Intended Learning Outcomes

The main intent of mathematics instruction is for students to value and use mathematics and reasoning skills to investigate and understand the world.

The Intended Learning Outcomes (ILOs) describe the skills and attitudes students should learn as a result of mathematics instruction. They are an essential part of the Mathematics Core Curriculum and provide teachers with a standard for evaluation of student learning in mathematics. Significant mathematics understanding occurs when teachers incorporate ILOs in planning mathematics instruction.

By the end of sixth grade students will be able to:

1. Demonstrate a positive learning attitude toward mathematics.

a.       Display a sense of curiosity about numbers and patterns.

b.       Pose mathematical questions about objects, events, and processes.

c.        Demonstrate persistence in completing tasks.

d.       Apply prior knowledge and processes to construct new knowledge.

e.       Maintain an open and questioning mind toward new ideas and alternative points of view.

2. Become mathematical problem solvers.

a.       Determine the approach, materials, and strategies to be used in setting up a problem.

b.       Model problem situations in a variety of ways.

c.        Develop understanding of new mathematical concepts and vocabulary by answering questions such as: What made you think that? Did anyone think of this in a different way? Where have we seen a problem like this before?

d.       Construct and use concrete, pictorial, symbolic, and graphical models to represent problem situations.

e.       Know when to select and how to use grade-appropriate mathematical tools and methods as a natural and routine part of the problem-solving process.

f.         Build new mathematical knowledge through problem solving.

g.       Solve problems in both mathematical and everyday contexts.

h.       Recognize that there may be multiple ways to solve a problem.

i.         Persevere in developing alternative problem-solving strategies if initially selected approaches do not work.

3. Reason mathematically.

a.       Draw logical conclusions and make generalizations.

b.       Determine the approach, materials, and strategies to be used in solving problems.

c.        Use models, known facts, and relationships to explain reasoning.

d.       Make precise calculations and check the validity of the results in the context of the problem.

e.       Make conjectures based on observation and information and test mathematical conjectures and arguments.

f.         Follow and construct logical arguments and judge their validity.

g.       Analyze mathematical situations by recognizing and using patterns and relationships.

h.       Justify answers and solution processes.

4. Communicate mathematically.

a.       Represent mathematical ideas with objects, pictures, and symbols.

b.       Express mathematical ideas to peers, teachers, and others through oral and written language.

c.        Engage in mathematical discussions through brainstorming, asking questions, and sharing strategies for solving problems.

d.       Explain mathematical work and justify reasoning and conclusions.

e.       Analyze, evaluate, and explain mathematical arguments and conclusions presented by others.

5. Make mathematical connections.

a.       Use one mathematical idea to extend understanding of another.

b.       Recognize the role of mathematics in the classroom, school, and community.

c.        Explore problems and describe and confirm results using various representations.

d.       Recognize the connections between mathematics and other content areas and apply mathematical thinking and problem solving in those areas.

6. Represent mathematical situations.

a.       Create and use representations to organize and communicate mathematical ideas.

Represent mathematical concepts using concrete, pictorial, and symbolic models.