At UCDS we purposely choose the
forms of assessment that best serve our students and teachers. Over the years we have researched, gathered and created a variety of assessment tools and practices that guide how and what we teach. UCDS teachers carefully choose and create assessments that not only give us information about a child’s academic performance but also provide insight into a child’s thinking process. In particular, we know that when students reflect on their own thinking they become successful independent learners. Through reflection on one’s own thinking process, an individual practices learning how to learn. In turn, each student develops independence
and the ability to generalize his or her thinking strategies to other problemsolving scenarios. In fact, we consider these reflective skills to constitute the core of our program, providing a platform on which academic growth occurs. Our curriculum is built from a continuum of skills or benchmarks (at right) that describe how we generally expect students to acquire academic abilities. We acknowledge that academic growth is not always a linear process, and the continua documents allow teachers to note where a child’s abilities currently lie without being constrained by his or her age or grade. These are living documents that we regularly review. Throughout
UCDS MATH CONTINUUM
Child
Emerging
Developing
Number Sense Operations, Patterns, Varialbles __ Rote counting to 31 __ Writes numerals to 10 __ Counts objects to 20 with one-to-one correspondence __ Skip counts by tens __ Uses language to describe quantity and relationship (more, less, equal) __ Adds using manipulatives __ Understands the concept of 1/2 __ Creates single variable patterns
Number Sense Operations, Patterns, Varialbles __ Rote counting to 100 __ Counts objects beyond 20 with one-to-one correspondence __ Compares and orders numbers to 100 __ Groups units into sets of ten __ Uses a combination of tens and ones to build two digit numbers __ Recognizes, interprets and records addition equations
Discovery (ages 3, 4, 5)
(ages 4, 5, 6)
Number Sense Operations, Patterns, Varialbles __ Rote counting to 10 __ Recognizes numerals to 10 __ Counts objects to 10 with one-to-one correspondence __ Makes marks to represent numbers or equations __ Recognizes patterns __ Extends single variable patterns Geometry and Measurement __ Recognizes basic shapes __ Builds basic shapes __ Draws circles __ Sorts objects by one attribute __ Compares relative size of objects (bigger, smaller, equal, etc...) __ Uses descriptive language (size, speed, temperature, etc...) Statistics and Probability __ Collects and counts objects or data __ Contributes data to a pictorial graph
Geometry and Measurement __ Combines 2-D shapes to form different shapes __ Sorts objects by 2 or more attributes __ Uses language to describe relative location (above, below, beside, etc...) __ Recognizes symmetry __ Measures length, width and height using non-standard units __ Uses time vocabulary (yesterday, today, tomorrow)
Statistics and Probability __ Records data __ Shares findings
Statistics and Probability __ Adds information to graphs and charts __ Compares and contrasts findings
Fluent
Proficient
Number Sense Operations, Patterns, Varialbles __ Applies multiplication facts __ Regroups using subtraction algorithm across zeros __ Applies multiplication algorithm __ Uses manipulatives for long division __ Builds improper fractions and mixed numbers __ Adds and subtracts fractions with unlike denominators __ Compares and orders fractions __ Reduces fractions __ Generalizes understanding of place value for whole numbers and decimals __ Adds and subtracts with decimals
Number Sense Operations, Patterns, Varialbles __ Applies division facts __ Uses long division algorithm __ Multiplies and divides with decimals __ Converts fractions to decimals __ Finds missing variable in simple addition, multiplication, subtraction and division equations __ Identifies relationship between fractions, decimals and percents Geometry and Measurement __ Creates angles according to their properties __ Recognizes symmetric figures and identifies lines of symmetry __ Identifies properties of polyhedra Statistics and Probability __ Predicts and finds likelihood of outcomes __ Uses mean, median, mode and range to analyze data __ Displays data in a variety of graphic forms
(ages 8-11)
(ages 9-12)
Number Sense Operations, Patterns, Varialbles __ Applies subtraction facts __ Demonstrates understanding of whole number place value __ Regroups using the subtraction algorithm __ Multiplies two-digit by two-digit numbers using partial products __ Builds simple division problems with remainders __ Builds equivalent fractions __ Adds and subtracts fractions with like denominators __ Understands decimals as parts of a whole Geometry and Measurement __ Identifies properties of geometric shapes (circles,squares, rectangles, triangles) __ Generalizes and applies rules for area and perimeter __ Uses manipulatives to find surface area and volume Statistics and Probability __ Interprets and generalizes information found in bar and line graphs
Geometry and Measurement __ Identifies properties of polygons __ Compares, contrasts, and identifies angles __ Generalizes and applies rules for volume and surface area Statistics and Probability __ Identifies relevant data __ Organizes data to create graphs __ Interprets information from a variety of graphs __ Calculates mean, median and mode
G
S
Demonstrates Sometimes with guidance demonstrates
GSFC GSFC GSFC GSFC GSFC GSFC
Takes risks Focuses attention Identifies salient information Displays eagerness towards mathematics Formulates a plan Makes informed predictions
Teachers
Number Sense Operations, Patterns, Varialbles __ Reads and writes numbers to 100 __ Skip counts by 2’s and 5’s __ Holds a number constant while counting on __ Regroups using manipulatives in addition __ Demonstrates understanding of 2-digit place value __ Demonstrates understanding of 3 digit place value __ Subtracts using manipulatives __ Recognizes and records sums up to 20 __ Relates pictures to symbols of 1/2, 1/3, 1/4 __ Creates multi-variable patterns Geometry and Measurement __ Divides 2-D shapes to form different shapes __ Identifies 2-D shapes in a variety of orientations __ Identifies and creates single line symmetry __ Measures, compares and estimates using manipulatives __ Identifies area and perimeter Statistics and Probability __ Reads, interprets and discusses information on simple graphs and charts
(ages 7, 8, 9)
Number Sense Operations, Patterns, Varialbles __ Recognizes numbers to 1000 __ Applies addition facts __ Regroups using the addition algorithm __ Uses repeated addition to multiply __ Regroups using manipulatives in subtraction __ Recognizes, interprets and records subtraction equations __ Divides using manipulatives __ Understands pictorial and symbolic representations of fractions __ Compares numbers using >, <, = Geometry and Measurement __ Identifies 3-D shapes __ Measures area and perimeter using manipulatives __ Uses tools to find metric and US measures Statistics and Probability __ Collects data for analysis __ Utilizes strategies for organizing data
Connecting
Continuing (through adulthood)
(ages 11-14)
Number Sense Operations, Patterns, Varialbles __ Applies order of operations to solve equations __ Uses ratios and proportions to solve problems __ Describes simple algebraic rules for patterns __ Multiplies fractions __ Divides whole numbers by fractions __ Finds percent of a known quantity Geometry and Measurement __ Measures angles and lengths to construct 2-D figures __ Measures angles and lengths to construct 3-D figures __ Finds area and circumference of a circle __ Applies knowledge of ratios to create a scale map or drawing Statistics and Probability __ Represents possible outcomes using a variety of methods (area or tree diagrams) __ Finds all possible outcomes for a given situation to determine probability
Problem Solving GSFC GSFC GSFC GSFC GSFC GSFC
Expanding
(ages 6, 7, 8)
(ages 10-13)
Approach
Domain Marking Key:
Reflective Thinking Profile
Continued >
Beginning
(ages 5, 6, 7)
Geometry and Measurement __ Identifies basic shapes in the environment __ Draws triangles and rectangles __ Demonstrates understanding of relative location (above, below, beside, etc.) __ Measures using non-standard units __ Uses comparative language __ Demonstrates awareness of time (before/after)
Bridging
the process of examining our reading, writing, and math continua, we sparked discussions about the problem solving skills that surround academic abilities. These skills seemed to fall under the bigger umbrella of Critical Thinking. As we considered the ways students communicate their understanding, approach and method to solve problems, we decided that these abilities were not unique to one academic content area. And so, with that realization, we were ready to embark on creating a continuum that would give a picture of each child’s Critical Thinking abilities.
Implements a variety of strategies Perseveres Asks questions to support process Modifies strategies Displays flexibility Estimates, predicts and assesses reasonableness of an outcome
Number Sense Operations, Patterns, Varialbles __ Finds and writes functional rules for linear and simple exponential relationships and patterns __ Explains numbers by comparing and sequencing whole numbers, fractions, decimals, percents, exponents and negative numbers __ Performs operations on real numbers __ Applies associative and commutative laws to problem solve and check work Geometry and Measurement __ Understands relationships between measuring systems __ Compares different measurable attributes of polygons and 3-D shapes (height, length, weight, capacity, area, volume and perimeter) __ Understands concept of rate Statistics and Probability __ Questions different interpretations of the same data __ Creates data analysis investigations: considers problem, collects and records data, describes and interprets data and develops hypotheses based on data
Communication GSFC GSFC GSFC GSFC
Effectively documents the process Expresses ideas with clarity Collaborates Reflects
Key W = winter S = spring
The UCDS Math Continuum (above) is one of several assessment documents developed by faculty and staff. F C These documents use a combination of developmental research, state and national learning-standards, and school-specific curricula to track student growth in each major subject area. Faculty use the Math, Reading and Writing Continua to assess student learning and communicate with parents on a regular basis. independently
Frequently Consistently demonstrates demonstrates independently independently
Continuum adapted by University Child Development School with permission from Bonnie Campbell Hill. No part of the Continuum may be reproduced or used without written permission of University Child Development School. Revised 09/2010.
Continuum adapted by University Child Development School with permission from Bonnie Campbell Hill. No part of the Continuum may be reproduced or used without written permission of University Child Development School.
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