gco a and b - plans.ednet.ns.ca
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1
GENERAL CURRICULUM OUTCOMES
COMPONENTS
SKILLS & CONCEPTS
SPECIFIC CURRICULUM OUTCOMES
Early Elementary Mathematical Literacy Assessment
EEMLA 2009-2010
EEMLA
WHAT WE HAVE LEARNED
Use this document in conjunction with the Report to School Administrators and Teachers and the
associated materials to probe further into the curriculum content that was assessed in the 2009-2010
EEMLA. In particular, areas that may need further development and instruction will be of interest.
Nova Scotia Department of Education Evaluation Services Division P.O. Box 578 2021 Brunswick Street Halifax NS B3J 2S9 Telephone: 902-424-7746 Fax: 902-424-0614
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GCO A: Number
Challenges
Mental Math
Using place value information effectively up to 9999 including tenths
Combining/renaming 100’s,10’s and 1’s (13 ones and 3 tens)
Number line
Using bench marks to compare, order, and count whole numbers and decimal tenths
Hundred chart
Knowing/using patterns and relationships in the chart
Counting
Money (know the value of coins and count in a variety of ways)
Reading and Writing Numbers
Larger whole numbers/decimals/fractions
Comparing
Multiplication/repeated addition
Fraction and decimal comparisons and placing these on the number line
Measurement comparisons(cm/dm)
Base ten block representations
Regrouping/conceptual understanding/ connecting to place value
Composing/Decomposing(hundreds in 1000)
Number identification
Using several clues such as even/odd, less than/more than, place value information … to
identify a specific number
Suggestions
General
Continue to provide a wide variety of questions that require students to use the concept of place
value including ordering and comparing numbers in a variety of contexts
Record and work with multiple representations of number and their equivalents(show different
representations of the same quantity/stress their equivalencies)
Number line
Teach strategies for using/finding helpful benchmarks
Change scale (stress importance of reference points) when comparing and ordering
Comparing/ordering decimal tenths and fractions
Hundred chart
More experience with parts/sections of the chart and using/knowing/applying patterns found in
the chart
Reading /Writing numbers
More experience using concrete materials and making connections to the symbolic
More practice recording and relating to the concrete/pictorial/verbal
More practice reciting number names; reading numbers correctly orally; counting(skip
counting) in sequence forward or backward(stress transitions to next 10,100,..); providing a
variety of starting points other than 0
Number identification
More experience using problem solving, logical reasoning, making an organized list and
eliminating incorrect choices.(use resources such as Roads to Reasoning to support this)
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Less than 50% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Reading/representing a number word involving decimal tenths to the standard numeral
2. Comparing and naming two fractional amounts
Less than 60% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Placing whole numbers, proper fractions, decimal tenths on a number line using the
benchmarks provided
2. Reading/representing a number word involving larger whole numbers or fraction to the
standard numeral
3. Identifying what fraction is represented by parts of a whole or parts of a set
4. Determining how many tens or hundreds in 1000 using base ten blocks
5. Using number clues to reason the number being described/ solving multi-step problems
Examples of challenging content:
There are 1064 students in a school.
What is this number in words?
O ten thousand sixty- four
O one thousand six hundred four
O one thousand sixty-four
O one hundred sixty-four
Choose the number that is the same as 25 tens.
O 250
O 2500
O 1025
O 2510
If the base ten rod represents one, what number do 4 rods and 3 small cubes represent?
O 403
O 43
O 4.3
O 3.4
What is 8257 rounded to the nearest hundred?
O 100 O 8200 O 8300 O 8000
4
Look at this shape.
Choose which picture shows one- half of this shape.
5
Which picture shows one-third of the rectangle shaded?
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GCO B: Operation
Challenges
Mental Math
Basic subtraction facts
Rounding to Estimate
Applying to computation
Applying in context
Paper and pencil calculations
Subtraction with and without regrouping
Horizontal presentation
Operational language (sum, difference, …)
Understanding/modeling of procedures
Using base ten blocks to show addition/subtraction with regrouping
Visual representation of a given operation
Word problems involving money and making change
Suggestions
Mental Math
Address fact learning/fact rehearsals as it is the basis for mental math skills
Use strategies such as ‘think addition’ and stress ‘fact families’ for addition as well as
subtraction
Rounding to Estimate
Purposeful use in addition and subtraction situations
Everyday contexts
Paper and Pencil/Modelling
Address place value understanding in addition and subtraction computations
Use manipulatives and other materials to model /represent operation concepts,
computations and word problems. Connect the pictorial to the abstract.
Helpful materials/manipulatives include but are not limited to:
Number lines
Counters
Linking cubes
Ten frames
Base ten blocks
Strengthen the connections by recording the symbolic representation for the operation
beside the model.
Understanding/Applying Procedures
Use mental math and estimation to focus on the relationships between the numbers and
the operation as opposed to simply memorizing rules for performing calculations.
Students need to work with more word/story problems in context (including money)
instead of working on isolated number calculations.
Students need to connect addition with subtraction and multiplication with division.
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Less than 50% of our Grade 3students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Rounding/Estimating to find a total amount
2. Rounding/estimating to find a difference in a real life context
3. Choosing the best estimate using a visual or measurement benchmark
4. Using ‘think addition’/fact families to solve a subtraction question
Less than 60% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Mentally finding 100 more/less or 10 more/less than a given number
2. Choosing the best estimate for a computational estimation involving subtraction
3. Interpreting a pictorial model of addition with regrouping
4. Calculating subtraction with regrouping involving two and/or three digit numbers
Examples of challenging content:
Calculate these answers. Show any work that you do.
Any method/strategy may be used including mental math, paper pencil, and models.
– 8 = 21
873 – 98
241 – 2
38 + 67
10 less than 347
25 + 651 + 75
400 – 60
100 more than 674
What is the best estimate for the difference of 794 and 317?
O 700 – 300
O 800 – 400
O 800 – 300
O 900 – 300
Which repeated addition is equal to 4 × 3?
O 3 + 3 + 3 + 3
O 4 + 4 + 4 + 4
O 4 + 3 + 4 + 3
8
Group 1
Group 2
If the small cube represents one, what is the sum if you add Group 1 and Group
2?
O 863
O 871
O 963
O 8611
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Which fact family do these pencils represent?
O 12 6 = 2
2 6 = 12
O 4 – 3 = 1
1 + 3 = 4
O 4 + 3 = 7
7 – 4 = 3
O 12 3 = 4
3 4 = 12
How can you find the total number of buttons?
O 5 6
O 5 + 6
O 5 5
O 6 6
10
Kim has 15 apples.
She puts 5 apples in each bag.
How many bags does she need?
O 3
O 5
O 10
O 15
Chen puts his toys in 3 rows.
There are 6 toys in each row.
How many toys does he have altogether?
O 3
O 9
O 18
O 24
Jen has 27 crayons, Marlo has 43 crayons and Bill has 19 crayons.
Estimate how many crayons the students have altogether.
Choose the best estimate.
O 70 crayons
O 80 crayons
O 90 crayons
O 100 crayons
Carlo has eight books.
Anil has twice as many books as Carlo.
How many books does Anil have?
O 4 books
O 8 books
O 10 books
O 16 books
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GCO C: Pattern
Challenges
Patterns in Tables/Charts
Identifying and extending
Counting patterns
Descending (counting back) with transitions over the next tenth, ten, hundred,..
Extending a pattern
Growing patterns
Suggestions
General
Patterns represent identified regularities based on rules describing the patterns’
elements. Any pattern can be represented in a variety of ways.
Continue to provide students with opportunities to identify, describe, extend numeric,
geometric (growing) and repeating patterns as well as solving simple open sentences.
(8 + 9 = + 10).
Use a variety of tools and strategies including more use of tables/charts, guessing/
applying/extending pattern rules, creating /representing patterns with concrete materials
and using a guess and check strategy to verify a pattern. Practice representing the same
pattern in more than one way.
Counting/Place value patterns
The place value system is based on patterns. Practice a counting sequence in a variety of
ways using both ascending and descending examples with transitions over the next
tenth, ten, hundred, …
Extending patterns
More practice in extending an existing pattern
Provide many opportunities to identify, describe and extend numeric, geometric and
repeating patterns
Provide many opportunities to solve/interpret simple open sentences and connect them
to ‘story problem’ structures (initial unknown, join unknown …)
Have students generate and analyze patterns
Use a variety of tools and strategies including tables, pattern rules, concrete materials
and guess and check to recognize and extend patterns and describe relationships
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In general, across the province, less than 60% of our Grade 3 students were successful with
questions concerning the following types of skills, concepts, and problem solving:
1. Identifying and extending a given pattern
2. Completing a descending counting sequence pattern with a transition over the next ten,
hundred… (e.g. 224, 219, 214, 209, 204, ___, …)
Examples of challenging content:
The number of squares in each shape forms a growing pattern.
Shape 1 Shape 2 Shape 3
4 squares 6 squares 8 squares
If this pattern continues, what is the number of squares in the next shape? (Draw it)
O 10 O 11 O 12 O 16
If this pattern continues, what is the number of squares in the 7th shape?
O 10 O 14 O 16 O 17
1.3, 1.2, 1.1, ___, ___, … What are the next two numbers in this counting pattern?
O 0, 0.9
O 1, 1.1
O 1, 0.9,
O 10, 9,
Look at this number machine.
What is the pattern rule used to get the number that comes Out of this number machine?
O add 3 to the number going In O subtract 3 from the number going In
O add 1 to the number going In O subtract 1 from the number going In
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GCO D: Measurement
Challenges
Telling time
Reading analog beyond hour and half hour
Elapsed time
Mass
Applying relevant concept and skill to situations measuring mass
Length
Working with length
Using and reading a ruler accurately
Ordering/comparing lengths with different units (cm, m, mm...)
Suggestions
Telling time
Use an analog clock in the classroom
More opportunities in context to determine elapsed time
Mass
More opportunities to use and develop benchmarks for grams/kilograms (small paper
clip about 1g / a dime is about 2g, a litre of water or milk has a mass of 1 kg)
More experience with using scales to measure mass
Length
Teach using and reading the ruler accurately
Teach students not to just look at units or not to just look at the magnitude (the size of
the number) both must be considered when comparing lengths.(e.g. 1m > 50cm)
Address renaming/comparing metric units using relationship of one unit to another
Have students rename lengths with different units using the same unit to help make
comparisons easier
Less than 50% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Calculating elapsed time
2. Choosing the best estimate using a visual referent or a measurement benchmark
Less than 60% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
3. Reading time beyond the hour or half hour on an analog clock
4. Estimating the mass of an object
5. Comparing lengths (cm, dm…)
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Examples of challenging content:
Three frogs were in a jumping contest.
Frog Distance jumped
Troy’s frog 1 m
Nina’s frog 142 cm
Jay’s frog 419 mm
Which one shows the jumps in order from longest to shortest?
O Jay’s, Nina’s, Troy’s
O Troy’s, Nina’s, Jay’s
O Nina’s, Jay’s, Troy’s
O Nina’s, Troy’s, Jay’s
Which of these objects can hold exactly one millilitre and exactly one litre?
O the small cube and the large cube in the base ten materials
O a water bottle and a water jug
O a puddle and a swimming pool
Which of these has a mass of about one kilogram?
O a medium sized hard covered book
O a pencil
O a small base 10 cube
O an apple
What time does the clock show?
O 7:45
O 8:09
O 8:45
O 9:08
Lunch starts at 12:30 and takes 45 minutes.
When is lunch over?
O 12:45 O 1:00 O 1:15 O 1:30
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GCO E: Geometry
Challenges
General
Students seem to have trouble interpreting mathematical language related to 2-D and 3-D
geometric concepts and applying it to the visual/spatial reasoning involved in working
with shape and space
Transformations
Turns
Decomposing/deconstructing shapes to make new shapes
Seeing shapes within shapes
Language
Edges
Suggestions
Transformations
Develop spatial sense by identifying, performing and describing transformations:
translations(slides), reflections(flips), with a special emphasis on rotations(turns)
Decomposing shapes and shape manipulation
Analyse two- and three-dimensional geometric shapes with an increased emphasis on
decomposing shapes and composing new shapes
Constructing/deconstructing, visualizing, drawing and measuring are important
experiences to support this ability
Use geometric tiles and blocks to make and analyze compound shapes
Use 3-D shapes to identify edges, faces and vertices
Language
Use and apply accurate 2-D and 3-D geometric language and properties
Teacher questioning techniques and language in directing student thinking are critical for
developing an understanding of geometric relationships and properties
Ask questions that require analysis of two- and three-dimensional geometric shapes
Use concrete and visual models to represent geometric ideas/concepts and to support
visualization, spatial reasoning, and solving problems
Determine what makes geometric figures alike and different
Develop spatial sense by identifying, performing and describing transformations
(translations, reflections, rotations)
16
Less than 50% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Identifying the number of edges for a 3-D figure
Less than 60% of our Grade 3 students were successful with questions concerning the
following types of skills, concepts, and problem solving:
1. Identifying a half turn/half turn image
2. Cutting and re-assembling a shape to make a new shape
Examples of challenging content:
Aman buys a kite.
It has an odd number of sides.
It has some angles less than a right angle.
It has only 1 set of parallel sides.
It has some right angles.
It has only one line of symmetry.
Which shape shows Aman’s kite?
O O O O
Which 3-D object has the most edges?
O O O
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Use a ruler. Divide the shape into these three shapes:
1) a trapezoid
2) a triangle 3) a rectangle
Make sure there are no gaps and no shapes overlap.
Find and outline a trapezoid Find and outline a parallelogram Find and outline a square
A student made this shape out of pattern blocks.
Which shape shows a one-quarter turn clockwise?
O O O
A)
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GCOs F and G: Data and Probability
Challenges
Graphing
Using/interpreting and labeling a graph
Interpreting a scale (other than 1:1)
Suggestions
Graphing
Model appropriate labeling conventions for graphs
Continue to provide opportunities to organize, display as well as read and interpret data
with graphs using scales
Probability
Continue to provide opportunities to express and represent the probability of an event
Examples of challenging content:
FAVOURITE VEGETABLES
CARROTS
BROCCOLI
PEAS
Key represents 5 students
Look carefully at the graph.
How many more students prefer carrots to broccoli?
O 1 student
O 2 students
O 5 students
O 10 students
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General Observations and Suggestions
Students had the greatest challenge with questions related to the following concepts:
Different, but equivalent, representations for a number
(especially representations for fractions and decimal tenths)
Estimation (numerical, computational and measurement related)
Operation concepts and procedures
(especially subtraction with regrouping and multiplication/division meanings)
Patterns
(especially growing patterns and representing relationships in a variety of ways)
Geometry (2-D/3-D language, spatial sense, transformations especially turns)
It is suggested to review instructional timelines to be sure these identified areas receive sufficient
teaching and learning time.
Opportunities to solve problems where solutions or solution strategies are not immediately
evident and that require multiple steps and/or multiple concepts should be provided regularly.
Students continue to make careless errors when responding to all types of math questions. A
quick reading of the question and a lack of attention to detail contributes to this problem.
Students continue to misinterpret important details in questions for all strands even when they are
bolded. Attention to text features, operation symbols, and other visual cues and symbols is
important. Consider using a math text for a guided reading lesson, small group instruction and
developing literacy connections across the curriculum. Students thinking about their thinking
(metacognition) and developing self assessment strategies is also a crucial step to address these
areas of concern.
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