guide to spiral planning · guide to spiral planning. gay sul, ... the focus then becomes to add to...

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 1 of 29

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.)


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.


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.


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 ----- 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).


- 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.


- 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.


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.


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


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.


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.


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 3-Point Approach for Words and Concepts

19

9 Vocabulary Chart Grade 1 20

10 Vocabulary Chart Grade 7 21

11 Math Journal Question Samples 22

12 Problem Solving Program Sample 23

13 Readiness Activities for Problem Solving

24

14 Stages and Activities in Problem Solving

25

15 Routine and Non-Routine Problem Solving

26

16 Math Facts Thinking Strategies 27

17 Sample Checklist 28

18 Blank Checklist 29

© 2001 Frontier School Division No. 48 12 of 29 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

___ to 15 ___ to 10

___ to 20 REVIEW

Gr. 2 – Read / Write Numerals up to 40 Read / Write Number Words up to 10

___ to 70 ___ to 15

___ to 100 ___ to 20


___ to 700 ___ to 70

___ to 1000 ___ to 100


___ to 7000 ___ to 700

___ to 10000 ___ to 1000

Edie Carlson Matheson Island (N-4 Teacher)


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)


Attachment 3 Gr. 6 YEAR PLAN

Strand: Number Concepts

1) Uses estimation strategies for determining quantities

- to 10 000

------------ to 100 000

------------ to 1 million & beyond

2) Reads & writes number words - to 10 000 - to tenths

------------ to 100 000 ------------ to hundredths

------------ to 1 million & beyond ------------ to thousandths

3) Demonstrates an understanding of place value (concretely, pictorially, symbolically)

- whole nos. and including tenths

------------ including hundredths

------------ review

4) Compares and orders whole numbers - to 10 000

------------ to 100 000

------------ to 1 million & beyond

5) Rounds numbers - to 1 000 - to unit - to tenth

------------ to 10 000 ------------ review ------------ to hundredth

------------ to 100 000 ------------ review ------------ review

6) No. characteristics - multiples & factors (1-20) - common multiples - LCM - common factors - GCF

------------ 1-50 ------------ ------------ ------------ ------------

- composites and primes

------------ 1-100 ------------ ------------ ------------ ------------ ------------ - prime factorization


Attachment 4 TERM PLAN (MULTI-GRADE) Week 1 Week 2 Week 3 Week 4 Week 5 Week 6

Number Concepts Reading / Writing Numerals / No.

Words

Number Concepts Names, Builds, Compares & Orders / Ordinals

Number Concepts Place Value

Number Concepts No. Characteristics

Odd/Even/Divisibility

Number Operations Number Operations

N/K Read / Write Numbers up to 5

Build / Compare / Order sets to 5 Terms – more than / greater than / same as / less than

Intro ways to represent Nos. up to 5

none Role play using map up to 5 Role play using map up to 5

Gr. 1 Read / Write Numbers up to 10 Read No. Words (poem) up to 5 Counts with Calculator up to 20

Build / Compare / Order sets to 20

Represent Nos. up to 20 Odds / Evens up to 20 Manipulative & Diagrams up to 10

Manipulative & Diagrams up to 10

Gr.2 Read / Write Numbers up to 140 Reads / Writes No. Words 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

Gr.3 Read / Write Numbers up to 400 Reads / Writes No. Words up 40

Represent Nos. up to 400 Place Value (concepts / pictorially) to 400



Gr.4 Read / Write Numbers up to 4000 Reads / Writes No. Words up 400

Build / Compare / Order sets to 400 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

Divisibility by 2’s, 5’s, 10’s Sort Nos. by Venn Diagram & Carrol Diagram *(Do this in Stats/Prob)

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

Edie Carlson, Matheson Island School


Attachment 5 Term Plan: Grade 3 Week 1

Aug 26-28 Week 2

Aug 31 – Sep 4 Week 3

Sep 7-11 Week 4

Sep 14-18 Week 5

Sep 21-25 Week 6

Sep 28 – Oct 2 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

Problem Solving: Guess & Test with addition Patterning: Identify similarities / differences among objects. Sort concretely / pictorially using 2 or more attributes. Number Concepts: skip counting forward / backward to 100 with random starting points

Problem Solving: Guess & Test with subtraction Data Analysis: Graphing pictorial graphs, composition of tallies, creating questions Number Concepts: Represents / describes numbers to 1000 using place value, greater/less than, expanded notation

Problem Solving: Create a question & picture using addition Shape & Space – Geometry: Identify / count faces, vertices, edges of 3D objects. Compare & Contrast objects Number Concepts: Represents / describes numbers to 1000 using place value, greater/less than, expanded notation

Problem Solving: Create a question & picture using subtraction Patterning: Sort and classify objects using 2 or more attributes. Creating venn diagrams & rules for venn. Shape & Space: Linear measurement: selects most approp. Unit (non/standard), ordering objects, introduce perimeter

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 7 Oct 5-9

Week 8 Oct 12-16

Week 9 Oct 19-23

Week 10 Oct 26-30

Week 11 Nov 2-6

Week 12 Nov 9-13

Problem Solving: Number Operations: Addition of 2&3 digit numbers, no regrouping, frames Probability: Predicts/communicates chance/probability using likely/unlikely/unequal chance

Problem Solving: Number Operations: Subtraction of 2&3 digit numbers, no regrouping, frames Patterning: continuing a given pictorial pattern. Introduce the term CORE

Problem Solving: Number Operations: Multiplication of 1&2 digit numbers with skip counting, frames Number Concepts: Illustrate and explain fractions (whole, half, quarter)

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

Problem Solving: Number Concepts: Rounding off numbers to the nearest ten Shape & Space: Mapping using terms front, back, left, right, description of object placement

Term 1 Exam

Grade 3, Jack River School


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

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.

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 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

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.R2

Grade 3/4 Same as previous day Mon. p.R3/4

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.

Statistics Statistics 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.

Problem Solving & Patterns

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.

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 Computation

Counting On Counting On Counting On Counting On Counting On Counting On

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


Attachment 7 Blank Weekly Planning Sheet (Enlarge to 11” x 17”) Specific Learning

Outcome Monday Tuesday Wednesday Thursday Friday Assessment

Statistics

Problem Solving

Math Facts / Mental Computation

Vocabulary

Manipulatives

Homework


Attachment 8 3-Point Approach for Words and Concepts

Word or Concept

Definition ____________________ ____________________ ____________________ ____________________ ____________________ ____________________

Synonym / Example

Diagram

Word or Concept

Definition ____________________ ____________________ ____________________ ____________________ ____________________ ____________________

Synonym / Example

Diagram

Word or Concept

Definition ____________________ ____________________ ____________________ ____________________ ____________________ ____________________

Synonym / Example

Diagram

Word or Concept

Definition ____________________ ____________________ ____________________ ____________________ ____________________ ____________________

Synonym / Example

Diagram

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)


Attachment 9 Grade 1 17) Geometry (SS-X.1.1) 2 marks

Teacher Note: You can read the words aloud to your students.

Draw a picture for each word.

Word It Looks Like

circle

rectangle

square

triangle

From: Frontier School Division divisional math assessment


Attachment 10 6) Vocabulary (Grade 7) 5 marks

Word It Looks Like It Means

Acute Angle

a.

- an angle that measures between 0° and 90°

Mode

b. - the number that occurs most frequently in a set of numbers

c.

1, 2, 3, 4, 5, 6

- one of the possible events in a probability situation

Intersecting

Lines

d. e.

From: Frontier School Division divisional math assessment


Attachment 11


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

The two problems used each week are matched by solution strategy. Specific hints such as “draw a picture” accompany problem statements.

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

The two problems used each week are matched by solution strategy. General solution strategy hints are provided.

Week 15

Week 16

Week 17

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


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.)


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

a) Create a question that can be answered for data that has

been presented. b) Problems are presented with missing information.

1) Getting to know the problem.

c) Problems are presented containing unnecessary information. a) Decide which operation to use with problems containing no

numbers. 2) Choosing what to do.

b) Make a simpler problem.

3) Trying it out. a) Practice solving different problems using a specific strategy. a) Use estimation to determine if the answer given for a

problem is reasonable. 4) Looking Back

b) A problem and its answer are presented. Use that number in a statement that answers the question in the problem.


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:

Gr. 1 Gr. 2 Gr. 3 Gr. 4-8 • 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: Teaching Problem Solving - What, Why and How by Randall Charles and

Frank Lester


Attachment 16 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: - x 0 - x 1 - 2 x (relate to "doubles" in addition) - 5 x • 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:

7 x 7 8 x 8 9 x 9 7 x 8 8 x 9 7 x 9

• can write number families (i.e., how multiplication and division are related): 2 x 4 = 8 8 ÷ 4 = 2 4 x 2 = 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.")


Attachment 17

Strand: Patterns

Names patterns

Creates patterns

Extends patterns

Predicts nth step

Notes

DATE Sept. 12 Sept. 12 Sept. 19 Sept. 19

Bob A.

Lori B. Makes

complicated patterns

Jack B.

Shyanne C.


Attachment 18

Strand:

Notes

DATE

guide to spiral planning · guide to spiral planning. gay sul, ... the focus then becomes to add to...

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