September 12, 2011

This is a list of the Capacities for Imaginative Learning.

- Education > General
- Education > Teaching Techniques/Best Practices

- Grade 1
- Grade 2
- Grade 3
- Grade 4
- Grade 5
- K
- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10
- Grade 11
- Grade 12

Explore, examine, and make observations about a social problem or mathematical situation

Interpret information correctly, identify the problem, and generate possible solutions

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 or using the calendar to teach counting)

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 problems

Explain to others how a problem was solved, giving strategies and justifications

Understand that mathematical statements can be true or false

Recognize that mathematical ideas need to be supported by evidence

Investigate the use of knowledgeable guessing as a mathematical tool

Explore guesses, using a variety of objects and manipulatives

Justify general claims, using manipulatives

Develop and explain an argument verbally or with objects

Listen to and discuss claims other students make

Use trial and error strategies to verify claims

Understand how to organize their thought processes with teacher guidance

Verbally support their reasoning and answer

Share mathematical ideas through the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations

Listen to solutions shared by other students

Formulate mathematically relevant questions

Use appropriate mathematical terms, vocabulary, and language

Recognize the connections of patterns in their everyday experiences to mathematical ideas

Understand the connections between numbers and the quantities they represent

Compare the similarities and differences of mathematical ideas

Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas

Understand meanings of operations and how they relate to one another

Understand how mathematical models represent quantitative relationships

Recognize the presence of mathematics in their daily lives

Recognize and apply mathematics to solve problems

Recognize and apply mathematics to objects, pictures, and symbols

Use multiple representations including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations

Share mental images of mathematical ideas and understandings

Use standard and nonstandard representations

Connect mathematical representations with problem solving

Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)

Use mathematics to show and understand social phenomena (e.g., count and represent sharing cookies between friends)

Use mathematics to show and understand mathematical phenomena (e.g., draw pictures to show a story problem, show number value using fingers on your hand)

Count the items in a collection and know the last counting word tells how many items are in the collection (1 to 100)

Count out (produce) a collection of a specified size (10 to 100 items), using groups of ten

Quickly see and label with a number, collections of 1 to 10

Count by 1's to 100

Skip count by 10's to 100

Skip count by 5's to 50

Skip count by 2's to 20

Verbally count from a number other than one by 1's

Count backwards from 20 by 1's

Draw pictures or other informal symbols to represent a spoken number up to 20

Identify that spacing of the same number of objects does not affect the quantity (conservation)

Arrange objects in size order (increasing and decreasing)

Write numbers to 100

Read the number words one, two, three...ten

Explore and use place value

Compare and order whole numbers up to 100

10 ones = 1 ten

10 tens = 1 hundred

Use a variety of strategies to compose and decompose one-digit numbers

Understand the commutative property of addition

Name the number before and the number after a given number, and name the number(s) between two given numbers up to 100 (with and without the use of a number line or a hundreds chart)

Use before, after, or between to order numbers to 100 (with or without the use of a number line)

Use the words higher, lower, greater, and less to compare two numbers

Use and understand verbal ordinal terms, first to twentieth

Develop and use strategies to solve addition and subtraction word problems

Represent addition and subtraction word problems and their solutions as number sentences

Create problem situations that represent a given number sentence

Use a variety of strategies to solve addition and subtraction problems with one- and two-digit numbers without regrouping

Demonstrate fluency and apply addition and subtraction facts to and including 10

Understand that different parts can be added to get the same whole

Estimate the number in a collection to 50 and then compare by counting the actual items in the collection

Determine and discuss patterns in arithmetic (what comes next in a repeating pattern, using numbers or objects)

Match shapes and parts of shapes to justify congruency

Recognize, name, describe, create, sort, and compare two-dimensional and three-dimensional shapes

Experiment with slides, flips, and turns of two-dimensional shapes

Identify symmetry in two-dimensional shapes

Recognize geometric shapes and structures in the environment

Recognize length as an attribute that can be measured

Use non-standard units (including finger lengths, paper clips, students' feet and paces) to measure both vertical and horizontal lengths

Informally explore the standard unit of measure, inch

Know vocabulary and recognize coins (penny, nickel, dime, quarter)

Recognize the cent notation as ¢

Use different combinations of coins to make money amounts up to 25 cents

Recognize specific times (morning, noon, afternoon, evening)

Tell time to the hour, using both digital and analog clocks

Know the days of the week and months of the year in sequence

Classify months and connect to seasons and other events

Select and use non-standard units to estimate measurements

Pose questions about themselves and their surroundings

Collect and record data related to a question

Display data in simple pictographs for quantities up to 20 with units of one

Display data in bar graphs using concrete objects with intervals of one

Use Venn diagrams to sort and describe data

Interpret data in terms of the words: most, least, greater than, less than, or equal to

Answer simple questions related to data displayed in pictographs (e.g., category with most, how many more in a category compared to another, how many all together in two categories)

Discuss conclusions and make predictions in terms of the words likely and unlikely

Construct a question that can be answered by using information from a graph