10.Concept Map

https://youtu.be/dnjbwJdcPj 

Standards for Mathematical Practice

4th Grade Standards

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up:

adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

1.Make sense of problems and persevere in solving them.

Word Problems

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.

2.Reason abstractly and quantitatively

Words to Numbers, Numbers to Words

Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Mathematically proficient students make sense of quantities and their relationships in problem situations

3.Construct viable arguments and critique the reasoning of others.

Word Problems

Mathematically proficient students are also able to compare the effectiveness of two plausible arguments distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

4.Model with mathematics.

Diagrams

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.  In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community.

Make sense of problems and persevere in solving them.

5.Use appropriate tools strategically

Shapes, Diagrams, Figures

These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Mathematically proficient students consider the available tools when solving a mathematical problem.