MSAD #55

Mathematics

Benchmarks/Performance Indicators

Math Skills

Grade 3

11-06

 

Number Sense

 

A.           Students will understand and demonstrate a sense of what numbers mean and how they are used.  Students will be able to:

 

1.                     Read, compare, order, classify, and explain whole numbers up to one thousand.

 

q        a.     Read and write numbers up to one thousand.

q        b.    Compare and order numbers up to one thousand (greater than, less than, equal to).

q        c.     Classify odd and even numbers.

q        d.    Explain the (place) value of given digits in a number up to 1,000.

 

 

2.             Read, compare, order, classify, and explain simple fractions through tenths.

 

q        a.     explain that fractional parts must be equal.

q        b.     read conventional fraction words, notation (1/2s, 1/3s, 1/6s)

q        c.     compare and orders halves, thirds, and sixths, and compares halves, fourths and eighths

 

 

3.             Demonstrate knowledge of the meaning of fractions, decimals, and integers, and an understanding of how they may be used.

 

q        a.     relate notation for common fractions with notations for decimals on the calculator.

q        b.     connect fractions to division.

q        c.     identify the values of coins and find the values of collections of coins to learn about decimals. 

 

Computation

                 

B.           Students will understand and demonstrate computation skills.  Students will be able to:

 

1.             Solve multi-step, real-life problems using the four operations with whole numbers up to 1,000.

 

2.             Solve real-life problems involving addition and subtraction of simple fractions.

 

q        a.     add and subtract fractions with like denominators.

 

 

3.       Demonstrate and explain the problem-solving process using appropriate tools and technology and defend the reasonableness of results.

 

q        a.     develop flexibility in solving problems by finding several ways to reach a solution.

q        b.     explore materials including the calculator to be used throughout the curriculum as tools for solving problems.

q        c.     use a variety of manipulatives to do problem solving and to explain the strategies used.

 

 

4.             Develop proficiency with the facts and algorithms of the four operations on whole numbers using mental math and a variety of materials, strategies, and technologies.

 

q        a.     skip count to represent multiples of the same number.

q        b.     use mental computation strategies to find an answer.

q        c.     multiply by 0, 1, 2, 5, 9, 10, 11.

q        d.   develop automaticity with facts and algorithms with addition and subtraction in whole numbers up to 1,000.

 

 

Data Analysis and Statistics

 

C.           Students will understand and apply concepts of data analysis.  Students will be able to:

 

1.             Make generalizations and draw conclusions using various types of graphs, charts, and tables.

 

2.             Read and interpret displays of data.

 

q        a.     organize and present data in tables and line plots, tally charts, bar graphs.

q        b.     collect, record, and graph data.

q        c.     describe and interpret data identifying least frequent, reading, using and comparing values.

 

Probability

 

D.           Students will understand and apply concepts of probability.  Students will be able to:

 

1.             Explain the concept of chance in prediction outcomes.

 

q        a.     identify fair and unfair games based on probability.

q        b.     describe events as likely, equally likely, and unlikely based on probability.

 

 

2.             Estimate probability from a sample of observed outcomes and simulations.

 

q        a.     predict expected outcomes.

q        b.     justify  predictions.

 

Geometry

 

E.           Students will understand and apply concepts from geometry.

 

1.                     Describe, model, and classify shapes and figures (triangles, rectangles, squares, using number of sides and angles or corners).

2.             Experiment  with shapes and figures to make generalizations regarding congruency, symmetry, and similarity.

3.             Use transformations such as slides, flips, and rotations.

 

q        a.     find patterns for covering a space.

q        b.     describe physical positions as a series of slide, flips, and turns.

q        c.     compare shapes to determine congruence through motions such as rotations (turns) and reflections( flips).

 

4.             Use the properties of shape and figures to describe the physical world.

 

Measurement

 

F.            Students will understand and demonstrate measurement skills.  Students will be able to:

 

1.              Solve and justify solutions to real-life problems involving the measurement of time, length, area, perimeter, weight, temperature, time, capacity, and volume.

 

q        a.     measure time, length, temperature, the ruler to an inch and whole cent.

q        b.     use standard measures (US standard or metric) to gather data about size and mass    

q        c.     measure the area of various objects.

 

 

2.             Select measuring tools and units of measurement both customary and metric that are appropriate for what is being measured.

 

q        a.     develop familiarity with inches, feet, and yards.

q        b.     develop awareness of centimeters and meters.

 

 

Patterns, Relationships, Functions

 

G.           Students will understand that mathematics is the science of pattern, relationships, and functions.  Students will be able to:

 

1.             Use the patterns of numbers, geometry, and a variety of graphs to solve a problem.

 

q        a.     become familiar with number patterns on the 100s chart and determine the next term or missing terms in patterns with numbers or shapes.

q        b.     use and identify geometric patterns to solve problems.

 

 

2.             Use variable and open sentences to express relationships.

 

q        a.     translate real life situations into addition and subtraction sentences.

 

Algebra Concepts

 

H.           Students will understand and apply algebraic concepts.  Students will be able to:

 

1.             Develop and evaluate simple formulas in problem-solving contexts.

 

q        a.     identify patterns in a number sequence and write any missing numbers.

q        b.     describe skip counting patterns.

q        c.     explore algebra by using manipulatives.

 

 

2.             Find replacements for variables that make simple number sentences true.

                                   

 

Discrete Mathematics

 

I.             Students will understand and apply concepts in discrete mathematics.  Students will be able to:

 

1.             Create and use organized lists, tree diagrams, Venn diagrams, and networks to generate possible outcomes and to solve problems.

 

 

Mathematical Reasoning

 

J.            The student will understand and apply concepts of mathematical reasoning. The students will:

 

1.             Generate alternative explanations to explain mathematical events.

 

q        a.     explore multiple ways to solve a problem.

 

 

2.             Understand that support for a claim should come from evidence of from observation and experimentation.

 

q        a.     use evidence to support a claim/answer. (i.e., show problem solving strategies).

 

 

Mathematical Communication

 

K.           Students will reflect upon and clarify their understanding of mathematical ideas and relationships.  The student will:

 

1.             Use simple tables and graphs to communicate ideas and information in presentations in a concise and clear manner. 

 

q        a.     construct graphs using various given data.

q        b.     construct tables using various given data.

q        c.     present information from his/her graph/table