2. Purpose
• Overview of the 2016 Mathematics Standards
of Learning and the Curriculum Framework
• Highlight information included in the Essential
Knowledge and Skills and the Understanding
the Standard sections of the Curriculum
Framework
2
3. Agenda
• Implementation Timeline
• Resources Currently Available
– Crosswalk (Summary of Revisions)
– Standards and Curriculum Frameworks
• Comparison of 2009 to 2016 Standards
– Number and Number Sense
– Computation and Estimation
– Measurement and Geometry
– Probability and Statistics
– Patterns, Functions, and Algebra
3
4. 4
Implementation Timeline
2016-2017 School Year – Curriculum Development
VDOE staff provides a summary of the revisions to assist school
divisions in incorporating the new standards into local written curricula
for inclusion in the taught curricula during the 2017-2018 school year.
2017-2018 School Year – Crossover Year
2009 Mathematics Standards of Learning and 2016 Mathematics
Standards of Learning are included in the written and taught curricula.
Spring 2018 Standards of Learning assessments measure the 2009
Mathematics Standards of Learning and include field test items
measuring the 2016 Mathematics Standards of Learning.
2018-2019 School Year – Full-Implementation Year
Written and taught curricula reflect the 2016 Mathematics Standards
of Learning. Standards of Learning assessments measure the 2016
Mathematics Standards of Learning.
5. 2016 SOL Revisions –
• Improve the vertical progression of mathematics
content
• Ensure developmental appropriateness of student
expectations
• Increase support for teachers in mathematics
content (including definitions, explanations,
examples, and instructional connections)
• Clarify expectations for teaching and learning
• Improve precision and consistency in mathematical
vocabulary and format
• Ensure proficiency of elementary students in
computational skills
5
6. Changes to the Curriculum Framework
• Reduction of columns from 3 to 2
– Understanding the Standard (US) – information that
supports mathematics content knowledge
– Essential Knowledge and Skills (EKS) – information that
provides expectations for student learning
• Indicators of SOL sub-bullet added to each bullet
within the Essential Knowledge and Skills
6
7. Support for Teachers
• Significant additions to the Understanding the
Standard column including
– Definitions
– Explanations
– Examples
– Instructional connections
• Improvements in precision, clarity, and consistency
in language K-12
7
8.
9. Overview of Changes in Grade 1
2009 2016
Strand # of Standards # of Standards Strand
Number and
Number Sense
3 5 Number and
Number Sense
Computation and
Estimation
3 2 Computation and
Estimation
Measurement
5
4
Measurement and
Geometry
Geometry
2
Probability and
Statistics
2 1 Probability and
Statistics
Patterns, Functions,
and Algebra
3 3 Patterns, Functions,
and Algebra
Total
18 15 Total
9
10. Mathematics Process Goals for Students
Mathematical
Understanding
Problem Solving
Connections
Communication
Representations
Reasoning
10
“The content of the mathematics standards is intended
to support the five process goals for students”
- 2009 and 2016 Mathematics Standards of Learning
11. Standards of Learning Curriculum Frameworks
Introduction includes:
• Mathematical Process Goals for Students
• Instructional Technology
• Computational Fluency
• Algebra Readiness
• Equity
11
15. 2009 SOL 2016 SOL
1.1 The student will
a) count from 0 to 100 and write the corresponding
numerals; and
b) group a collection of up to 100 objects into tens
and ones and write the corresponding numeral
to develop an understanding of place value.
[Moved to 1.2a]
1.2 The student will count forward by ones, twos,
fives, and tens to 100 and backward by ones
from 30. [Moved to 1.1c, d]
1.1 The student will
a) count forward orally by ones to 110, starting at
any number between 0 and 110 [Moved from
1.2];
b) write the numerals 0 to 110 in sequence and
out-of-sequence;
c) count backward orally by ones when given any
number between 1 and 30; [Moved from 1.2]
and
d) count forward orally by ones, twos, fives, and
tens to determine the total number of objects
to 110. [Moved from 1.2]
Revisions:
• 1.1a – Counting forward orally increased from 100 to 110
• 1.1b – Write numerals in sequence and out-of-sequence
• 1.1c – Counting backward orally by ones when given any number between 1 and 30
• 1.1d – Skip count as strategy for determining total number of objects up to 110
16. 2009 SOL 2016 SOL
1.2 The student, given up to 110 objects, will
a) group a collection into tens and ones and write
the corresponding numeral; [Moved from 1.1b]
b) compare two numbers between 0 and 110
represented pictorially or with concrete objects,
using the words greater than, less than or equal
to; and
c) order three or fewer sets from least to greatest
and greatest to least.
Revisions:
• 1.2b – Compare two numbers between 0 and 110 represented pictorially or with objects
using the words greater than, less than or equal to
• 1.2c – Order three or fewer sets (of up to 110 objects) from least to greatest and greatest to
least
17. 2009 SOL 2016 SOL
1.3 The student, given an ordered set of ten objects
and/or pictures, will indicate the ordinal
position of each object, first through tenth.
[Moved from K.3]
Revisions:
• New – Ordinal numbers first through tenth moved from K.3
18. 2009 SOL 2016 SOL
1.3 The student will identify the parts of a set and/or
region that represent fractions for halves, thirds,
and fourths and write the fractions.
1.4 The student will
a) represent and solve practical problems involving
equal sharing with two or four sharers; and
b) represent and name fractions for halves and
fourths, using models.
Revisions:
• Greater emphasis on conceptual understanding of fractions through practical problems
involving equal sharing with two or four sharers (halves and fourths)
19. 2009 SOL 2016 SOL
1.4 The student, given a familiar problem situation
involving magnitude, will
a) select a reasonable order of magnitude from
three given quantities: a one-digit numeral, a
two-digit numeral, and a three-digit numeral
(e.g., 5, 50, 500); and
b) explain the reasonableness of the choice.
[Moved from Computation and Estimation Strand to
Number and Number Sense Strand]
1.5 The student, given a familiar problem situation
involving magnitude, will
a) select a reasonable order of magnitude from
three given quantities: a one-digit numeral, a
two-digit numeral, and a three-digit numeral
(e.g., 5, 50, 500); and
b) explain the reasonableness of the choice.
Revisions:
• Moved from Computation and Estimation Strand 1.4
21. 2009 SOL 2016 SOL
1.5 The student will recall basic addition facts with
sums to 18 or less and the corresponding
subtraction facts. [Moved to 1.7b; fluency for 11
to 18 included in 2.5b]
Revisions:
• Fluency for addition and subtraction to 10 moved to 1.7b
• Fluency for addition and subtraction for 11-18 already included in 2.5b
22. 2009 SOL 2016 SOL
1.6 The student will create and solve one-step story
and picture problems using basic addition facts
with sums to 18 or less and the corresponding
subtraction facts.
1.6 The student will create and solve single-step
story and picture problems using addition and
subtraction within 20.
Revisions:
• Create and solve single-step story and picture problems using addition and subtraction
increased from 18 to 20
• New EKS – Combine parts contained in larger numbers up to 20 by using related
combinations (e.g., 9 + 7 can be thought of as 9 broken up into 2 and 7; using doubles 7 + 7 =
14; 14 + 2 = 16 or 7 broken up into 1 and 6; making a ten 1 + 9 = 10; 10 + 6 = 16)
• New EKS – Explain strategies used to solve addition and subtraction problems within 20
using spoken words, objects, pictorial models, and number sentences
• Problem Type Chart – Included in the Understanding the Standard Section of Curriculum
Framework
23. 2009 SOL 2016 SOL
1.7 The student will
a) recognize and describe with fluency part-whole
relationships for numbers up to 10; and
b) demonstrate fluency with addition and
subtraction within 10. [Moved from 1.5]
Revisions:
• 1.7a – Recognize and describe with fluency part-whole relationships for numbers up to 10
• 1.7a EKS – Recognize and describe with fluency part-whole relationships for numbers up to
10 in a variety of configurations
• 1.7b – Demonstrate fluency for addition and subtraction limited to within 10 [Moved from
1.5]
• Fluency for addition and subtraction for 11-18 already included in 2.5b
25. 2009 SOL 2016 SOL
1.7 The student will
a) identify the number of pennies equivalent to a
nickel, a dime, and a quarter; [Included in K.7]
and
b) determine the value of a collection of pennies,
nickels, and dimes whose total value is 100 cents
or less.
1.8 The student will determine the value of a
collection of like coins (pennies, nickels, or
dimes) whose total value is 100 cents or less.
Revisions:
• Identifying equivalencies has been deleted [Included in K.7]
• Determining the value of a collection of coins has been limited to a collection of like coins
(pennies, nickels, or dimes)
• New EKS – Group a collection of pennies by fives and tens as a way to determine the value of
the collection limited to 100 cents or less
26. 2009 SOL 2016 SOL
1.8 The student will tell time to the half-hour, using
analog and digital clocks.
1.9 The student will investigate the passage of time
and
a) tell time to the hour and half-hour, using analog
and digital clocks; and
b) read and interpret a calendar. [Moved from
1.11]
Revisions:
• Tell time to the hour moved from K.9
• Read and interpret a calendar [Moved from 1.11]
• New EKS – Identify different types of clocks (analog and digital) as instruments to measure
time [Moved from K.8]
• New EKS – Determine the days/dates before and after a given day/date (e.g., today is the
30th, so yesterday must have been the ?)
27. 2009 SOL 2016 SOL
1.9 The student will use nonstandard units to
measure length, weight/mass, and volume.
1.10 The student will compare, using the concepts of
more, less, and equivalent,
a) the volumes of two given containers; and
b) the weight/mass of two objects, using a
balance scale.
[Compare combined with new 1.10]
1.10 The student will use nonstandard units to
measure and compare length, weight, and
volume.
Revisions:
• 1.9 and 1.10 – Measure and compare length, weight, and volume combined
28. 2009 SOL 2016 SOL
1.11 The student will use calendar language
appropriately (e.g., names of the months,
today, yesterday, next week, last week).
[Moved to K.8 and 1.9b]
Revisions:
• Names of the months moved to K.8 and 1.9b
29. 2009 SOL 2016 SOL
1.12 The student will identify and trace, describe,
and sort plane geometric figures (triangle,
square, rectangle, and circle) according to
number of sides, vertices, and right angles.
[Moved to 1.11a]
1.13 The student will construct, model, and describe
objects in the environment as geometric
shapes (triangle, rectangle, square, and circle)
and explain the reasonableness of each choice.
[Moved to 1.11b]
1.11 The student will
a) identify, trace, describe, and sort plane figures
(triangles, squares, rectangles, and circles)
according to number of sides, vertices, and
angles; and
b) identify and describe representations of circles,
squares, rectangles, and triangles in different
environments, regardless of orientation, and
explain reasoning. [Moved from 1.13]
Revisions:
• 1.12 and 1.13 combined to form new 1.11
31. 2009 SOL 2016 SOL
1.14 The student will investigate, identify, and
describe various forms of data collection (e.g.,
recording daily temperature, lunch count,
attendance, favorite ice cream) [Examples
moved to 1.12 US], using tables, picture graphs,
and object graphs. [Moved to 1.12a]
1.15 The student will interpret information
displayed in a picture or object graph, using the
vocabulary more, less, fewer, greater than, less
than, and equal to. [Moved to 1.12b]
1.12 The student will
a) collect, organize, and represent various forms of
data using tables, picture graphs, and object
graphs; and
b) read and interpret data displayed in tables,
picture graphs, and object graphs, using the
vocabulary more, less, fewer, greater than, less
than, and equal to. [Moved from 1.15]
Revisions:
• 1.14 and 1.15 combined to form new 1.12
33. 2009 SOL 2016 SOL
1.16 The student will sort and classify concrete
objects according to one or more attributes,
including color, size, shape, and thickness.
[Attributes included in EKS]
1.13 The student will sort and classify concrete
objects according to one or two attributes.
Revisions:
• Limited to no more than two attributes
• New EKS – Label attributes of a set of objects that has been sorted
• New EKS – Name multiple ways to sort a set of objects
34. 2009 SOL 2016 SOL
1.17 The student will recognize, describe, extend,
and create a wide variety of growing and
repeating patterns.
1.14 The student will identify, describe, extend,
create, and transfer growing and repeating
patterns. [Transfer included to match EKS]
Revisions:
• Transfer added to SOL – content was already included in 2009 EKS
35. 2009 SOL 2016 SOL
1.18 The student will demonstrate an understanding
of equality through the use of the equal sign.
1.15 The student will demonstrate an understanding
of equality through the use of the equal symbol.
Revisions:
• 1.15 EKS – Identify equivalent values and represent equalities through the use of objects,
words and the equal symbol
• 1.15 EKS – Identify and describe expressions that are not equal (using words)
Welcome to the Grade 1 overview of revisions to the Mathematics Standards of Learning from 2009 to 2016.
It would be helpful to have a copy of the Grade 1 – Crosswalk (Summary of Revisions) and a copy of the 2016 Grade 1 Curriculum Framework to reference during this presentation.
The purpose of this presentation is to provide an overview of the revisions and to highlight information included in the Essential Knowledge and Skills and Understanding the Standards sections of the Curriculum Framework. This presentation serves as a brief overview and is not a comprehensive list of all the revisions. The Curriculum Framework should be referenced for additional information regarding the 2016 standards.
The implementation timeline will be shared followed by a brief overview of the Crosswalk and Curriculum Frameworks, and lastly a side by side comparison, by strand, of the 2009 standards to the new 2016 (two thousand sixteen) standards.
During the (two thousand sixteen/two thousand seventeen) 2016-2017 school year – school divisions should begin incorporating the new standards into local curricula to be taught during the 2017-2018 school year.
During the Crossover Year 2017 and 2018 both the 2009 and 2016 standards should be taught. The Spring 2018 assessments will measure the 2009 standards and include field test items measuring the 2016 standards.
Full implementation of the 2016 standards will occur in the 2018-2019 school year.
The revisions focus on improving vertical progression of the content, ensuring developmental appropriateness, increasing support for teachers (including definitions, explanations, examples, and instructional connections), clarifying expectations both for teaching and for student learning, improving precision and consistency in mathematical vocabulary and format, and to better ensuring computational fluency at the elementary level.
The Curriculum Framework will have a somewhat different look for K-8. The reduction in the number of columns from 3 to 2 was made in order to provide consistency in format to other disciplines and consistency within mathematics K-12. The Understanding the Standard column has information that supports mathematical content knowledge and provides background information for teachers. The Essential Knowledge and Skills column provides the expectations for learning and assessment.
Corresponding EKS bullets and SOL bullets are indicated with the same letter. An example will be provided on the next slide.
Teachers are encouraged to read both the Essential Knowledge and Skills and the Understanding the Standard columns.
Additional support for teachers was added to the Understanding the Standard column in the Curriculum Frameworks to include definitions, explanations, as well as many examples and some instructional connections. These edits result in better precision, greater clarity, and consistency in language across K-12.
This is a page from the Grade One Curriculum Framework. It is very important that teachers spend time exploring the new Curriculum Frameworks. Here you see underlined examples of definitions and explanations.
In some standards, examples have also been included such as the number frames and dot cards shown here.
In addition, following each EKS bullet a letter has been added to show which SOL indicator this bullet most closely corresponds with. During any given lesson, multiple EKS bullets may be represented.
There was an overall reduction in the number of standards from 285 to 259 in K-12; specifically in Grade One there was a reduction from 18 to 15 standards. This is a result of -- consolidation of related concepts and skills; a reduction of repetition, an improvement in the developmental progression, and/or deletion of content.
The changes occurring in Grade One will be addressed in greater detail later in this presentation. Note that the strands of measurement and geometry have been combined and now represent one strand titled “measurement and geometry.”
In the next several slides, we will take a quick look at changes to the Curriculum Framework document.
It is important to note that the mathematical process goals for students continue to be emphasized throughout the 2016 standards. The content of the mathematics standards is intended to support the following five goals for students: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations.
Four additional sections have been included in the introduction to the 2016 Curriculum Framework -- Instructional Technology, Computational Fluency, Algebra Readiness, and Equity.
The content of each section addresses the impact on students’ learning and instruction. We encourage educators to review these sections of the introduction.
This is a snapshot of the Grade 1 Crosswalk and Summary of Revisions page one. There are four quadrants – additions, deletions, parameter changes or clarifications, and moves within the standards.
The upper left quadrant represents the additions, the standards referenced are the 2016 numbers and include additions to the EKS as well as the standard. Moves from other grade levels are indicated within brackets.
The upper right quadrant identifies deletions from the 2009 standards and indicates where that content was moved.
The bottom left quadrant indicates parameter changes (for example 1.1a– counting forward has been increased to 110 as well as the addition of starting at any number between 0 and 110). In the bottom right quadrant, moves within a grade level are indicated with the first number being the 2009 SOL number and the number in the brackets representing the 2016 number.
On page 2 and the remaining pages of the crosswalk, a side by side comparison of the 2009 and 2016 standards can be found. There was an attempt to keep the standards in numerical order for both columns. When deleted content was moved or already found in another grade, it is indicated in brackets.
See the examples shown on the screen. Empty boxes on the right indicate that the 2009 content has either been deleted or removed.
Empty boxes on the left typically indicate that the 2016 standard is new to that grade level. For example, 1.7a is new to grade one while 1.7b was moved from 1.5.
We’ll now dig deeper into the crosswalk and Curriculum Framework by taking a look at the Number and Number Sense strand.
SOL 1.1a and 1.2 have been combined to form the new 1.1.
Counting in SOL1.1a has been clarified as ‘oral counting’ and has been increased from 100 to 110. In addition, students should be able to count forward starting at any number between 0 and 110.
Additional parameters have been included for SOL1.1b, 1.1c, and 1.1d. In SOL1.1b students are now expected to write numerals from 0 to 110 in sequence and out-of-sequence. In SOL1.1c students will now count backward orally by ones when given any number between 1 and 30. Lastly, in SOL1.1d, students will skip count as a strategy for determining the total number of objects limited to 110.
The new SOL 1.2a was moved from 1.1b.
1.2b and c – Comparing and ordering numbers is new to grade one.
Students will compare two numbers between 0-110 represented pictorially or with concrete objects, using the words greater than, less than, or equal to.
When ordering numbers the number of sets will be limited to no more than three, with each set containing up to 110 objects.
SOL1.3 was moved from K.3 and is new to grade one.
Students, when given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth.
Please refer to the Curriculum Framework for additional information.
SOL 1.3 is now SOL 1.4.
In the 2016 standards, greater emphasis has been placed on the development of conceptual understanding of fractions through representing and solving practical problems that involve equal sharing with two or four sharers. Young children intuitively understand equal sharing problems based on their experiences sharing objects with siblings or friends. While students should use the terms halves and fourths they are not be expected to use fraction notation at this level.
Additional information, including examples of problems, can be found in the Understanding the Standard section of the Framework.
SOL 1.4 is now SOL 1.5.
This standard was moved from the 2009 Computation and Estimation Strand to the 2016 Number and Number Sense Strand.
We will now take a look at the Computation and Estimation Strand.
The content of SOL 1.5 - fluency with addition and subtraction within 10 has moved to 1.7b. Fluency with addition and subtraction between 11 and 18 has been removed from grade one; however, remains in grade two.
Several edits have been made to SOL 1.6.
The parameters for creating and solving single-step story and picture problems involving addition and subtraction have been increased from 18 to 20.
Several new EKS bullets have been added to SOL 1.6:
1. Students will combine parts contained in larger numbers by using related combinations. For example, when adding 9 + 7 a student might break up 7 into 1 and 6, add the 1 to the 9 to get 10 and then add 6 to equal 16. Another new EKS bullet reads
2. Students will explain strategies used to solve addition and subtraction problems within 20 using spoken words, objects, pictorial models, and number sentences.
Additional information, including a chart containing problems types, can be found in the Understanding the Standard section of the Curriculum Framework.
SOL 1.7a - recognize and describe with fluency part-whole relationships for numbers up to 10 is NEW content for grade one. The Essential Knowledge and Skills bullet states that students will recognize and describe part-whole relationships for numbers up to 10 in a variety of configurations.
SOL 1.7b - demonstrate fluency for addition and subtraction is now limited to within 10. This content was moved from the 2009 SOL 1.5; note that fluency with addition and subtraction for 11-18 has been removed from grade one but remains in grade two.
Additional information and examples of part-whole relationships and understandings, including examples of appropriate models can be found in the Understanding the Standards section of the Curriculum Framework.
We will now take a look at the Measurement and Geometry strand.
SOL 1.7a - identifying the number of pennies equivalent to a nickel, dime, and quarter was already included in K.7 and has therefore been removed from grade one.
SOL 1.7b is now SOL 1.8 with edits. Determining the value of a collection of coins has been limited to a collection of like coins (pennies, nickels, or dimes).
A new EKS bullet for this standard states that students will group a collection of pennies by fives and tens as a way to determine the value of the collection limited to 100 cents or less.
SOL 1.8 is now SOL 1.9a
Telling time to the hour was removed from Kindergarten and is now included in SOL 1.9a.
In addition, a new EKS bullet was moved from K.8 which reads that students in grade one will identify different types of clocks, both analog and digital, as instruments to measure time.
SOL1.9b Reading and interpreting a calendar was moved from SOL1.11. As part of this standard, students will read a calendar to locate a given day or date. Students will also determine the day or date before and after a given day or date. For example, if today is the 30th, yesterday must have been the 29th.
SOL 1.9 and SOL 1.10 have been combined to form the new SOL 1.10.
Note: Students at this age have often struggle to understand the difference between weight and mass; therefore, the term weight will be used at this level.
The content from 1.11 has been moved to K.8 and 1.9b
SOL 1.12 and SOL 1.13 have been combined to form the new SOL 1.11.
We will now take a look at the Probability and Statistics strand.
SOL 1.14 and SOL 1.15 have been combined to form the new SOL 1.12.
Let’s take a look at the Patterns, Functions and Algebra strand.
SOL 1.16 is now SOL 1.13.
Students will now sort and classify objects using no more than two attributes. Kindergarten is limited to sorting and classifying using one attribute. The attributes formerly listed within this standard are now included in the EKS bullets.
Two new EKS bullets have been added which state that students will:
label attributes of a set of objects that has been sorted; and
name multiple ways to sort a set of objects.
SOL 1.17 is now SOL 1.14.
Transferring a pattern from one form to another was part of the EKS bullets for 2009. This has now been added to 2016 standard.
SOL 1.18 is now SOL 1.15.
Revisions made to the Essential Knowledge and Skills include:
Students will identify equivalent values and represent equalities through the use of objects, words and the equal symbol; and
Students will identify and describe expressions that are not equal (using words not symbols). For instance, 4 minus 3 is not equal to 3 + 5.
This concludes the presentation on the 2016 Grade 1 Mathematics Standards of Learning revisions. You are encouraged to refer to the Curriculum Frameworks where additional information can be found.
Should you have any questions, feel free to contact a member of the Mathematics Team at Mathematics@doe.virginia.gov.
