Problem SolvingView Resources
Students will build new mathematical knowledge through problem solving.
Explore, examine, and make observations about a social problem or mathematical situation
Interpret information correctly, identify the problem, and generate possible solutions
Students will solve problems that arise in mathematics and in other contexts.
Act out or model with manipulatives activities involving mathematical content from literature and/or story telling
Formulate problems and solutions from everyday situations (e.g., counting the number of children in the class, using the calendar to teach counting).
Students will apply and adapt a variety of appropriate strategies to solve problems.View Resources
Use informal counting strategies to find solutions
Experience teacher-directed questioning process to understand problems
Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking
Use manipulatives (e.g., tiles, blocks) to model the action in problems
Use drawings/pictures to model the action in problemsView Resources
Students will monitor and reflect on the process of mathematical problem solving.
Explain to others how a problem was solved, giving strategies
Reasoning and Proof
Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
Understand that mathematical statements can be true or false
Students will make and investigate mathematical conjectures.
Investigate the use of knowledgeable guessing as a mathematical tool
Explore guesses, using a variety of objects and manipulatives
Students will develop and evaluate mathematical arguments and proofs.
Listen to claims other students make
Students will organize and consolidate their mathematical thinking through communication.
Understand how to organize their thought processes with teacher guidance
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Share mathematical ideas through the manipulation of objects, drawings, pictures, and verbal explanations
Students will analyze and evaluate the mathematical thinking and strategies of others.
Listen to solutions shared by other students
Formulate mathematically relevant questions with teacher guidance
Students will use the language of mathematics to express mathematical ideas precisely.
Use appropriate mathematical terms, vocabulary, and language
Students will recognize and apply mathematics in contexts outside of mathematics.
Recognize the presence of mathematics in their daily lives
Use counting strategies to solve problems in their daily lives
Recognize and apply mathematics to objects and pictures
Students will create and use representations to organize, record, and communicate mathematical ideas.
Use multiple representations, including verbal language, acting out or modeling a situation, and drawing pictures as representations
Use standard and nonstandard representations
Students will use representations to model and interpret physical, social, and mathematical phenomena.
Use objects to show and understand physical phenomena (e.g., guess the number of cookies in a package)
Use objects to show and understand social phenomena (e.g., count and represent sharing cookies between friends)
Use objects to show and understand mathematical phenomena (e.g., draw pictures to show a story problem, show number value using fingers on your hand)
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.View Resources
Numerically label a data set of 1 to 5
Verbally count by 1’s to 20
Verbally count backwards from 10View Resources
Represent collections with a finger pattern up to 10
Draw pictures or other informal symbols to represent a spoken number up to 10
Draw pictures or other informal symbols to represent how many in a collection up to 10View Resources
Visually determine how many more or less, and then using the verbal counting sequence, match and count 1-10
Use and understand verbal ordinal terms, first to tenthView Resources
Students will understand meanings of operations and procedures, and how they relate to one another.View Resources
Students will recognize, use, and represent algebraically patterns, relations, and functions.View Resources
Use a variety of manipulatives to create patterns using attributes of color, size, or shapeView Resources
Students will apply transformations and symmetry to analyze problem solving situations.View Resources
Students will apply coordinate geometry to analyze problem solving situations.View Resources
Students will determine what can be measured and how, using appropriate methods and formulas.View Resources
Units of MeasurementView Resources
Name, discuss, and compare attributes of length (longer than, shorter than)View Resources
Compare the length of two objects by representing each length with string or a paper strip
Relate specific times such as morning, noon, afternoon, and evening to activities and absence or presence of daylight
Help to make simple pictographs for quantities up to 10, where one picture represents 1View Resources
Represent data using manipulativesView Resources