Number and Operations Grade 1

K-12 Enduring Understanding 1: Relationships among numbers and number systems form the foundations of number sense and

mathematics communication.

Systems Discipline Level Concept: Relationships

Essential Standard Grade Band K-2:

Develop the ability to deal with numbers mentally and to use number sense to reason with numbers in complex ways

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary

All students will:

Develop an

understanding of the

relative position and

magnitude of whole

numbers to at least 200

Connect number words

and numerals to the

quantities they represent,

using various physical

models and

representations.

Count with

understanding and

recognize "how many"

in sets of objects of at

least 100, using grouping

strategies, particularly

twos, fives and tens.

Use multiple models to

develop the

understanding that a

written number is a

representation of groups

of tens and ones.

Understand that a

fraction represents a part

of a whole.

Understand that

fractional parts are equal

shares of a whole.

Knowledge/Comprehension Level:

Give students set of objects 16, 33, 67, and 98. Ask students to count the objects

and write the corresponding number.

Application/Analysis Level:

Synthesis/Evaluation Level:

set

number

ones

twos

fives

tens

forward

backward

skip count

half

third

fourth

SOL:

Number and Operations Grade 1

K-12 Enduring Understanding 1: Relationships among numbers and number systems form the foundations of number sense and

mathematics communication.

Systems Discipline Level Concept: Relationships

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.

1.2 The student will count forward by ones, twos, fives, and tens to 100, and backward by ones from 30.

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.

Number and Operations Grade 1 Mathematics Enduring Understanding 8: Patterns and relationships among operations are essential to making estimates and computing fluently.

Change and Interactions Discipline Level Concept: Patterns

Essential Standard Grade Band K-2: Understand the meaning of, and relationship between addition and subtraction to compute fluently

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Model joining and

separating situations (word problems) including missing addend, part unknown, and separate unknown, using a variety of models including objects, length based models, and number lines.

Compose and decompose single digit numbers using various models (dot cards, five and ten frames, counters) with particular attention to the number ten.

Understand the basic number combinations for addition and how they are related to subtraction facts.

Understand the magnitude (size) of whole numbers and use this knowledge to estimate quantities that result from joining and separating situations.

Develop strategies for adding and subtracting whole numbers (to 20)

Knowledge/Comprehension Level: Give the students the number sentence 2 + 3 = 5. Ask the students to write

down the other number sentences in the fact family. Application/Analysis Level:

When I subtract two numbers the answer is 6. One number is 9. What is the other number?

Synthesis/Evaluation Level:

A soccer player scored 9 points in two games. What might her scores in each of the games be?

fact family

addition

joining

combining

subtraction

minus

take away

separating

magnitude

digit

Number and Operations Grade 1 Mathematics Enduring Understanding 8: Patterns and relationships among operations are essential to making estimates and computing fluently.

Change and Interactions Discipline Level Concept: Patterns

on the basis of their earlier work with small numbers (counting on, plus 1, plus 2, doubles, doubles plus 1, make 10).

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.

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 2: Spatial relationships can be described using coordinate geometry and other representational systems.

Systems Discipline Level Concept: Relationships

Essential Standard Grade Band K-2: Describe, name, and interpret relative positions, directions, and distances in space

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand that the

proximity of objects in space can be described in order to gain essential navigations skills.

Understand that objects

maintain their shape regardless of their orientation.

Knowledge/Comprehension Level: Direct students to indicate a position as you say it. For example, tell

students to put their hands above their head, to put knees under the desk, and to stand next to the sink.

near

far

close

by

below

above

up

down

beside

next to

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 2: Spatial relationships can be described using coordinate geometry and other representational systems.

Systems Discipline Level Concept: Relationships

Application/Analysis Level: Have students draw an illustration to match each sentence in

“Where’s Bear?”

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 2: Spatial relationships can be described using coordinate geometry and other representational systems.

Systems Discipline Level Concept: Relationships

Synthesis/Evaluation Level: Students create their own “proximity” book with the related

vocabulary in sentences and create illustrations to match.

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 3: Attributes of objects can be measured using processes and quantified units, and using appropriate techniques, tools, and formulas.

Systems Discipline Level Concept: Quantifying Representation

Essential Standard Grade Band K-2: Understanding attributes of measurement by directly comparing objects, and selecting an appropriate unit and tools

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand that objects

can be ordered by measurable attributes, including length, weight/mass, volume, value, time and temperature.

Understand that there are tools that measure specific attributes.

Understand how to measure using non-standard and standard units.

Knowledge/Comprehension Level: Tell students to place six teddy bears on one side of a balance scale

and four unifix cubes on the other side. Ask students to compare the weights of the unfix cubes and teddy bears by answering the question:

heavier than The teddy bears are lighter than the cubes. the same as

Application/Analysis Level: Using the balance scale: How many teddy bears will equal the same

weight as eight unifix cubes? Synthesis/Evaluation Level Determine what object in our room will weigh less than eight unifix

cubes. Test your theory on the balance scale to prove that your prediction is correct.

penny

nickel

dime

quarter

value

analog clock

digital clock

minute hand

hour hand

half hour

length

weight

nonstandard units

volume

compare

greater than

less than

balance scale

lighter

heavier

the same

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 3: Attributes of objects can be measured using processes and quantified units, and using appropriate techniques, tools, and formulas.

Systems Discipline Level Concept: Quantifying Representation

compare

SOL: 1.7 The student will: a) identify the number of pennies equivalent to a nickel, a dime, and a quarter; 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 tell time to the half hour, using an analog or digital clock. 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.

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 11: Analyze characteristics and properties of 2- and 3-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Communication Discipline Level Concept: Reasoning and Justification

Essential Standard Grade Band K-2: Represent and compare 2- and 3- dimensional shapes through drawings, block construction, dramatizations, and words

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Recognize, name, build,

draw, compare, and sort 2D shapes.

Describe attributes and parts of 2D shapes.

Investigate and predict the results of putting together and taking apart 2D shapes.

Knowledge/Comprehension Level: Give students a sheet with a triangle, square, rectangle, and circle on

it. Tell students to: color all circles red or color all triangles blue. Application/Analysis Level: (Attachment 11,1) Cut out the shape cards and sort them into two or more groups. Glue them on to a piece of paper. Label each group. Synthesis/Evaluation Level: Assessment Task:

Build a structure using 3 or 4 Geoblocks. Draw what you made. Rubric:

Advanced Student accurately creates a 2-D representation of the 3-D shapes used in block structure

Proficient Student attempts to show size and thickness in representation

Student is able to describe characteristics of the Geoblocks

Near Proficient Student uses 3 or 4 blocks Student represents each block in the structure by

drawing only 1 face of that block (2-D) Student effectively shows how many blocks are

arranged Needs Improvement Student uses incorrect number of blocks

Student does not distinguish individual block (may draw outline of whole construction)

Student is unable to show how blocks are arranged

triangle

square

rectangle

circle

side

corner

square corner

two-dimensional

three-dimensional

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..

Supporting SOL: 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.

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 11: Analyze characteristics and properties of 2- and 3-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Communication Discipline Level Concept: Reasoning and Justification

Geometry and Measurement Strand Grade 1 Mathematics Enduring Understanding 12: Transformations, symmetry, and spatial reasoning can be used to analyze and model mathematical situations.

Communication Discipline Level Concept: Reasoning and Justification

Essential Standard Grade Band K-2: Develop an understanding of transformations and symmetry with shapes

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Recognize, name, build,

draw, compare, and sort 2D shapes.

Knowledge/Comprehension Level: Ask students to identify real life 2-dimensional shapes that are shown. (ex.: a picture of a clock- circle, television- square, yield sign- triangle, door- rectangle) Application/Analysis Level: Ask students to choose a real life object in the classroom that has the shape of a triangle, square, rectangle, or circle and draw it on a piece of paper. Synthesis/Evaluation Level: Ask students to create a shape that is symmetric and design a way to cut it out of a folded piece of folded paper.

triangle

square

rectangle

circle

side

corner

square corner

symmetry

rotate

two-dimensional

three-dimensional

SOL: 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.

Supporting 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..

Data Analysis and Probability Grade 1 Mathematics Enduring Understanding 5: Mathematical models are used to predict and make inferences about data.

Properties and Models Discipline Level Concept: Models

Essential Standard Grade Band K-2: Discuss events related to student experiences by conducting surveys and reading graphs of student information

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand that they can

gather data about themselves and their surrounding in order to answer questions.

Understand that the data gathered and analyzed from observations and surveys can have an impact on our everyday lives.

Understand that picture graphs, object graphs, and bar graphs can be used to answer questions.

Understand that interpretation of the data could lead to additional questions to be investigated.

Knowledge/Comprehension level Show students a bar/picture graph. Have students answer questions about the data (which has more, fewer, most, how many more). Application /Analysis level Students conduct a survey of their classmates’ favorite foods and create a simple graph to display the data. Synthesis/Analysis level Students make an observation about their data, draw a conclusion about why their observation occurs, and make a recommendation to the cafeteria based on the results (i.e. Most students like pizza because it tastes great, so the cafeteria should serve pizza more often.).

more less fewer greater than less than equal to

SOL: 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.

Data Analysis and Probability Strand Grade 1 Mathematics Enduring Understanding 6: Data can be collected, organized, and displayed in purposeful ways.

Properties and Models Discipline Level Concept: Analysis and Evaluation

Essential Standard Grade Band K-2: Pose questions, gather, and use various methods to represent data about themselves and their surroundings

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand that data can

be collected and presented in an organized manner.

Understand that data can be represented using pictures, tables, and picture/object graphs.

Knowledge/Comprehension level After graphing the lunch count, attendance, or other representative data, ask student to indicate the number for each category. Example: How many students voted for pizza? How many students voted for chicken nuggets? Application /Evaluation level A class of first grade students did a survey of what they like to eat for lunch. Make a representation of the survey results.

Class Lunch Survey A Class of first grade students did a survey of what they like to eat for lunch. There were 25 students present the day they took the survey.

Make a representation of these survey results.

data vote survey tally marks

Data Analysis and Probability Strand Grade 1 Mathematics Enduring Understanding 6: Data can be collected, organized, and displayed in purposeful ways.

Properties and Models Discipline Level Concept: Analysis and Evaluation

Synthesis/Analysis level Make a class graph that represent these criteria:

1. Three ice cream flavors. 2. Chocolate is the favorite flavor. 3. Vanilla is the least favorite flavor.

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), using tables, picture graphs, and object graphs.

Data Analysis and Probability Grade 1 Mathematics Enduring Understanding 7: Various statistical methods can be used to observe, analyze, predict, and make inferences about data.

Properties and Models Discipline Level Concept; Analysis and Evaluation

Essential Standard grade band K-2: Describe parts of the data and a set of data to determine what the data show

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary Analyze and interpret data

and make inferences such as comparing the frequency of events (most, least, more, fewer).

The data gathered and analyzed from observations and surveys can have an impact on our everyday lives.

Knowledge/Comprehension level Show students a bar/picture graph. Have students answer questions about the data (which has more, fewer, most, how many more). Application /Analysis level Students conduct a survey of their classmates’ favorite foods and create a simple graph to display the data. Synthesis/Analysis level Students make an observation about their data, draw a conclusion about why their observation occurs, and make a recommendation to the cafeteria based on the results (i.e. Most students like pizza because it tastes great, so the cafeteria should serve pizza more often.).

data objects representation graph more fewer most least survey pictorial graph compare table collect observation

Data Analysis and Probability Grade 1 Mathematics Enduring Understanding 7: Various statistical methods can be used to observe, analyze, predict, and make inferences about data.

Properties and Models Discipline Level Concept; Analysis and Evaluation

Supporting 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), using tables, picture graphs, and object graphs.

Data Analysis and Probability Grade 1 Mathematics Enduring Understanding 13: Probability and data analysis can be used to make predictions.

Communication Discipline Level Concept: Theory

Essential Standard Grade Band K-2: Discuss events as likely or unlikely

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand the likelihood

of an event can be described in varying degrees (impossible, unlikely, equally likely, more likely, and certain).

Understand that

experiments with spinners, two-colored counters, dice, tiles, and coins are dictated by chance.

Knowledge/Comprehension level Students will describe what happens when you drop five two-colored counters. Application /Analysis level Students will drop an even number of two-colored counters and describe the results. Ask students, “Are you likely to see the same results if you repeat this activity?” Have students repeat the activity, and describe the results. Synthesis/Analysis level Students will use a multicolored spinner to investigate the chances of spinning one color compared to another. Ask “Which color are you most likely to spin?” and “Which color are you least likely to spin?” Have students spin the spinner 5 times and record the results.

unlikely equally likely more likely certain chance experiment two-colored counters spinner

Patterns and Algebra Grade 1Mathematics Enduring Understanding 4: Situations and structures can be represented, modeled and analyzed using algebraic symbols.

Properties and Models Discipline Level Concept: Models

Essential Standard Grade Band K-2: Illustrate and model general principles and properties of operations

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Model simple joining

and separating situations with objects.

Knowledge/Comprehension Level: Have the students draw a picture to go with the following problem:

Bill had 4 apples his mom gave him 2 more. How many does he have in all? Application/Analysis Level:

Have the student write a number sentence to go with the problem Synthesis/Evaluation Level:

Have the student create and solve a story problem

Addition

Sum

Joining

Subtraction

Minus

Difference

Supporting 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.

Patterns and Algebra Strand Grade 1 Mathematics Enduring Understanding 9: Patterns, relations, and functions can be recognized and understood mathematically.

Change and Interactions Discipline Level Concept: Patterns

Essential Standard Grade Band K-2: Recognize, describe, and extend patterns: and sort and classify objects

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Understand that the

same set of objects can be sorted and classified in different ways.

Identify, duplicate, describe, create, and extend simple patterns, numeric patterns and sequential patterns.

Knowledge/Comprehension Level: Draw what comes next.

Application/Analysis Level Materials Needed: Pattern Blocks and Attribute Blocks Ask the student to make a pattern and describe it using color, shape or thickness then have them clap or make noise to describe the pattern. Synthesis/Evaluation Level

Show the students this diagram from appendix 4. Some people say this is a pattern.

Do you think so? Ask them to defend why or why not they think this design is a pattern.

Sort

Attributes

Extend

Describe

Repeat

Color

Size

Shape

Thickness

Patterns and Algebra Strand Grade 1 Mathematics Enduring Understanding 9: Patterns, relations, and functions can be recognized and understood mathematically.

Change and Interactions Discipline Level Concept: Patterns

1.16 The student will sort and classify concrete objects according to one or more attributes, including color, size, shape, and thickness. 1.17 The student will recognize, describe, extend, and create a wide variety of growing and repeating patterns. 1.18 The student will demonstrate an understanding of equality through the use of the equal sign.

Patterns and Algebra Grade 1 Mathematics Enduring Understanding 10: Change, in various contexts, both quantitative and qualitative, can be identified and analyzed.

Change and Interactions Discipline Level Concept: Cause and Effect

Essential Standard Grade Band K-2: Describe change both qualitatively and quantitatively

Performance Indicators Assessment Samples – SOL/Blooms Vocabulary All students will: Identify, duplicate,

describe, create, and extend simple patterns, numeric patterns and sequential patterns.

Describe patterns in skip counting and use those patterns to predict the next number or numbers in the skip counting sequence (forward and backward).

Knowledge/Comprehension Level: Continue the pattern 2, 4, 6,___, ____,____ Application/Analysis Level: Extend the pattern 15, 14, 13, _____,_____,______ Synthesis/Evaluation Level: Say, “If you walked by a classroom and heard the children say 25, 30, 35, what do you think you would hear next?”

Skip count

Calculator

Pattern

Twos

Fives

Tens

Forward

Backwards

Analyze

Supporting SOL: 1.3 The student will count forward by ones, fives, and tens to 100, by twos to 20, and backward by ones from 30. 1.17 The student will recognize, describe, extend, and create a wide variety of growing and repeating patterns.