Math Support
Comment Idea Bank
Classroom Observation and Classroom Support
Classroom Observations:
Stays on task
Follows verbal instructions well
Follows written instructions well
Frequent monitoring assists ______to stay on task
Displays difficulty staying on task
Is prepared for class
Asks questions for clarification
Positive attitude toward math
Displays difficulty attending to verbal instruction
Requires a great deal of support with organization data
Benefits from repetition of skills, vocabulary, and concepts in order to experience
success in math
Needs additional time to complete tasks
Difficulty transferring information from concrete to abstract
Pays attention during instruction
Does not understand the meaning of…….
Understands the meaning of …………
Can use a …………to……………
Easily distracted
Often comes unprepared for class (no duo-tang, pencil, eraser, loose-leaf, homework is incomplete
Is distracted by manipulatives or is not able to use them properly
Lacks self-confidence in his/her math abilities
Needs additional encouragement to finish/complete class work and participate in class
Quite often relies on fingers for addition and subtraction
Needs to be encouraged to take a more active part in math activities
Requires more effort to become an independent learner
Finds pencil/paper tasks challenging
Finds it difficult to work independently and to follow directions
Lacks confidence in his or her math testing abilities
Transfer (from hands-on) to paper is challenging
Classroom Observations: Strand A: Number Sense:
Cannot yet model numbers to 99 999
Is more comfortable with numbers to 9 999 or 999
Cannot yet record numbers to 99 999
Having difficulty comparing and ordering whole numbers
Is unable to identify and model fractions
Is unable to identify and model mixed numbers
Is experiencing difficulty interpreting and modeling tenths and hundredths
Is unable to compare and order fractions
Is unable to rename fractions
Is unable to rename fractions without models
Cannot yet compare and order decimals
Cannot yet compare and order decimals without models
Has difficulty visualizing 10 more & 10 less
Has difficulty recognizing days of the week
Has difficulty with ordinal numbers
Cannot model numbers to 3 places or compare and order numbers by size
Strand B: Number Operations:
Difficulty understanding and solving word problems
Struggles to create word problems
Mental math computations lack strategies
Struggles when applying strategies to solve mental computations
Difficulty understanding the meaning of division
Struggles to multiply two and three digit numbers by a single digit using
pictures, concrete materials or symbols
Multiplication tables continue to present problems
Cannot recall multiplication facts within a reasonable working time limit
Cannot relate multiplication facts to division
Has difficulty estimating sums, differences, products and quotients
Struggles with understanding the meaning of multiplication
Difficulty adding and subtracting fractions with like denominators
with and without concrete materials
Has not yet achieved the multiplication facts to 9 x 9
Is unable to recall their basic + and – facts to 20 (Still counts on fingers)
Is unable to skip count by 2’s, 5’s, 10’s, & 25’s
Is unable to skip count by 2’s, 5’s & 10’s from various starting points
Is unable to add 2 and 3 digit numbers with and without grouping
Can not add simple fractions with common denominators
Difficulty using the mental math strategies taught (i.e.: double + 1, make 10, front-end)
Struggles with separating ones, tens & hundreds
Does not understand the concept of regrouping to the next place value
Struggles with placing decimal tenths on a number line
Still relies on fingers for addition and subtraction
Difficulty in connecting/relating number operations to real world situations
Needs to more actively participate during mental math activities
Does not understand the importance of estimating in problem solving in the real world
Can show multiplication facts in a table, but not on a graph
Strand C: Patterns and Relations:
When adding decimals does not place the decimal point correctly
Can not apply patterns when multiplying by increasing powers of 10
Difficulty recognizing patterns when solving computational problems
Limited understanding of how changing a or b in an operation will affect the result of the computation
Can show multiplication facts in a table but not on a graph
Can complete open sentences in which the open frame is the result; however is unable to do so when the open frame is within the equation
Is experiencing difficulty with number patterns
Cannot recognize, extend and create simple place value patterns
Difficulty recognizing patterns when solving computational problems
Strand D: Shape and Space: Measurement:
Uses appropriate unit of measure
Does not use appropriate unit of measure
Uses appropriate terms
Does not use appropriate terms
Can compute area
Cannot compute area
Can find perimeter of an object
Cannot find perimeter of an object
Needs to be able to read and understand measurement vocabulary such as; kilometres, metres, decimeters, centimetres, millilitres, litres, grams and milligrams
Has difficulty measuring area using non-standard units and square centimetres
Has difficulty choosing appropriate units of measurement for capacity and mass
Has difficulty reading an analog clock to the hour, ½ hour, ¼ after, ¼ to the hour, or to the nearest 5 minutes
Strand E: Shape and Space: Geometry:
Needs visual and concrete supports to draw various nets for rectangular prisms and cubes
Is able to construct models for cones and cylinders but needs more practice constructing prisms and pyramids
Requires extra practice and one-to one support to construct shapes when given isometric drawings
Is able to recognize some relationship among 3D shapes such as the differences between prisms and pyramids but needs direct teaching to see the relationships between cones and cylinders
Is able to recognize and name acute and obtuse angles but has difficulty describing and constructing these angles
Is able to recognize and name equilateral triangles but has difficulty describing and constructing isosceles and scalene triangles
Needs guidance and direct teaching to make generalizations about the angles, side length and parallel side properties of the various quadrilaterals
Has difficulty sorting quadrilaterals under property headings
With concrete materials the student is able to make some low level generalizations about the number of vertices, edges, and faces of various prisms, pyramids, cones and cylinders
Student has difficulty using a ruler and dot paper to draw nets
Student has difficulty tracing or drawing a net
Student has difficulty perceptually viewing the shape
Student has difficulty folding the net to form a 3-D object
Student has difficulty making real life connections to objects of that shape
Student does not recognize the difference between prisms and pyramids; as well as cones and cylinders
Student does not understand or recognize the characteristics of 3-D objects (edges, faces, vertices)
Student has difficulty drawing various views of shapes and figures with isometric paper
Student has difficulty transferring characteristics of shape to paper
Student has difficulty recognizing different views and characteristics of shape to paper
Student has difficulty recognizing properties of 3-D shapes
Student has difficulty identifying shapes with the same number of faces
Finding all possible composite figures that can be made from a given set of figures
Recognize, name, describe, and construct acute and obtuse angles
Recognize, name, describe, and construct equilateral, isosceles, and scalene triangles
Student has difficulty using a ruler and other manipulative tools to construct angles and triangles
Student has difficulty recognizing the characteristics of angles and triangles
Student has difficulty utilizing a mira
Student has difficulty recognizing the properties of quadrilaterals
Student has difficulty with naming the various quadrilaterals
Student does not understand or recognize the characteristics of 3-D objects (edges, faces, vertices)
Is able to predict and confirm the results of various 2-D figures under slides, reflections, and quarter/half turns
Strand F: Data Management and Probability: Data Management:
Still has difficulty being able to collect and organize data
Can collect data but has difficulty organizing data
Has difficulty understanding range and frequency
Requires assistance interpreting pictographs in which symbols represent more than one item
Has difficulty creating bar graphs
Needs guidance labeling graphs (title(s), scale, axes)
Has difficulty distinguishing between bar graphs and histographs
Has difficulty describing data using mean
Has difficulty creating and interpreting stem and leaf plots
Requires guidance to interpret graphs using level two and level three questioning skills
Strand G: Data Management and Probability: Probability:
Has difficulty predicting probabilities as close to 0, near 1, or near ½
Rarely identifies very high and very low probabilities in every day events
Rarely identifies very high and very low probabilities in occurrence of numbers
Unable to use fractions to describe experimental probabilities
Struggles with the appropriate use of tools to create the appropriate probability
Classroom Support:
Flexible group work
Differentiated Instruction
Common tasks with multiple entry points
Open Ended Questions
Scaffolding
Working with manipulatives to support the concept
Time to verbalize learning
Real world connections
Partnering or working with a buddy
Demonstrate and modelpositive examples
Use and give clear concise instructions
Chunking with feedback on each step
Individualized instruction
Develop confidence to ask for help
Assistive Technology
Help students understand how they learn best
Read directions
Using a variety of representation and strategies when problem solving
Practice test-taking strategies
“I Have, Who Has” card games for different math concepts
Visual examples and games
Math word wall for vocabulary and Math wall to display math concepts and ideas
Classroom Support: Strand A: Number Sense:
Provide direct instruction with smaller numbers ( hundreds,
thousands etc.) using base ten manipulatives and drawings
Review of numbers to 999 and then 9999
Practise ordering numbers to 999 and 9999 using number lines and
base ten manipulatives
Using a variety of manipulatives (fraction factory, pattern blocks,
fraction strips, base ten) and pictures to model simple fractions
Using a variety of manipulatives (fraction factory, pattern
blocks, fraction strips, base ten) and pictures to model mixed
fractions
Using a variety of manipulatives (fraction factory, pattern blocks,
fraction strips, base ten) and pictures to model tenths and hundredths
Use number lines, base ten blocks and ten frames to support addition and subtraction
Use a hundreds chart to add and skip count
Use The Learning Carpet to teach place value
Daily mental math strategies
Daily Estimation Strategies
Blank laminate calendar with a daily message; today is ______
Daily weather chart calendar
Calendar Bingo
“Take it to Your Seat” matching cards
Use pennies, dimes, etc. to model base 10 groupings
Strand B: Number Operations:
Use concrete materials and pictures to model adding, subtracting, multiplying and division
Practice rounding numbers using a number line
Base 10 materials & place value charts to help with addition, subtraction; as well as reading and writing numbers
Use money to practice counting by 25
Use base 10 manipulatives to skip count by 10
Use a 100 chart to skip count by 10
Use The Learning Carpet to skip count by 10, 20, 25
Use pictorial presentations to reinforce multiplication
Relate multiplication to division using real life situations
Create simple story problems involving addition, subtraction, multiplication and division
Review addition/subtraction strategies to 18
Multiplication Strategies (Curriculum Document) to 9 x 9
Estimation Strategies (Curriculum Document)
Use 2 sided counters to show multiplication sentences
Have students draw arrays of multiplication sentences
Use manipulatives such as pattern blocks, square tiles, fractions pieces and geoboards to model addition and subtraction of fractions with common demoninators
Strand C: Patterns and Relations:
Look in the newspaper for any decimal numbers and chart how they are used
Practice adding decimals using a place value chart that includes the decimal point; do it as if it were a whole number, and then add the decimal place; use place value diagrams to build understanding of why this works
Use calculators to discover the patterns; then practice with other examples
Use hands on manipulatives to reinforce patterns
Use hands on manipulatives to reinforce the changing of items in an operation
Use manipulatives to create concrete graphs showing the multiplication facts
Use manipulatives to show the equations and figure out the missing item; then practice using the opposite operation to discover the missing item
Use grid paper to draw a rectangle and shade in 0.1, 0.2, 0.37 and 3.12
Use base ten to model addition, subtraction, multiplication and division of decimals
Strand D: Shape and Space: Measurement:
Use tiles to make different figures with the same area; make different figures with the same area on a geoboard; determine the area of different pre-made figures on grid paper
Use tiles to make different figures with the same area, then calculate the perimeter; use geoboards to make figures with the same area then calculate perimeter of the figures
Fill a box with different materials (linking cubes, pennies, marshmallow, etc.) to determine volume
Estimate how many cubes are needed to fill a box with centicubes and then do the activity and then count the cubes
Use a ruler to draw and measure when working with perimeter and area
Use The Learning Carpet to teach time with the analog clock
Use a cueing system for units of measurement
Use yogurt containers for measuring capacity
Strand E: Shape and Space: Geometry:
Find all possible composite figures that can be made from a given set of figures
Use nets to create 3-D shapes
Use geostrips to recognize, name, describe, and construct acute and obtuse angles
Use a ruler and other manipulative tools to construct angles and triangle
Use triangular dot paper to construct isometric drawings
Use patterns blocks and geostrips to measure right angles
Use the Mira to predict and confirm results of various 2-D figures when teaching transformational geometry (slides, reflections and rotations; quarter and half turns)
Provide visual and concrete supports to draw various nets for rectangular prisms and cubes (geo blocks)
Use polydrons to construct nets for pyramids and prisms
Provide one-to one support to construct shapes given isometric drawings
Make real world connections using picture books such as the Greedy Triangle
Use various materials such as straws and geostrips to construct angles of various sizes
Use graph paper and other materials such as geostrips and straws to describe and construct isosceles and scalene triangles
Construct quadrilaterals to help make generalizations about the angles, side length and parallel side properties of these quadrilaterals
Explain to students what is meant by the properties of quadrilaterals and look at each property in isolation
Use concrete materials to make generalizations about the number of vertices, edges, and faces of various prisms, pyramids, cones and cylinders
Collect food boxes and use to create the net of the box by taking the box apart
Strand F: Data Management and Probability: Data Management:
Modeling appropriate and inappropriate data graphs
Modeling appropriate and inappropriate survey questions
Guidance in breaking down collection and organization of data into small steps
Using physical models to show bar graphs
Use of The Learning Carpet to show bar graphs or pictographs
Communicate steps to follow verbally in conjunction with other cues
Use visual cues to help guide steps of collection and organization of data
Computer programs to help with creating and interpretations of graphs
Opportunities to create graphs using real world situations
Smart board software to create pictographs, bar graphs, stem and leaf plots
Provide graph paper for creating bar graphs
Visual organizers for developing pie charts
Use T-Tables to organize data for graphing
Modes of different graphs for student to refer to as anchors
Step-by-step procedures for creating various graphs (combine visual with written)
Collecting data – use a clipboard with an organizer
Models of different types of data
Opportunities to collect data that interests the student, may use a peer tutor to collect data and make decisions about how to organize the data
Use a calculator to calculate the mean (for a student who has difficulty with computation of large numbers or many numbers)
Strand G: Data Management and Probability: Probability:
Use a number line to confirm probabilities as either close to 0, near ½, or near 1
Use prior knowledge of everyday events that have high or low probabilities
Use concrete models, such as number cubes, spinners, coins, to reinforce concept of high or low probabilities –
Discuss examples of extreme chance situations (i.e. the sun will rise tomorrow morning; you will have two birthdays this year)
Probability Line – Impossible or certain (p. 342, Teaching Student-Centered Math, 3-5)
Design a bag activity (p. 342, Teaching Student-Centered Math, 3-5)-visual representation of probability