Mathematical Reasoning and Number Sense

GOAL: SORT AND CLASSIFY OBJECTS OR PICTURES OF OBJECTS

GOAL: DUPLICATE AND CONTINUE LINEAR PATTERNS 

GOAL: PERCEIVE AND RECOGNIZE SHAPES AND SIZES

GOAL: USE SIMPLE MEASUREMENT SKILLS AND SERIATE OBJECTS

GOAL: QUANTIFY GROUPS OF OBJECTS

GOAL: COMPARE WRITTEN NUMERALS 

GOAL: DEVELOP AN UNDERSTANDING OF ADDITION AND SUBTRACTION  

GOAL: IDENTIFY MONEY

Identify pairs of objects as the same or different, with different pairs varying in gross details.

Identify pair of objects or pictures as the same or different, with different pairs increasingly similar, varying only in one or more minor detail(s) and with images becoming more abstract and symbolic.

Given a sample object/picture and verbal description of the selection criteria, sort objects/ pictures according to a single criterion: Sort objects by color.

Classify by color.

Given a sample object/picture and verbal description of the selection criteria, sort objects/ pictures according to a single criterion: Sort objects by shape.

Classify by shape.

Given a sample object/picture and verbal description of the selection criteria, sort objects/ pictures according to a single criterion: Sort by size (small-medium-large).

Given a sample object/picture and verbal description of the selection criteria, sort objects/ pictures according to a single criterion: Sort by function.

Indicate whether an object belongs to a given collection. 

Classify by size.

Classify by function. 

Classify by other conceptual categories

Verbally label the single common attribute or characteristic of a group of objects or pictures.

Verbally label the difference or criteria used for classification of several groups of objects or pictures.

Select an object or picture according to a description that includes two properties.

Use the criteria along the horizontal and vertical axes of a double entry table to complete the interior squares of the table.

Duplicate a pattern of six to ten objects in which one property is alternated.

Match objects arranged in a pattern with corresponding pattern card.

Continue a complex, two-color pattern of objects represented by a pattern card.

Continue a given pattern of five objects, represented by actual objects or a pattern card, in which one property is alternated (color, size, shape).

Represent on paper “in written form” an alternat- ing pattern of one property or a two-color pattern.

Create and verbally describe a pattern of concrete objects.

Complete puzzles of at least ten interlocking pieces.

Complete puzzles of at least 18 interlocking pieces.

Match rectangular, square, circular, and triangular shapes to outlines of the same configuration and size.

Given a collection of assorted shapes, sort and name the circles.

Given a collection of assorted shapes, classify and name the circles, rectangles and triangles.

Find examples of circles or rectangles in everyday objects.

Divide one item into approximately equal pieces for two people.

Compare pairs of objects: length (long-short).

Compare pairs of objects: height (tall-short).

Compare pairs of objects: large-small, thick-thin, wide-narrow.

Compare pairs of objects: volume (full-empty).

Compare pairs of objects: mass (heavy-light).

Compare pairs of objects: temperature (hot-cold).

Use an arbitrary tool of measurement to compare the length and height of objects, using comparative vocabulary (longer-taller-shorter).

Use a straight edge to compare the length and height of objects, using comparative vocabulary (longer-taller-shorter).

Seriate at least three items by length, height or size in ascending or descending order, using comparative vocabulary (longest-shortest, tallest-shortest, largest-smallest).

Recite the number sequence, 1–4.

Recite the number sequence, 1–10.

Compare two groups of no more than four objects per group and use quantitative vocabulary to describe the groups (more than, less than, the same as).

Compare two groups of no more than six objects per group and use quantitative vocabulary to describe the groups (more than, less than, same as).

Demonstrate one-to-one correspondence with concrete objects, up to four objects.

Demonstrate one-to-one correspondence with concrete objects, up to six objects.

Construct a collection of objects so that it has the same number of objects as another group, up to four objects.

Construct a collection of objects so that it has the same number of objects as another group.

Count groups of objects with up to four items per group.

Count groups of objects with up to six items per group.

Given an oral number, create a group with the correct number of objects, up to four objects in a group.

Given an oral number, create a group with the correct number of objects, up to six objects.

Name the quantity/amount for one to four items.

Match numerals 1–4 with corresponding quantities.

Name the quantity/amount for one to six items

Write numerals 1–6.

Arrange or write the numbers 1–6 in sequential order.

Identify ordinal position for first and last.

Play a simple game that involves moving one’s marker the number of spaces shown on a single die.

Organize and read quantitative data in simple bar graphs.

Compare sets pairs of numerals, 1–4, to deter mine more and less or greater than and less than.

Compare pairs of numerals, 1–6, to determine more and less or greater than and less than.

Illustrate the concept of “put together” and Critical Skill “take away” with sets of one to four objects, with four items being the maximum in any set. 

Illustrate the concept of “put together” and Critical Skill “take away” with sets of one to six objects, with six objects being the maximum in any set.

Label the action of “put together” as adding and “take away” as subtraction.

Add or subtract problems represented by numerals, 1–4, 4 being the largest numeral, using objects or pictures as needed. 

Identify and count up to four pennies.

Identify and count up to six pennies.

Identify a one-dollar bill.

Identify a quarter.

Indicate that one dollar bill has more value than a penny or quarter.