GRADE 1

EALR 1: The student understands and applies concepts and procedures of mathematics.

Number and numeration

1.1.1        Understand different representations of whole numbers.

·   Represent a number to at least 100 in different ways (e.g., numerals, pictures, words, physical models) and translate from one representation to another. [CU]

·   Group and regroup objects into 1's and 10's.

·   Count sets of objects less than 100 using a variety of grouping strategies.

1.1.2 Understand sequential relationships among whole numbers.

·   Order three or more numbers to at least 100 from smallest to largest. [RL]

·   Use comparative language (e.g., less than, more than, equal to) to compare numbers to at least 100. [CU]

·   Skip count by 2, 5, and 10.

·   Count forward and backward, from a given number that is less than 100.

Computation

1.1.5 Understand the meaning of subtraction.

·   Express stories involving subtraction (e.g., separate) with models, pictures, and symbols. [CU, MC]

·   Show relationships between addition and subtraction using physical models, diagrams, and acting out problems. [CU]

1.1.6 Understand and apply procedures for addition of whole numbers with fluency.

·   Use strategies (e.g., count on, count back, doubles) for addition to at least sums to 12. [SP, RL]

·   Recall addition facts through at least sums to 12.

·   Solve problems involving addition using procedures and explaining those procedures. [SP, RL, CU]

1.1.7 Understand and apply strategies and appropriate tools for adding with whole numbers.

·   Use strategies and appropriate tools from among mental math, paper and pencil, manipulatives, or calculator to compute in a problem situation. [SP, RL]

·   Use counting strategies to combine whole numbers with sums under 12. [SP, RL]

Estimation

1.1.8 Understand and apply estimation strategies to determine the reasonableness of answers.

·   Use a known quantity (e.g., chunking) to make reasonable estimates. [RL]

·   Use numbers that are easy to add or subtract to make a reasonable estimate of a sum (e.g., 9 + 8 should be about 20, since 9 is about 10, 8 is about 10, and 10 + 10 is 20). [RL]

Attributes, units, and systems

1.2.1 Understand and apply attributes to describe and compare objects.

·   Order three or more objects according to an attribute (e.g., pencil lengths, students’ hand span, and thickness of books). [RL]

·   Read a clock with only the hour hand and use approximate language (e.g., almost 7, a little after 7). [CU]

·   Identify coins (penny, nickel, dime, quarter) and state their value. [CU]

Procedures, precision, and estimation

1.2.4 Understand and apply procedures to measure with non-standard or standard units.

·   Select units appropriate to the object being measured (e.g., measure length of classroom with footprints, not beans) and explain why it was selected. [CU]

·   Use a uniform unit to measure an object (e.g., cubes, paper strips, ruler).

·   Measure a variety of objects using appropriate non-standard tools (e.g., arm length, hand width, lengths of rope).

·   Use a variety of records of time (e.g., calendar, seasonal plants, animal migrations, moon phases, tides, shadows).

·   Use physical models of measuring units to fill, cover, match, or make the desired comparison of the attribute with the unit. [SP, RL]

·   Explain the need for appropriate tools for measurement. [CU]

Properties and relationships

1.3.2 Understand how to compare figures based on their characteristics.

·   Describe two-dimensional figures based on their characteristics (e.g., number of sides, number of equal sides). [CU]

·   Identify, compare, and sort two-dimensional figures in their surroundings (e.g., by lengths of sides, general shape). [RL, MC]

·   Describe figures using accurate terminology (e.g., square, rectangle, triangle).

Locations and transformations

1.3.3 Understand the locations of numbers on a positive number line.

·   Indicate whether a number is above or below a benchmark number (e.g., greater than or less than 100).

·   Describe the location of a given number between 1 and 100 on a number line. [CU]

·   Identify a point up to 100 on a positive number line.

Statistics

1.4.3 Understand how data can be organized and displayed.

·   Display results of data collection by making student-invented and conventional displays. [CU]

·   Construct bar graphs with physical materials and record pictorially (e.g., shoes, cats, crops, egg rolls, tacos). [CU]

·   Collect data related to questions and organize the data into useful categories in familiar situations (e.g., how many students like apples? How many students do NOT like apples?).

1.4.5 Understand how a display provides information.

·   Answer questions about bar graphs or pictographs (e.g., how many dancers, plants, canoes, pets?). [CU]

Patterns, functions, and other relations

1.5.1 Understand the concept of patterns.

·   Create and describe a variety of repeating patterns using sounds, objects, and symbols. [CU]

·   Describe and extend a repeating pattern (e.g., ABAC, ABAC; snap, clap, snap, stomp). [CU]

·   Identify the unit in a repeating pattern (e.g., in A-A-B-A-A-B the unit is A-A-B). [RL]

·   Identify and describe numerical patterns in the 100’s chart. [CU, RL]

·   Identify geometric patterns in art, textiles, and ceramics.

Symbols and representations

1.5.3 Understand the meaning of symbols and labels used to represent equality in situations.

·   Demonstrate equality by recording number sentences with balance using the “=” symbol (e.g., 9 = 4 + 5, 4 + 5 = 2 + 7, 9 = 9). [CU]

·   Complete open sentences showing equalities (e.g., 5 = ____).

·   Explain, using pictures or words, the meaning of equality. [CU]

·   Give an example of equality in real life (e.g., on the first turn, Juan scored 4 points, on the second turn, he scored 5 points. On the first turn, Ivana scored 2 points, on the second turn, she scored 7 points. After two turns, they are tied with the same number of points). [MC]

EALR 2: The student uses mathematics to define and solve problems.

Example: A classroom is presenting a play and everyone has invited two guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

2.1.1 Understand how to define a problem in a familiar situation with teacher guidance.

·   State information presented in a teacher-led discussion to determine if there is a problem (e.g., a classroom is having a play and each student invited two guests. Chairs are needed for the guests. There are some chairs available in the classroom).

·   State the problem in own words (e.g., there aren’t enough chairs for the guests. How many more chairs do we need?).

·   Generate questions that would need to be answered in order to solve the problem (e.g., how many guests are attending?  How many more chairs do we need?).

·   Identify known and unknown information with teacher guidance (e.g., known ─ number of students, number of guests invited, number of chairs in classroom; unknown ─ number of guests attending, number of chairs needed). [1.1.5]

2.2.1 Understand how to create a plan to solve a problem with teacher guidance.

·   Gather and organize categorical data (e.g., in a teacher-guided activity, create a two-column chart ─ one column for student names and the other to record the number of guests attending the play). [1.4.3]

2.2.2 Apply mathematical tools to solve the problem with teacher guidance. 

·   Use strategies (chart to count, skip count, cluster, or physical models). [1.1.1, 1.1.5]

·   Use appropriate tools from among mental math, paper and pencil, manipulatives, or calculator (e.g., to determine the total number of guests attending and the total number of chairs needed for the class play). [1.1.7]

·   Recognize when an approach is unproductive and try a new approach.

EALR 3: The student uses mathematical reasoning.

Example: A classroom is presenting a play and everyone has invited two guests. Enough chairs are needed to seat all the guests. There are some chairs in the classroom.

3.1.1 Understand how to compare information presented in familiar situations.

·   Restate understanding of the situation (e.g., each guest attending the play will require a chair; there are not enough in the classroom).

3.2.1 Understand how to make a reasonable prediction based on prior knowledge and the information given in a familiar situation.

·  Predict a numerical solution for a problem (e.g., predict how many more chairs will be needed).

·  Use known information to make a reasonable prediction (e.g., if two numbers are each less than 10, the sum will be less than 20).

·  Make an inference based on information provided (e.g., the boys in class did a better job convincing their guests to attend because there are more guests coming for the boys than the girls).

3.2.2 Understand how to draw conclusions based on prior knowledge and the information given in a familiar situation.

·   Draw conclusions from displays using comparative language (e.g., more students have two guests coming, or fewer students have only one guest coming) and provide examples from displays to support conclusions.

3.2.3 Analyze procedures used to solve problems in familiar situations with teacher guidance.

·   Justify the importance of counting in a situation rather than making a guess at a number of items for a specific purpose (e.g., counting the number of chairs needed for the play rather than guessing).

3.3.1 Understand how to justify results using evidence.

·   Check reasonableness of results by using pictures, physical models, or acting it out (e.g., students raise one hand for one guest attending and two hands if two guests are attending).

3.3.2 Understand how to validate thinking about numerical, measurement, geometric, or statistical ideas by using models, known facts, patterns, or relationships.

·   Explain why a strategy or tool was used in solving a problem (e.g., why a two-column chart was helpful to gather the information needed about the number of guests attending the play).

EALR 4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.1.1 Understand how to develop and follow a simple plan for collecting information for a given purpose.

·        Determine what information is needed and how to collect it for a given purpose (e.g., to help explain something, to find out if something is needed) and who the information is for (e.g., for the classroom, for the adults at home, for the librarian).

·         Develop and follow a plan to gather data about an event (e.g., how many students will attend the Saturday Movie Afternoon at school?).

4.1.2 Understand how to extract information for a given purpose from one or two different sources.

·        Follow simple written directions for creating an art project using a model (e.g., requiring cutting and folding geometric shapes).

·        Generate questions that could be answered using informational text (e.g., TV ads, books, menus, cereal boxes).

4.2.1 Understand how to organize information to communicate to a given audience with teacher guidance.

·  Organize and display data on a chart to communicate solution for the given audience (e.g., use a two- or three-column chart to display the number of guests per student attending a class play and, if there is a chair for each guest, inform the custodian as to how many more chairs are needed). 

·  Display results of data collection by making student-invented and conventional displays (e.g., hair color, eye color, teeth missing).

4.2.2 Understand how to communicate or represent ideas or information using mathematical language or notation.

·       Explain or represent ideas using mathematical language from:

• Number sense (e.g., numbers to at least 100) [1.1.1];
• Measurement (e.g., order three or more objects according to an attribute and identify the chosen attribute) [1.2.1];
• Geometric sense (e.g., name and describe two-dimensional figures based on their characteristics) [1.3.1];
• Statistics (e.g., construct bar graphs with physical materials) [1.4.3];
• Algebraic sense (e.g., explain the meaning of equality). [1.5.3]

EALR 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1.1 Understand how to use concepts and procedures from any two of the content components from EALR 1 in a given problem or situation.

·  Interpret results and draw conclusions from student-made displays using comparative language (e.g., more, fewer). [1.4.4, 3.2.2]

·  Measure objects using non-standard tools and place resulting numbers in order from shortest (smallest) to longest (largest). [1.2.3, 1.1.2]

5.1.2 Understand how to recognize and create equivalent mathematical models and representations in familiar situations.

·  Identify different representations of a number to at least 100 (e.g., numerals, pictures, physical models). [1.1.1]

·  Express stories involving subtraction (e.g., separate) with models, pictures, and symbols. [1.1.5]

5.2.1 Apply and analyze the use of mathematical patterns and ideas in familiar situations in other disciplines.

·  Use the characteristics of two-dimensional shapes in art projects and recognize the use of geometric shapes in artwork.

·  Use a clock to determine when it is time for recess or lunch time.

·  Explain how math is used whenever we use money for a purchase.

5.2.2 Know the contributions of individuals and cultures to the development of mathematics.

·  Recognize the contributions of women, men,, and people from different cultures (e.g., look at symbols used for numbering in the Mayan culture).

5.3.1 Understand how mathematics is used in everyday life.

·   Generate examples of mathematics in everyday life:

o       counting (e.g., the pennies in the penny jar);

o       comparing measurements (e.g., standing up against the mark on the wall to check for growth);

o       building things (e.g., a snowman with three spheres, a dog house made of a box with a triangular roof);

o       playing games (e.g., when counting spaces on a board or knowing money is needed)

·   Describe familiar two-dimensional shapes based on their geometric characteristics (e.g., sharp corners, sides of different lengths).

·   Identify and sort two-dimensional shapes in their surroundings.

·   Skip count by 5s or 10s (e.g., with nickels or dimes).