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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



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

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Look at this shape.

Choose which picture shows one- half of this shape.

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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


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



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


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

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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

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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, ___, …)


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



1. Calculating elapsed time

2. Choosing the best estimate using a visual referent or a measurement benchmark



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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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)

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1. Identifying the number of edges for a 3-D figure



1. Identifying a half turn/half turn image

2. Cutting and re-assembling a shape to make a new shape


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


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.

Download - GCO A and B - plans.ednet.ns.ca

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