathematics Achievement Academy, Grades K-1