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• Number Sense
• Algebra and Functions
• Measurement and Geometry
• Statistics, Data Analysis and Probability
• Mathematical Reasoning

Mathematical Reasoning

SCOPE AND SEQUENCE
MATHEMATICAL REASONING X = TEACH   /    M = REINFORCE & MAINTAIN
PROBLEM SOLVING PROCESS	K	1	2	3	4	5	6
SET UP/APPROACH PROBLEM
Determine strategy	X	X	X	X	X	X	X
Determine materials	X	X	X	X	X	X	X
Model problem	X	X	X	X	X	X	X
Analyze problem
Relationships				X	X	X	X
relevant/irrelevant information		X	X	X	X	X	X
sequencing/prioritizing				X	X	X	X
Patterns		X	X	X	X	X	X
Determine when to break into simpler parts				X	X	X	X
Formulate conjectures based on problem							X
SOLVE PROBLEM
Use concrete objects	X	X	X	X	X	X	X
Use pictorial representation	X	X	X	X	X	X	X
Make calculations	X	X	X	X	X	X	X
Use results of simpler problem				X	X	X	X
Use mathematical notation/terms/clear language				X	X	X	X
Estimate solution graphically							X
EXPLAIN/JUSTIFY REASONING OR SOLUTION
Explain reasoning with concrete objects	X	X	X	X	X	X	X
Explain reasoning with pictorial representations	X	X	X	X	X	X	X
Explain reasoning using a variety of methods				X	X	X	X
Defend reasoning		X	X	X	X	X	X
Check solution based on context	X	X	X	X	X	X	X
Justify procedure used		X	X	X	X	X	X
Use estimation to check			X	X	X	X	X
Defend solutions verbally and symbolically				X	X	X	X
Exact vs. estimated answers				X	X	X	X
GENERALIZE
Between problems		X	X	X	X	X	X
Apply solution to similar problem				X	X	X	X
State/apply generalizations				X	X	X	X
Evaluate reasonableness in context of problem				X	X	X	X
PROBLEM SOLVING STRATEGIES/SKILLS	K	1	2	3	4	5	6
HEURISTIC		X	X	X	X	X	X
STRATEGIES
Use logical reasoning	X	X	X	X	X	X	X
Predict and test				X	X	X	X
Make a table or graph	X	X	X	X	X	X	X
Find a pattern	X	X	X	X	X	X	X
Draw a picture or diagram	X	X	X	X	X	X	X
Write a number sentence		X	X	X
Work backward				X	X	X	X
Break a problem into simpler parts/solve a simpler problem			X	X	X	X
Make a model or act it out	X	X	X	X	X	X	X
Write an equation					X	X	X
Make an organized list			X	X	X	X	X
Choose a strategy		X	X	X	X	X	X
SKILLS
Identify relationships			X	X	X	X	X
Estimate or exact answer	X	X	X	X	X	X	X
Sequence events			X	X	M	M	M
Too much/too little information		X	X	X	X	X	X
Multistep problems		X	X	X	X	X	X
Choose the operation			X	X	X	X	X
Draw conclusions		X	X	X	X	X	X
Interpret the remainder				X	X	X	X
Use a graph	X	X	X	X	X	X	X
Make generalizations				X	X	X	X
Sequence information				X	X	X	X
Evaluate reasonableness of answers		X	X	X	X	X	X
Use a table		X	X	M	M	M	M
Use a formula						X	X
Make decisions						X	X
Sequence and prioritize information						X	X
Relevant or irrelevant information						X	X
APPLICATIONS
Number Sense	X	X	X	X	X	X	X
Algebra and Functions	X	X	X	X	X	X	X
Measurement and Geometry	X	X	X	X	X	X	X
Statistics, Data Analysis, and Probability	X	X	X	X	X	X	X
CRITICAL THINKING AND LOGICAL REASONING
Classify and sort	X	X	X	X	X	X	X
Identify, extend, and use patterns	X	X	X	X	X	X	X
Order and sequence	X	X	X	X	X	X	X
Make generalizations		X	X	X	X	X	X
Compare and contrast	X	X	X	X	X	X	X
Draw conclusions		X	X	X	X	X	X
Use logical reasoning	X	X	X	X	X	X	X
Make and test predictions	X	X	X	X	X	X	X
Explain and justify answers	X	X	X	X	X	X	X
Evaluate evidence and conclusions				X	X	X	X
Interpret charts, tables, and graphs	X	X	X	X	X	X	X
Check reasonableness of results	X	X	X	X	X	X	X
VISUAL THINKING AND LOGICAL REASONING
Spatial relationships	X	X	X	X	X	X	X
Visual patterns	X	X	X	X	X	X	X
Use visual representations to solve problems	X	X	X	X	X	X	X
DECISION MAKING
Decide when to estimate				X	X	X	X
Decide on a computation method				X	X	X	X
Decide whether answer is reasonable	X	X	X	X	X	X	X
Choose from options or alternatives	X	X	X	X	X	X	X
CREATIVE THINKING
Solve nonroutine problems		X	X	X	X	X	X
Generate problems	X	X	X	X	X	X	X
Choose alternative ways to solve problems		X	X	X	X	X	X
PROCESSES
COMMUNICATION
Drawing	X	X	X	X	X	X	X
Writing		X	X	X	X	X	X
Talking	X	X	X	X	X	X	X
CONNECTIONS
Mathematical	X	X	X	X	X	X	X
Cross-curricular	X	X	X	X	X	X	X
Everyday	X	X	X	X	X	X	X
MULTIPLE REPRESENTATIONS
Different manipulatives	X	X	X	X	X	X	X
Different models	X	X	X	X	X	X	X
Manipulatives and models	X	X	X	X	X	X	X
Manipulatives, words, and symbols	X	X	X	X	X	X	X
Models, words, and symbols	X	X	X	X	X	X	X
TOOLS
Calculator		X	X	X	X	X	X
Software	X	X	X	X	X	X	X
Manipulatives	X	X	X	X	X	X	X
Measuring tools	X	X	X	X	X	X	X
Ruler		X	X	X	X	X	X
Protractor					X	X	X
Compass					X	X	X

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