Standard 4: Mathematical Connections

In grades K-4, the study of mathematics should include opportunities to make connections so that students can:

• Link conceptual and procedural knowledge
 
Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
State the purpose of each step in a calculation.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Make sketches to aid in explaining procedures or ideas.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Write instructions that others can follow in carrying out a procedure.

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget).
 

• Relate various representations of concepts or procedures to one another
 
Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
Numbers can be written in different forms depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed.
 
• Recognize relationships among different topics in mathematics

Benchmarks 12E (Habits of Mind: Critical-Response Skills)
Grades K-2, page 268
One way to describe something is to say how it is like something else.

Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 3-5, page 27
Mathematical ideas can be represented concretely, graphically, and symbolically.

Benchmarks 11C (Common Themes: Constancy and Change)
Grades 3-5, page 273
Some features of things may stay the same even when other features change. Some patterns look the same when they are shifted over, or turned, or reflected or seen form different directions.
 

• Use mathematics in other curriculum areas

Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Different models can be used to represent the same thing. What kind of model to use and how complex it should be depends on its purpose. The usefulness of a model may be limited if it is too simple or if it is needlessly complicated. Choosing a useful model is one of the instances in which intuition and creativity come into play in science, mathematics, and engineering.
 

• Use mathematics in their daily lives

Benchmarks 11D (Common Themes: Scale)
Grades K-2, page 277
Things in nature and things people make have very different sizes, weights, ages, and speeds.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Use whole numbers and simple, everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences.

Benchmarks 11B (Common Themes: Models)
Grades 3-5, page 268
Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.