Guide to
SPIRAL PLANNING
Gay Sul, Area 3 Math Consultant
© 2001 Frontier School Division
Updated: Frontier Math Consultants
September 2008
© 2001 Frontier School Division No. 48
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Spiral planning* is a systematic approach to the planning of how
to teach the math curriculum. The key elements in this approach
are:
• planning
• review
• and assessment.
How It Works:
The school year is divided into three terms according to reporting periods. A
possible way to break the year into 3 terms is:
- 1st term: September to Christmas holidays
- 2nd term: January to March Break
- 3rd term: April to end of the year
A decision is made about every outcome in the curriculum as to whether it can be
broken up into parts and which term to teach it. For example, if the outcome is to
read and write numbers to a million it could be broken up like this:
1st term:
read and write numbers to 10 000
2nd term:
read and write numbers to 100 000
3rd term:
read and write numbers to 1 000 000
In the second term, the previous material is reviewed before the new content is
taught. In the third term, both first and second term material is reviewed before
introducing new concepts.
Spiral planning does NOT mean that you teach a different concept each day or
even that that you must have topics from all the strands each week.
The Plans (A Suggestion)
• In deciding when to teach each outcome (or parts of it) you create your year
plan. (See attachments #1, 2, 3.)
• Then on a single page you lay out which concepts are taught each week for that
term to make a term plan. (See attachments #4, 5.)
• From that weekly list of outcomes, you would create your weekly plan (i.e. decide
which activities you would do each day so your students would learn that
concept). A blank weekly planning sheet is also attached. It needs to be
enlarged to fit an 11 x 17 sheet of paper. (See attachments #6, 7.)
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Assessment:
An assessment should be done each week or at the most every 2 weeks. Each
student has an assessment folder. The assessment does not need to be lengthy.
Other Components:
• Student work is organized.
• Assessment folders keep track of student work.
• Vocabulary words are posted. Each student has a vocabulary notebook.
• Journals are done at least once a week or every 2 weeks.
• Problem solving is taught at least 2-3 times per week. Non-routine strategies
are posted.
• A problem solving scoring scale helps students know what is expected.
• Math facts are worked on for 5-10 minutes per day. Thinking strategies are
taught and practiced during that time. Strategies are posted.
• Mental computation strategies are also taught.
• A checklist keeps track of what concepts/skills each student has mastered.
Time Allotment:
It is strongly suggested that a 1-hour block of time is allotted for math each day.
What We Found:
The first thing teachers would tell you about the spiral planning is that it is a lot of
work. (There was a lot of “pulling of hair” and “gnashing of teeth” as everyone tried
to make sense of this approach and make the plans "their own.") However, the
second year is so much easier because everyone has their plans ready and only need
to make minor changes. Now teachers have a foundation upon which they can build
on. The focus then becomes to add to teachers' repertoire of activities as well as
teaching and assessment strategies.
Spiral planning has been used by teachers from Nursery-Gr. 8 – and even in
classrooms with 5 grades in a room! This approach can work in any classroom.
Gay Sul
Area 3 Math Consultant
Updated: Frontier Math Consultants
* The idea of spiral planning in Frontier School Division was first started by Kelly
Eckford, Pamela Lee, and Karyn Hope. They were Gr. 3 teachers at Jack River
School in Norway House.
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Details About Each of the Components
1) Organizing Work
- Student work needs to be organized. Loose worksheets are to be avoided
whenever possible.
- Scribblers, duotangs, binders, or stapled booklets can be used. Some teachers
chose to have binders organized according to the different strands.
- Duotangs/binders can also be divided into different sections. (Possible sections
are: daily work, problem solving, journal, mental math, vocabulary.)
2) Assessment Folder
- It can take different forms such as a scrapbook or a file folder, with construction
paper dividing the work into different strands. Whatever form it takes, this
collection of pieces needs to be organized (preferably according to strands).
- This folder is a collection of different pieces of student work that answer the
question, "How do you know that the student learned what you were teaching?"
- Assessment is to be done every week or every 2 weeks.
- Some examples of what it can contain:
- journal entries
- a finished piece of work (such as a graph from a spreadsheet)
- observational notes
- the solution to a problem
- paper and pencil tests
Please note that a test need not be lengthy. Having 3-5 questions is sufficient to tell you
the child’s level of understanding.
- Each piece of work needs to be dated.
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3) Vocabulary
- The teaching of math vocabulary is based on the 3-point approach from the
Success For All Learners document. (See attachment #8.) The definition section
was for students to write the meaning in their own words, NOT copy an
explanation off the board. Examples of a simple chart students can make in their
notebook are also included. (See attachments #9 and 10.)
- Gr. 1 and Gr. 2 teachers can adapt the approach so that students print the word
and draw pictures of it.
- The vocabulary words need to be in their own section of the binder/duotang or in
a separate notebook/duotang. One of the most useful ways is if they are grouped
according to strand.
- Working on vocabulary should become part of the regular routine. One of the
teachers at Jack River School had the students work in their vocabulary notebook
every Friday (after they had been learning about and using the word all week).
Another teacher at Stevenson Island School had students work in groups to come
up with common definitions for words they had been working with during the
week. Then these definitions were shared.
- Vocabulary words need to be POSTED with a diagram.
Example:
4
+6
Sum -----Æ 10
Some teachers make students responsible for making the posters.
- Early Years (K-3) teachers should also be using math poems and fingerplays.
4) Journals
- Student responses to journal questions is another good way to get an idea of what
students are thinking. The question needs to be more than "What have you
learned this week?"
- To get started some students will need a frame sentence such as:
• I thought the most likely colour to come up on the spinner would be
_________ because ___________ .
• The strategy I used to get the highest sum in this addition game
was ____________ .
- Some possible journal questions are attached. (See attachment #11).
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- A suggestion would be to use journals about once a week on a regular basis (such as
every Monday).
- A list of vocabulary words is available on the Manitoba Education website
(www.educ.gov.mb.ca).
5) Problem Solving
- Problem solving should be scheduled for a minimum of 2-3 times per week.
- All the problems the students work on need to be kept in a separate section of
the duotang or binder. Problem solving booklets can also be made. Please do NOT
have students spend their time copying problems off the board.
- A sheet outlining how to set up a problem solving program is included. (See
attachment #12.)
A program needs to include:
•
readiness activities for Gr. 1-2 (See attachment #13) or strategy
activities for Gr. 3-8 (See attachment #14.)
•
routine problems: problems where you need to only add, subtract,
multiply, or divide.
E.g., I have 6 cookies. I give you 2. How many do I have left?
•
non-routine problems: problems that require a strategy such as guess
and check, draw a picture, make a table, etc.
E.g., Farmer Brown has some cows and pigs. He counts 20 legs.
How many chickens and pigs does he have? (You need to draw a
picture to answer this question.)
- An excellent reference is Problem Solving Experiences in Mathematics by Randall
Charles (Addison-Wesley). There is one book for every grade (K-Gr. 8). Starting
at Gr. 4, they all follow the same format so it does not matter whether you use a
different grade level - only the numbers and context changes. (The format is a
strategy activity, 2 routine problems, 2 non-routine problems using the same
strategy, and then the cycle repeats).
- Post each non-routine strategy as it is taught so students can refer back to it.
(See attachment #15.)
- In problem solving, the most important part of the whole process is the students
SHARING how they solved the problem.
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- Several effective ways that can be used to help students overcome difficulties in
reading and understanding the problem is:
1) Put the problem on the board or overhead.
-
Give students a couple of minutes to read it, or read it aloud yourself,
or have another student in class read it.
-
Cover the problem or turn off the overhead.
-
Then ask SEVERAL students the following questions:
(i)
What is the question? (or What are you being asked to find
out?)
(ii)
What is the important information?
(iii) Retell the problem in your own words.
2) Instead of putting the problem on the board or overhead, just tell it
orally. (Then follow the rest of the steps outlined above.)
3) Draw the key information on the board. Write the question in words.
(Then follow the rest of the steps outlined above.)
4) Use pencil/pen/markers/pencil crayons to highlight the question in the
problem in one color and a different colour for the important
information.
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6) Problem Solving Scoring Scale
"You can't hit the target if you don't know what it is."
- Richard Stiggins
Posting a scoring scale on the wall and using it to mark student work is really
helpful. Students then know what the expectations are and what they are aiming
for. Teachers who tried this idea out in past years found that it made students
much more conscious of what they were doing in problem solving and really
improved the quality of work.
A suggested scale is a very simple one that we have used on the divisional
assessment:
1 mark - Work is clearly shown
1 mark - Plan used will solve the problem
1 mark - Correct answer
1 mark - Answer is in a sentence
1 mark - Problem solving strategy correctly named (for non-routine problems)
5 marks
Go over what each part of the scale means. You can also give your class sample
problems to mark using the scale. After a problem has been done in class,
students can trade papers and mark each other's work.
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7) Math Facts
- Math facts go up to 9 + 9 for addition (or 18 - 9 for subtraction) and 9 x 9 for
multiplication (or 81 ÷ 9 for division).
Mad Minutes should NOT be used on a regular basis because they do
not teach anything – timed tests assess, not teach. They can be used to
give you a snapshot of where students are but do not tell you what kind
of thinking strategies are being used. A math facts interview is a very
effective way to determine what strategies the students are using.
- The thinking strategies are listed at the back. (See attachment #16.)
- For addition and subtraction facts, a good resource is the Mental Math in the
Primary Grades book. The lessons are all explained.
- Focus on one thinking strategy for at least a week, such as doubles + 1 (e.g., 4+5,
7+8). Approximately 5-10 minutes each day would be spent on learning/practicing
that strategy.
- A possible teaching approach could be:
Day 1: -
Introduce the strategy by showing a fact question on the board
(such as 4 + 5 for doubles + 1) and ask students how they would solve
it. If no one suggests that particular strategy, then explain it.
- Give students a practice sheet with 20 questions that has only that
strategy on it. This sheet should NOT be timed.
Day 2: -
Review how the thinking strategy works (e.g., "You think of the
doubles fact and then add one more"). You can say the same fact
questions (about 10) orally and students can write the answer in
their notebook. Give the answers immediately afterwards.
-
Then give them some time to play a game to practice. Two examples
are:
a)
Concentration - Make up a set of flashcards with only the facts
using that specific strategy as well as another set with the
corresponding answers. Student A turns over 2 cards and tries
to find a match. If they match, he keeps the set. If they don't,
then it's Student B's turn. The game continues until all the
cards are matched up. Person with the most pairs wins.
b)
Use a commercial game like "Snakes and Ladders." Make up a set
of flashcards with only the facts using that specific strategy.
Students take turns turning over a card. If they can answer the
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question, then they can roll the die and take a turn. If they
cannot answer the question, they lose their turn. (At the
beginning, have students explain. Example: "4 + 5 is 4 plus 4 plus
one. That equals 9.")
Day 3 and 4: Repeat above (untimed practice sheet and games).
Day 5: Give the same fact sheet as on Day 1, only this time it should be timed 1 minute for 20 questions (3 seconds/question).
•
If you need to continue practicing that strategy the next week, then do so.
•
Remember to continually review previously learned strategies.
•
Let students use addition or multiplication tables when you are teaching a
concept like long multiplication. They should NOT use them when you are
working on the strategies.
8) Mental Computation (of larger numbers)
- Knowing math facts forms the basis for calculating larger numbers (eg., 90 + 60).
- The empty number line is an extremely helpful strategy to transition all learners
to working with larger numbers mentally and is especially useful for students who
are still working on mastering facts.
- Mental Math in the Middle Grades and Mental Math in Junior High by Jack Hope
are excellent resources.
9) Homework
Homework should be meaningful. It should also be accomplishable so students can
feel successful. It needs to take a reasonable amount of time to finish.
Some ideas for math homework that students could do:
• teach a parent or sibling a math game (such as those
from Box Cars and One-Eyed Jacks)
• create a problem that is similar to one that was
worked on in class
• complete a journal entry (e.g., How would you explain
_________ to a student who was absent today? OR
List 5 examples of cylinders in your home.)
• complete a vocabulary chart.
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10) Checklist
A checklist is simply a tool to help you keep track of which students have mastered
outcomes that have been taught and which students need more help on certain
outcomes. A sample as well as a blank checklist are attached. (See attachments
#17 and 18.)
Here's what to do:
• Use a duotang or binder.
•
•
Have a different sheet for each strand (or part of a strand):
- number
- geometry
- statistics
- measurement
- probability
- patterns
Also include sections for other components of your program:
- problem solving
- math facts
- mental computation (where applicable)
•
Every teacher is assessing what they taught each week (or every 2 weeks at the
most). After you assess, add the outcome at the top of the checklist and the
date.
•
Put a "√" if the student has mastered the outcome or an "O" if the student has
not. (This is only a suggestion. If you have a different system you want to use
for recording, then do so.)
•
Once a child has mastered that outcome that you can go back and put a "√"
inside that "O".
•
For problem solving, list the non-routine strategies (guess and check, draw a
picture, etc.) as well as having a section for routine problems.
•
For math facts as well as mental computation, list across the top of the
checklist the thinking strategies that were taught.
11) Tell Students What They Are Going to be Learning
Tell students at the beginning of each week and each lesson what it is they will be
learning. Otherwise, it's like going to a meeting and sitting there for an hour
without knowing what the agenda was. (Doesn't that sound like a frustrating
experience?) Students need to know what the "big picture" is.
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ATTACHMENTS
Attachment
Title
Page
1
Year Plan Multi-grade Sample
12
2
Year Plan Multi-grade (cont’d)
13
3
Year Plan Grade 6 Sample
14
4
Term Plan Multi-grade Sample
15
5
Term Plan Grade 3 Sample
16
6
Weekly Plan Multi-grade Sample
17
7
Weekly Plan (Blank)
18
8
19
9
3-Point Approach for Words and
Concepts
Vocabulary Chart Grade 1
20
10
Vocabulary Chart Grade 7
21
11
Math Journal Question Samples
22
12
Problem Solving Program Sample
23
13
24
16
Readiness Activities for Problem
Solving
Stages and Activities in Problem
Solving
Routine and Non-Routine Problem
Solving
Math Facts Thinking Strategies
17
Sample Checklist
28
18
Blank Checklist
29
14
15
25
26
27
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Attachment 1
YEAR PLAN (MULTIGRADE)
Strand: Numbers (reading / writing) Numerals / No. words
Term 1
Term 2
Term 3
N – Read / Write Numerals up to 5
Read / Write Numerals to 8
___ to 10
K – Read / Write Numerals up to 5
___ to 10
REVIEW
Gr. 1 - Read / Write Numerals up to 10
Reads Number words (Poems) up to 5
(Skip counting 1 + __ = ==)
Counts with calculator up to 20
Gr. 2 – Read / Write Numerals up to 40
Read / Write Number Words up to 10
___ to 15
___ to 10
___ to 20
REVIEW
___ to 70
___ to 15
___ to 100
___ to 20
Gr. 3 – Read / Write Numerals up to 400
Read / Write Number Words up to 40
___ to 700
___ to 70
___ to 1000
___ to 100
Gr. 4 – Read / Write Numerals up to 4000
Read / Write Number Words up to 400
___ to 7000
___ to 700
___ to 10000
___ to 1000
Edie Carlson
Matheson Island
(N-4 Teacher)
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Attachment 2
YEAR PLAN (MULTIGRADE)
Strand: Number (Names, Builds, Compares & Orders)
Term 1
Term 2
Term 3
N – Build / compare sets / Order sets to 5
Terms – more than / same as
___ to 8
___
___ to 10
___
K – Build / compare sets / Order sets to 5
Terms – more than / greater than / same as
___ to 10
less than
REVIEW
equal to
Gr. 1 - Build / compare sets / Order sets
to 20
___ to 35
___ to 50
Gr. 2 – Build / compare sets / Order sets
to 40
___ to 70
___ to 100
Gr. 3/4 – Build / compare sets / Order
sets to 400
___ to 700
___ to 1000
Edie Carlson
Matheson Island
(N-4 Teacher)
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Attachment 3
Gr. 6 YEAR PLAN
Strand: Number Concepts
1) Uses estimation strategies for determining
quantities
- to 10 000
2) Reads & writes number words
- to 10 000
- to tenths
------------Æ to 100 000
------------Æ to 1 million & beyond
------------Æ to 100 000
------------Æ to hundredths
------------Æ to 1 million & beyond
------------Æ to thousandths
3) Demonstrates an understanding of place
value (concretely, pictorially, symbolically)
- whole nos. and including tenths
------------Æ including hundredths
------------Æ review
4) Compares and orders whole numbers
- to 10 000
------------Æ to 100 000
------------Æ to 1 million & beyond
------------Æ to 10 000
------------Æ review
------------Æ to hundredth
------------Æ to 100 000
------------Æ review
------------Æ review
------------Æ 1-50
------------Æ
------------Æ
------------Æ
------------Æ
- composites and primes
------------Æ 1-100
------------Æ
------------Æ
------------Æ
------------Æ
------------Æ
- prime factorization
5) Rounds numbers
- to 1 000
- to unit
- to tenth
6) No. characteristics
- multiples & factors (1-20)
- common multiples
- LCM
- common factors
- GCF
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TERM PLAN (MULTI-GRADE)
Attachment 4
N/K
Gr. 1
Gr.2
Gr.3
Gr.4
Week 1
Week 2
Week 3
Number Concepts Reading
/ Writing Numerals / No.
Words
Read / Write Numbers up
to 5
Number Concepts Names,
Builds, Compares &
Orders / Ordinals
Build / Compare / Order
sets to 5
Terms – more than /
greater than / same as /
less than
Build / Compare / Order
sets to 20
Number Concepts Place
Value
Read / Write Numbers up
to 10
Read No. Words (poem) up
to 5
Counts with Calculator up
to 20
Read / Write Numbers up
to 140
Reads / Writes No. Words
up to 10
Read / Write Numbers up
to 400
Reads / Writes No. Words
up 40
Read / Write Numbers up
to 4000
Reads / Writes No. Words
up 400
Intro ways to represent
Nos. up to 5
Week 4
Number Concepts No.
Characteristics
Odd/Even/Divisibility
none
Week 5
Week 6
Number Operations
Number Operations
Role play using map up to 5
Role play using map up to 5
Represent Nos. up to 20
Odds / Evens up to 20
Manipulative & Diagrams up
to 10
Manipulative & Diagrams up
to 10
Build / Compare / Order
sets to 40
Represent Nos. up to 40
Place Value (concepts /
pictorially) to 40
Odds / Evens up to 40
Manipulative, Diagrams and
Symbols up to 40
Manipulative, Diagrams and
Symbols up to 40
Build / Compare / Order
sets to 400
Represent Nos. up to 400
Place Value (concepts /
pictorially) to 400
Divisibility by 2’s, 5’s, 10’s
Sort Nos. by Venn Diagram
& Carrol Diagram
*(Do this in Stats/Prob)
Manipulative, Diagrams and
Symbols up to 400
Manipulative, Diagrams and
Symbols up to 400
Manipulative and Diagrams
up to 4000
P.S. (twice a week)
Gr1/2
Gr3/4
Patterns (twice a week)
Stats/Prob.
Survey, Tally, Graph &
Lower level questions every
Friday
-Math facts daily
-Vocab. Every Friday
-Assess every Friday
Manipulative and Diagrams
up to 4000
P.S. (twice a week)
Gr1/2
Gr3/4
Patterns (twice a week)
Stats/Prob.
Survey, Tally, Graph &
Lower level questions every
Friday
-Math facts daily
-Vocab. Every Friday
-Assess every Friday
Ordinals
N/K – none
Gr1 – none
Gr2 – up to 31 calendar
Gr3 – up to 40
Gr4 up to 400
Represent Nos. up to 4000
Place Value (concepts /
pictorially) to 4000
Compares & Orders Nos. up
to 400
Edie Carlson, Matheson Island School
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Term Plan: Grade 3
Attachment 5
Week 1
Aug 26-28
Number Concepts: skip
counting to 100 forward /
backward with random
starting points
Number concepts:
Hundreds chart activities
Number concepts: place
value (ones & tens) up to 100
Week 2
Aug 31 – Sep 4
Week 3
Sep 7-11
Problem Solving: Guess &
Test with addition
Problem Solving: Guess &
Test with subtraction
Patterning: Identify
similarities / differences
among objects. Sort
concretely / pictorially using
2 or more attributes.
Data Analysis: Graphing
pictorial graphs, composition
of tallies, creating questions
Number Concepts: skip
counting forward / backward
to 100 with random starting
points
Number Concepts:
Represents / describes
numbers to 1000 using place
value, greater/less than,
expanded notation
Week 7
Oct 5-9
Problem Solving:
Week 8
Oct 12-16
Problem Solving:
Week 9
Oct 19-23
Problem Solving:
Number Operations:
Addition of 2&3 digit
numbers, no regrouping,
frames
Number Operations:
Subtraction of 2&3 digit
numbers, no regrouping,
frames
Number Operations:
Multiplication of 1&2 digit
numbers with skip counting,
frames
Probability:
Predicts/communicates
chance/probability using
likely/unlikely/unequal
chance
Patterning: continuing a
given pictorial pattern.
Introduce the term CORE
Number Concepts:
Illustrate and explain
fractions (whole, half,
quarter)
Week 4
Sep 14-18
Week 5
Sep 21-25
Problem Solving: Create a
question & picture using
addition
Problem Solving: Create a
question & picture using
subtraction
Shape & Space – Geometry:
Identify / count faces,
vertices, edges of 3D
objects. Compare & Contrast
objects
Patterning: Sort and classify
objects using 2 or more
attributes. Creating venn
diagrams & rules for venn.
Number Concepts:
Represents / describes
numbers to 1000 using place
value, greater/less than,
expanded notation
Week 10
Oct 26-30
Problem Solving:
Number Operations: Division
using skip counting, frames,
Number Concepts:
Recognizes/explains if a
number is divisible by 2
Shape & Space: Capacity –
estimate, measure, compare,
record, order containers by
capacity
Shape & Space: Linear
measurement: selects most
approp. Unit (non/standard),
ordering objects, introduce
perimeter
Week 11
Nov 2-6
Problem Solving:
Number Concepts: Rounding
off numbers to the nearest
ten
Week 6
Sep 28 – Oct 2
Shape & Space: Money –
identify coins and bills to
$20.00. Counting like couns
to $5.00
Shape & Space: Linear
measurement: Selects most
approp. Unit (cm, m, km)
Shape & Space: Identify
common polygons – sides,
corners, angles, type of
lines, symmetry
Week 12
Nov 9-13
Term 1 Exam
Shape & Space: Mapping
using terms front, back, left,
right, description of object
placement
Grade 3, Jack River School
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Attachment 6
WEEKLY PLAN (MULTIGRADE)
Week 1 – Number Concepts (Reading / Writing Nos. / No. Words
Specific Learning
Outcome
Monday August
28, 2000
Tuesday August
29, 2000
Wednesday
August 30, 2000
Thursday August
31, 2000
Friday Sept. 1,
2000
Assessment
N/K Reads / Writes Nos
up to 5
Gr1 Read/Writes Nos up
to 10; No words up to 5
(poems)
Counts with calculator up
to 20
Gr2 Read/Write Nos up
to 40
ReadWrite No. Words up
to 10
Learn Poem – Beehive
Fingers
Write it on chart paper.
Create a structure using
a given No.
Record your structure on
grid paper
Chant “Beehive Fingers”
Sort by number
Have them cut out
pictures showing groups
of up to 5, 10
Chant “Beehive Fingers”
Display train cubes of
various nos. (1-10) In
front of them. Have
them sort into groups
Chant “Beehive Fingers”
Make number books (1-5
(1-1)
Use construction paper.
Find pictures to
correspond with each no.
Teacher makes no. from
plastercine. Stu. make a
set that corresponds
with that no.
Chant “Beehive Fingers”
N/K/1 Roll cube and
make a group of objects
(with one less or one
more than no. shown)
Check list N/K/1
Put 5, 10, 40 objects on a
mat and ask “How many?”
Have them count them.
Check for the following:
says nos 0-40
touches objects
moves objects
counts visually
counts objects to…
Gr3 Rread/Write Nos up
to 400 / No. words up to
40
Gr 3/4 Replace all
number words with
numerals / all numerals
with no. words p.R1
Grade 3/4 Same as
previous day Mon.
p.R5/6
Grade 3/4 Math Test
(Reading & Writing)
Numerals / No. Words
Gr3/4 In your Math
Journal, print 5
sentences using No.
words. Print nos. greater
than 40. Print 5 nos. less
than 35.
Make up 2 no. riddles in
your Math Journal. Print
the next 5 no. words
after 65. Print the next
5 no. words after 39.
Gr 1/2 write nos/words under each activity
Provide a variety of materials – play dough, toothpicks for them to form nos.
Trace nos. on a variety of mediums – finger paint, sandpaper
Use calculator to display a no that answers the teachers’ questions
Grade 3/4 Same as
previous day Mon.
p.R2
Grade 3/4 Same as
previous day Mon.
p.R3/4
Statistics
Problem Solving &
Patterns
Statistics
Patterns (Base Ten
Blocks Job cards) Card 1
Cover the shapes with
ones – blocks and look
for a pattern in the way
the shapes get larger.
Use that pattern to build
the next 2 shapes.
Counting On
Problem Solving
Gr 1/2/3 Guess/Check
Insects in the Garden p6
Gr4 Guess/Check Card
No 4
Patterns (BT,BJ) Card 2
Same Instructions as
Monday
Problem Solving
Gr 1/2/3 Guess/Check
Insects in the Garden p7
Gr4 Guess/Check Card
No 5
Math Facts / Mental
Counting On
Counting On
Counting On
Counting On
Counting On
Computation
Vocabulary digit – 0,1,2,3,4,5,6,7,8, and 9 are digits that are used in our no. system. Any no. can be described or made using these 10 digits. A 1 digit, 2 digit, 3 digit no etc. number.
Numeral – symbols that represent a no. five, 5, 2+3, 8-3 etc.
Number – the idea of quantity ex: 5, you think
© 2001 Frontier School Division No. 48
Attachment 7
Blank Weekly Planning Sheet
(Enlarge to 11” x 17”)
Specific Learning
Outcome
Statistics
Problem Solving
Math Facts /
Mental
Computation
Vocabulary
Manipulatives
Homework
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Monday
Tuesday
Wednesday
Thursday
Friday
Assessment
© 2001 Frontier School Division No. 48
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Attachment 8
3-Point Approach for Words and Concepts
Definition
____________________
____________________
____________________
____________________
____________________
____________________
Word or Concept
Definition
____________________
____________________
____________________
____________________
____________________
____________________
Word or Concept
Definition
____________________
____________________
____________________
____________________
____________________
____________________
Word or Concept
Diagram
Synonym / Example
Diagram
Synonym / Example
Diagram
Synonym / Example
Definition
Word or Concept
Diagram
____________________
____________________
____________________
Synonym / Example
____________________
____________________
____________________
Three-Point Approach: Adapted from Simons, Sandra M. Strategies for Reading
Nonfiction. Copyright ©1991 by Spring Street Press. Used by Permission of the
publisher.
From: Success for All Learners (Manitoba Education & Training)
© 2001 Frontier School Division No. 48
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Attachment 9
17) Geometry (SS-X.1.1)
Grade 1
2 marks
Teacher Note: You can read the words aloud to your students.
Draw a picture for each word.
Word
circle
rectangle
square
triangle
From: Frontier School Division divisional math assessment
It Looks Like
© 2001 Frontier School Division No. 48
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Attachment 10
6)
Vocabulary (Grade 7)
Word
5 marks
It Looks Like
It Means
a.
Acute Angle
- an angle that
measures between
0° and 90°
b.
- the number that
occurs most
frequently in a
set of numbers
Mode
c.
1, 2, 3, 4, 5, 6
d.
Intersecting
Lines
From: Frontier School Division divisional math assessment
- one of the
possible events in
a probability
situation
e.
© 2001 Frontier School Division No. 48
Attachment 11
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© 2001 Frontier School Division No. 48
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Attachment 12
Table 2. Time Guidelines
Type
Frequency
Length
Readiness experiences or strategy activities
1 per week
5-10 minutes
Solving 1-step routine problems
1 per week
5-10 minutes
Solving multiple-step routine problems
1 per week
10-20 minutes
Solving non-routine (process) problems
2 per week
10-20 minutes each
An Instructional Sequence for Process Problems
Week 1
Guess and check
Week 2
Draw a picture
Week 3
Make an organized list
Week 4
Make a table
Week 5
Work backwards
Week 6
Look for a pattern
Week 7
Use logical reasoning
Week 8
Guess and check
Week 9
Draw a picture
Week 10
Make an organized list
Week 11
Make a table
Week 12
Work backwards
Week 13
Look for a pattern
Week 14
Use logical reasoning
Week 15
Week 16
Week 17
The two problems used each week are matched by
solution strategy. Specific hints such as “draw a picture”
accompany problem statements.
The two problems used each week are matched by
solution strategy. General solution strategy hints are
provided.
The two problems used each week are not matched by
solution strategy. Solution strategy hints are not
provided.
From: Teaching Problem Solving: What, Why & How by Randall Charles & Frank Lester
© 2001 Frontier School Division No. 48
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Attachment 13
Readiness Activities For Problem Solving
Grades 1 & 2
- For Grades 1 and 2 children need to do readiness activities. The purpose of these
activities is to build children's confidence and have students form mental images of
stories and matching pictures and stories.
Examples:
• Tell the children to close their eyes. Then read a story problem and tell them to
imagine clearly what is described.
• Give a picture and have the students make up a story that involves addition
(subtraction).
• Give an addition (subtraction) sentence and have the student make up a story.
• Give a story problem and have the students write a similar problem by changing the
setting. For example, if the story is about fish, change it so it's a story about
rabbits.
• Make a list of places where they see numbers (for example, in a store or on the
phone) and discuss what the numbers are used for.
• Tell a story and draw a picture telling the story.
(The above examples are from the book Teaching Problem Solving: What, Why & How
by Randall Charles and Frank Lester.)
© 2001 Frontier School Division No. 48
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Attachment 14
Stages in Problem Solving
People usually work through these 4 stages when solving a problem:
1) Getting to know the problem
- What question is asked?
- What information in the problem is important?
2) Choosing what to do
- Decide on a strategy (plan of action) to use.
3) Trying it out
- Try out the strategy.
- If it doesn't work out, go back to stage 1 or 2.
4) Looking back
- Is the answer reasonable?
- Is it clearly stated?
ACTIVITIES THAT CAN BE USED FOR EACH STAGE
STAGE
ACTIVITY
1) Getting to know the problem.
a) Create a question that can be answered for data that has
been presented.
b) Problems are presented with missing information.
c) Problems are presented containing unnecessary information.
2) Choosing what to do.
a) Decide which operation to use with problems containing no
numbers.
b) Make a simpler problem.
3) Trying it out.
a) Practice solving different problems using a specific strategy.
4) Looking Back
a) Use estimation to determine if the answer given for a
problem is reasonable.
b) A problem and its answer are presented. Use that number in
a statement that answers the question in the problem.
© 2001 Frontier School Division No. 48
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Attachment 15
Problem Solving
A. Routine Problems
•
are 1-step and multiple-step problems that require addition, subtraction,
multiplication and/or division. (E.g., I have 6 cookies. I gave 2 to my
friend. How many do I have left?).
B. Non-Routine Problems
•
•
•
•
•
•
•
•
•
use strategies such as:
guess and check
draw a picture
use objects or act it out
look for a pattern
work backwards
make an organized list
make a table
use logical reasoning
From:
Gr. 1
√
√
√
----√
Gr. 2
√
√
√
----√
Gr. 3
√
√
√
√
√
√
√
√
Gr. 4-8
√
√
-√
√
√
√
√
Teaching Problem Solving - What, Why and How by Randall Charles and
Frank Lester
© 2001 Frontier School Division No. 48
Attachment 16
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Math Facts
1)
Addition strategies
• knows + 0
• knows + 1
• uses these strategies:
- counting on (counts on from largest addend)
- doubles (e.g., 3 + 3, 5 + 5)
- doubles + 1 (or -1) (e.g., 3 + 4, 5 + 6)
- doubles + 2 (or -2) (e.g., 3 + 5, 5 + 7)
- combinations that equal 10 (e.g., 7 + 3, 4 + 6)
- adding 10 to a 1-digit number (e.g., 10 + 6, 10 + 8)
- adding 9 (it's 1 less than adding 10)
- adding 8 (Use 10 as a "bridge." For example, 8 + 5; 8 and 2 are 10, then 3 more is 13)
2)
Subtraction strategies
• uses these strategies:
- counting back
This strategy is used when subtracting small amounts, for example, 10 - 2. The child says
10 to himself and then counts back, "9, 8." The child may need to use fingers to keep
track.
- counting up to subtract
- counting up to subtract
This strategy is used when subtracting larger numbers, for example, 10 - 7. The child
counts up from 7, "8, 9, 10." The child may need to use fingers to keep track.
- using a known addition fact
To solve 7 - 4 = __, think ___ + 4 = 7.
• can write number families (i.e., how addition and subtraction are related):
2+4=6
6-4=2
4+2=6
6-2=4
3)
Multiplication strategies
• uses these strategies:
-x0
-x1
- 2 x (relate to "doubles" in addition)
-5x
• use a helping fact (e.g., If a child knows 3 groups of 6 = 18, then
4 groups of 6 is 6 more.)
- do 3x (it's one group more than 2x)
- then do 4x (it's one group less than 2x or one group more than 3x)
- then do 6x (it's one group more than 5x)
- The only facts that are left now are:
7x7
8x8
9x9
7x8
8x9
7x9
• can write number families (i.e., how multiplication and division are related):
2x4=8
8÷4=2
4x2=8
8÷2=4
4)
Division strategies
• uses these strategies:
- thinks of the corresponding multiplication fact (if a child is trying to figure out 18 ÷ 6, then he
should think, "Six times what is 18.")
© 2001 Frontier School Division No. 48
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Attachment 17
Strand:
Patterns
DATE
Bob A.
Names
patterns
Creates
patterns
Extends
patterns
Predicts
nth step
Sept. 12
Sept. 12
Sept. 19
Sept. 19
9
9
9
{
Lori B.
9
9
9
9
Jack B.
{
9
9
{
{
9
9
9
Shyanne C.
Notes
Makes
complicated
patterns
© 2001 Frontier School Division No. 48
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Attachment 18
Strand:
Notes
DATE