Notes from Math Mapping Meetings July 12 - July 15, 2010...
Math Mapping July 12, 2010 8:00 am - 3:00 pm Present: Michelle Donlon, Carol Kelly, Katrina Rubino, Heidi Racioppo, Robin DePew Christine Williams, Elizabeth Turner Content: What do you want them to know? (“concept”) Skills: What do you want them to do?
Look at each map…
Feedback in general… a list of suggestions…
Content (conceptual statements)
Vocabulary List & Compare to NYS Standards
Skills & compare to NYS Standards
Revisit the Concepts and Skills before you create an assessment.
Do one unit at a time.
Skills that are not in state standards… will not be official assessments in that grade level. This doesn’t mean that that grade level can’t touch upon it.
Everything on these maps is bare minimum. It doesn’t mean that you don’t do more, but don’t do any less.
You can touch on those skills in other areas (science, social studies, calendar time, etc.)
If we find a skill/concept that REALLY is apparent and important in a grade level, but is not in NYS standards, can’t we add it to the consensus map?
Would we assess those skills, even though they are not expected to be mastered until next year? How do we note it on the map? (classify this information as: introduce, develop, mastery, enrichment)
If we put it in the map, we are going to assess it!
The math program is not the curriculum. It’s a resource. The math program goes above and beyond the state standards. There are places it is very basic.
Picture these maps as a “first year teacher” coming into the grade level… Would that person be able to follow the curriculum map and know the necessary content and skills that need to be introduced and mastered & assessed each month?
How accurate are the state’s resources?? (standards and vocabulary) What if they missed something??
For example, some terms appear on the 1st grade list, not on the 2nd grade list, but then reappear on the 3rd grade list. We may want to look at some of those terms… and say, “we want to review these words even though they’re not on the state’s list.” Remember, the list is a suggested list.
Why are we cutting things out that are important for our students and they can and should be doing them?!?! Kindergarten Did they just go through the math book? Is the book driving the mapping train or is the state?
Why is October through January the same exact unit? These concepts and skill should be broken up more.
The Skills aren’t necessarily matching the Standards. There are standards that are not in the skills… too many standards. Look at these areas some more… make sure the skills match the standards.
Content section needs to have “conceptual statements.” October: It looks like the standards are building. Don’t restate the standards previously taught. Just list the “new” standards. Vocabulary not needed in Key Terms: different, same, numbers. Different & same could be classified as “High Frequency” words. Need to add: “as long as” and “longer” to Key Terms list.
Each month… “What’s the new stuff?” Only reflect the new skills in the standards. Only have new standards. Connect the new skills to the new standards… don’t repeat the standards, unless it’s under a new concept/skills.
It’s difficult to “map” kindergarten math because there is a lot of continuous review and repetition throughout the year. October – January: Why are they the same exact units? March/April: What does “explore symmetry” mean? Missing Key Term “after” in list.
The only words missing from KEY TERMS: as long as, longer, after February Add “survey” to KEY TERMS (introduce) 1st Grade Content section needs to have “conceptual statements.”
Vocabulary should be separated one word on a line and in ABC order.
Geometry needs to be looked at. September:
Need to write heading: “Key Terms” (bold and underlined)
Vocabulary: Do we need “pattern unit”? (What is a pattern unit?)
Words that should be RED because they have been previously introduced in Kindergarten:
After
before
Count
Count backwards
Between
Symmetry
Space out your skills with a space between each one… easier to read. J Why is Hexagon & Rhombus a Key Term? October:
“plan” “solve” “check” & “understand” are words that should be listed as “HIGH FREQUENCY” words.
“take away” (Nov.) & “doubles” (January) are not on the NYS suggested list… Check them. Maybe explain why they’re used. January:
Do you need “equal” if you have “equal to”? May:
Take out the Fractions Unit! It’s not in the standards until 3rd grade. J You have “estimate” on the list twice.
Repeat words from the beginning of the year… they should be RED:
Greater than, less than, between, equal to
You have “round” and “regroup” on the list, but they are not on the NYS list.
For “ones” and “tens”… you need to say “ones place” and “tens plans” June:
Repeat words from the beginning of the year… they should be RED:
Addend, difference, estimate, ones place, place value, skip count, sum, tens place, round
For “ones” and “tens”… you need to say “ones place” and “tens plans” Missing Key Terms: Arrange, compose, decompose, decrease, greatest, increase, minus sign, ordinal numbers (1st-20th), plus sign, subtraction fact, flip (reflection), similar, slide (translation), turn (rotation), amount, autumn (fall), calendar, estimation, months of the year, night, seasons in relation to the months, spring, summer, week, winter, year, chart, data. Extra Key Terms (not on NYS list): Plan, solve, check, understand, add, equals, even, compare, count by…, in addition to, more, next to, odd, fact families, take away, pattern unit, regroup, hexagon, rhombus, round, half hour, value, worth, tally, tally chart, data table à “Count by…” should be a skill, not a Key Term November Add “survey” to KEY TERMS as a red review word. Tomorrow: Review 2nd grade map… Correct the content statements and re-organize the units.
Look at key terms closely… color code them. Make sure the content statements/skills/standards are matched.
Then… take a look at assessments. Math Mapping July 13, 2010 8:00 am - 3:00 pm Present: Katrina Rubino, Heidi Racioppo, Robin DePew Christine Williams, Elizabeth Turner, Angela Rion 2nd Grade Need to look at multiplication/division readiness by repeated addition, repeated subtraction and fair share. 2.N.1, 2.N.2, 2.N.3, 2.N.4, 2.N.20, 2.N.21
Geometry really has to get looked at. 3-D shapes are in 1st grade (cone, cube, cylinder), but nothing in 2nd grade.
Addition Strategies: doubles, doubles + 1, near doubles, make 10, count on, Should we have: making teens, add 9… 3rd grade is going to introduce.
Need to reorganize units across the 10 months.
Need to revise the key terms.
Need to add in content statements.
Need to check that skills reflect content and the standards reflect content and skills. (all inter-related)
Unit assessments are recommended to be done after each unit. TIME: K – introduce hour
1st – hour and ½ hour
2nd – 5 minute interval
3rd – ¼ hour and nearest minute
4th – review all time and elapsed time FACTS! Daily fact practice in every grade! We can’t just spend one month on it and expect the kids to remember those facts several months later. It needs to be constantly revisited and practiced. J 2nd grade… addition and subtraction
3rd grade… addition & subtraction and multiplication & division
4th grade… multiplication & division 2nd grade… subtract 2-digit numbers with regrouping Problem Solving Strategies When do we introduce problem solving strategies?
How do we reflect that in the curriculum map?
Should we have PROBLEM SOLVING STRATEGIES as a separate heading under CONTENT or under SKILLS? Key Terms would reflect the problem solving strategies.
CONTENT
KEY TERMS
HIGH FREQUENCY WORDS
PROBLEM SOLVING STRATEGIES
Restructuring math in the classroom…
Have two different times of the day for math…
in the morning à introduce new math concepts…
in the afternoon à have a “fun” math lab to review previously taught math skills.
Have mixed groups. Use teams of classes to specialize in different skills. When we feel like the curriculum is too easy or watered down, think…
Can these kids do it and do it well?
We want to make sure we build STRONG basic skills before moving on to more difficult concepts!
It’s developmental philosophy.
Are we aligned to neighboring schools’ maps? How are we the same? How are we different?
Divide curriculum map into sub-units. Each new content gets its own “sub-unit”.
Where would KEY TERMS go?
Be aware of using the proper terminology of NYS standards language when creating your skills, content, and essential questions.
Color-coding and bold facing is helping us to organize our maps.
BOLD à any key terms that has been taught that year in previous units.
RED à review taught in previous years.
PINK à things that have been changed and want to check with math cabinet
PURPLE à things that need to be looked at (notations were made in parentheses)
GREEN à high frequency words
TOMORROW:
2nd grade: finish updating key terms, content, skills, standards (start with February)
Then get to work on assessments.
Math Mapping July 14, 2010
8:00 am - 3:00 pm
Present: Katrina Rubino, Heidi Racioppo, Robin DePew, Christine Williams, Angela Rion, Michelle Donlon, Sue Gillis
Good resource:http://nylearns.org/ PROBLEM SOLVING: 2nd, 5th, 7th grade is going to need to add in problem solving skills throughout the map. 3rd grade has been putting in problem solving strategies in the content, skills, and included PS standards.
All of the other strands also need to be put into maps… Reasoning and Proof; Communication; Connections; and Representation Strands.
We need to look at the specific problem solving strategies and when they’re going to be introduced throughout the year as well as across grade levels. (act it out, draw a picture, use a number sentence, find a pattern, trial and error, guess and check, process of elimination, logic, etc.)
How do we progress from simple facts to more complex larger numbers?
How do we help the students decide which math computation to use.
How do we build the skills to multiple step problem solving at the end of 3rd grade?
Each time a new operation is introduced, the problem solving strategies that are best used need to be reviewed with that new operation. GEOMETRY: This was a tricky topic… We had a big discussion about geometry as to when and where we should have particular skills at each grade level, specifically between 2nd and 3rd while relating it to skills in K, 1, and 4.
2nd grade NYS standards do not mention 2-D shapes… However, 3-D figures are on NYS standards for kindergarten and 1st grade. So these are all review in 2nd grade. Concepts that are new for 2nd grade: regular figures, irregular figures, compose, decompose, line symmetry, & properties.
CONTENT STATEMENTS vs. BIG IDEA
What are we calling 2nd Grade: When using Math Connects as a resource… SKIP chapters 9, 10, & 14. These chapters could be used as enrichment.
Finished tweaking each month… relating content, key terms, skills, and standards… Even added in the corresponding chapters from the Math Connects program.
Next steps: Need to add in problem solving skills and eventually the other process strands. Need to add content statements to most units.
5th grade… finished vocabulary for whole school year. Physically realigned the maps
3rd grade… Dec-June… went through key terms, organized them and color coded them; added content statements to most months.
Kindergarten… began to update mapping. Will do more work.
Math Mapping July 15, 2010 8:00 am - 3:00 pm Present: Christine Williams, Robin DePew, Katrina Rubino, Michelle Donlon, Jackie VanNosdall, Elizabeth Turner Tech Paths is down this morning… So… Robin and Christine are working on problem solving strategies in 2nd & 3rd grade. Katrina decided to leave. Problem Solving: ** All grade levels should adopt the 4-step plan from Math Connects. (Understand, Plan, Solve, Check) It’s a common plan with common vocabulary. There should be a chart and it should be posted in the room. Problem solving is MORE than just looking for key words. There are multiple strategies that could be used for solving problem solving. Possible format for problem solving assessment:
Underline the question sentence. (1/2 point)
Circle the important information with labels. (1/2 point)
Name the strategy. (1 point)
Show their work. (2 points & needs to match the stated strategy)
Put a box around the answer. (1 point for correct answer)
Have an area with manipulatives out for the students to use if needed. J We feel there should be a quarterly problem solving assessment. We went through and updated a 1st quarter 3rd grade problem solving assessment. Next Steps: develop benchmark problem solving assessments for each grade/each quarter. Why do we need to learn computation? To help transition to larger numbers in word problems… First, use single-digits in word problems. Then have the students replace the single-digit, with 2-digit numbers and have them solve it again with bigger numbers. Talk to students about how certain strategies are quicker and more efficient than others. Act it out and draw a picture may not work because it is too time consuming and allows for more error… Where using a number sentence will solve that problem. We are matching language from state standards with the state’s list of vocabulary words and cross referencing that with the Math Connects program to make a list of problem solving strategies for each grade level K-4. Problem Solving Strategies Kindergarten: {Possible Skills: Explore Guesses}
Act it Out
Use Manipulatives
Draw a Picture
1st Grade: {Possible Skills: explore guesses, use trial and error, model with manipulatives}
Act it Out
Use Manipulatives
Draw a Picture
2nd Grade:
Logical Reasoning
Act it Out with Manipulatives
Draw a Picture
Guess & Check (Trial and Error)
Use a Number Sentence
Look for a Pattern
3rd Grade:
Logical Reasoning
Act it Out with Manipulatives
Draw a Picture/Diagram
Guess & Check/Trial and Error
Write a Number Sentence
Look for a Pattern
Make a Table/Chart
Make an Organized List (combinations)
Process of Elimination (multiple choices)
4th Grade:
Logical Reasoning
Act it Out with Manipulatives
Draw a Picture/Diagram
Guess & Check/Trial and Error
Write a Number Sentence
Look for a Pattern
Make a Table/Chart
Make an Organized List (combinations)
Process of Elimination (multiple choices)
3.CM.1 “Understand and explain how to organize their thought process.” This is the reason we kept Logical Reasoning as a problem solving strategy in 2nd grade and up. NYS says “Chart”… Math Connects says “Table” Common vocabulary is good, but not always appropriate… The vocabulary has to grow with the kids. It’s not age appropriate for little kids to say those big words. When new terms/vocabulary is introduced, it should be noted what the “younger” term is and now what the “older” term is. Language needs to grow with our children. 2nd Grade: Looking at the problem solving strategies list above… Go through math map and take out certain problem solving strategy lessons from math book. (Problem Solving Lessons to take out: 1-3, 4-4, 5-3; Remember, we are not using Chapters 9, 10, nor 14 at all.) Conclusion: Tech Paths did come back on line, however, we had a much richer discussion through the process of looking at the problem solving strategies. We took a lot of time to look at the NYS Standards, NYS vocabulary, and the resources from the Math Connects curriculum. This process helped us to develop the problem solving continuum K-4. Next Steps: Add the problem solving strategies, skills, and standards into the maps. Work on common benchmark assessments for each unit and quarter in each grade level. We need to discuss… Skills based unit assessments as well as quarterly problem solving assessments. The skills based assessments could include problem solving questions, but the quarterly problem solving assessment would be more specific to the problem solving strategies that are being used. The focus of the quarterly assessment could be problem solving strategies. The focus of the unit assessment could be more skills based, specific to the content of the unit. We should also talk about the type of assessments we use. (pencil and paper, performance task, etc.)
Math Mapping
July 12, 2010
8:00 am - 3:00 pm
Present: Michelle Donlon, Carol Kelly, Katrina Rubino, Heidi Racioppo, Robin DePew Christine Williams, Elizabeth Turner
Content: What do you want them to know? (“concept”)
Skills: What do you want them to do?
Look at each map…
Revisit the Concepts and Skills before you create an assessment.
Do one unit at a time.
Skills that are not in state standards… will not be official assessments in that grade level. This doesn’t mean that that grade level can’t touch upon it.
Everything on these maps is bare minimum. It doesn’t mean that you don’t do more, but don’t do any less.
You can touch on those skills in other areas (science, social studies, calendar time, etc.)
If we find a skill/concept that REALLY is apparent and important in a grade level, but is not in NYS standards, can’t we add it to the consensus map?
Would we assess those skills, even though they are not expected to be mastered until next year? How do we note it on the map? (classify this information as: introduce, develop, mastery, enrichment)
If we put it in the map, we are going to assess it!
The math program is not the curriculum. It’s a resource. The math program goes above and beyond the state standards. There are places it is very basic.
Picture these maps as a “first year teacher” coming into the grade level… Would that person be able to follow the curriculum map and know the necessary content and skills that need to be introduced and mastered & assessed each month?
How accurate are the state’s resources?? (standards and vocabulary) What if they missed something??
For example, some terms appear on the 1st grade list, not on the 2nd grade list, but then reappear on the 3rd grade list. We may want to look at some of those terms… and say, “we want to review these words even though they’re not on the state’s list.” Remember, the list is a suggested list.
Why are we cutting things out that are important for our students and they can and should be doing them?!?!
Kindergarten
Did they just go through the math book? Is the book driving the mapping train or is the state?
Why is October through January the same exact unit? These concepts and skill should be broken up more.
The Skills aren’t necessarily matching the Standards. There are standards that are not in the skills… too many standards. Look at these areas some more… make sure the skills match the standards.
Content section needs to have “conceptual statements.”
October: It looks like the standards are building. Don’t restate the standards previously taught. Just list the “new” standards. Vocabulary not needed in Key Terms: different, same, numbers. Different & same could be classified as “High Frequency” words. Need to add: “as long as” and “longer” to Key Terms list.
Each month… “What’s the new stuff?” Only reflect the new skills in the standards. Only have new standards. Connect the new skills to the new standards… don’t repeat the standards, unless it’s under a new concept/skills.
It’s difficult to “map” kindergarten math because there is a lot of continuous review and repetition throughout the year.
October – January: Why are they the same exact units?
March/April: What does “explore symmetry” mean? Missing Key Term “after” in list.
The only words missing from KEY TERMS: as long as, longer, after
February
Add “survey” to KEY TERMS (introduce)
1st Grade
Content section needs to have “conceptual statements.”
Vocabulary should be separated one word on a line and in ABC order.
Geometry needs to be looked at.
September:
Need to write heading: “Key Terms” (bold and underlined)
Vocabulary: Do we need “pattern unit”? (What is a pattern unit?)
Words that should be RED because they have been previously introduced in Kindergarten:
- After
- before
- Count
- Count backwards
- Between
- Symmetry
Space out your skills with a space between each one… easier to read. JWhy is Hexagon & Rhombus a Key Term?
October:
“plan” “solve” “check” & “understand” are words that should be listed as “HIGH FREQUENCY” words.
“take away” (Nov.) & “doubles” (January) are not on the NYS suggested list… Check them. Maybe explain why they’re used.
January:
Do you need “equal” if you have “equal to”?
May:
Take out the Fractions Unit! It’s not in the standards until 3rd grade. J
You have “estimate” on the list twice.
Repeat words from the beginning of the year… they should be RED:
Greater than, less than, between, equal to
You have “round” and “regroup” on the list, but they are not on the NYS list.
For “ones” and “tens”… you need to say “ones place” and “tens plans”
June:
Repeat words from the beginning of the year… they should be RED:
Addend, difference, estimate, ones place, place value, skip count, sum, tens place, round
For “ones” and “tens”… you need to say “ones place” and “tens plans”
Missing Key Terms:
Arrange, compose, decompose, decrease, greatest, increase, minus sign, ordinal numbers (1st-20th), plus sign, subtraction fact, flip (reflection), similar, slide (translation), turn (rotation), amount, autumn (fall), calendar, estimation, months of the year, night, seasons in relation to the months, spring, summer, week, winter, year, chart, data.
Extra Key Terms (not on NYS list):
Plan, solve, check, understand, add, equals, even, compare, count by…, in addition to, more, next to, odd, fact families, take away, pattern unit, regroup, hexagon, rhombus, round, half hour, value, worth, tally, tally chart, data table
à “Count by…” should be a skill, not a Key Term
November
Add “survey” to KEY TERMS as a red review word.
Tomorrow:
Review 2nd grade map… Correct the content statements and re-organize the units.
Look at key terms closely… color code them. Make sure the content statements/skills/standards are matched.
Then… take a look at assessments.
Math Mapping
July 13, 2010
8:00 am - 3:00 pm
Present: Katrina Rubino, Heidi Racioppo, Robin DePew Christine Williams, Elizabeth Turner, Angela Rion
2nd Grade
Need to look at multiplication/division readiness by repeated addition, repeated subtraction and fair share. 2.N.1, 2.N.2, 2.N.3, 2.N.4, 2.N.20, 2.N.21
Geometry really has to get looked at. 3-D shapes are in 1st grade (cone, cube, cylinder), but nothing in 2nd grade.
Addition Strategies: doubles, doubles + 1, near doubles, make 10, count on,
Should we have: making teens, add 9… 3rd grade is going to introduce.
Need to reorganize units across the 10 months.
Need to revise the key terms.
Need to add in content statements.
Need to check that skills reflect content and the standards reflect content and skills. (all inter-related)
Unit assessments are recommended to be done after each unit.
TIME:
K – introduce hour
1st – hour and ½ hour
2nd – 5 minute interval
3rd – ¼ hour and nearest minute
4th – review all time and elapsed time
FACTS!
Daily fact practice in every grade! We can’t just spend one month on it and expect the kids to remember those facts several months later. It needs to be constantly revisited and practiced. J
2nd grade… addition and subtraction
3rd grade… addition & subtraction and multiplication & division
4th grade… multiplication & division
2nd grade… subtract 2-digit numbers with regrouping
Problem Solving Strategies
When do we introduce problem solving strategies?
How do we reflect that in the curriculum map?
Should we have PROBLEM SOLVING STRATEGIES as a separate heading under CONTENT or under SKILLS? Key Terms would reflect the problem solving strategies.
CONTENT
KEY TERMS
HIGH FREQUENCY WORDS
PROBLEM SOLVING STRATEGIES
Restructuring math in the classroom…
Have two different times of the day for math…
- in the morning à introduce new math concepts…
- in the afternoon à have a “fun” math lab to review previously taught math skills.
Have mixed groups. Use teams of classes to specialize in different skills.When we feel like the curriculum is too easy or watered down, think…
- Can these kids do it and do it well?
- We want to make sure we build STRONG basic skills before moving on to more difficult concepts!
- It’s developmental philosophy.
Are we aligned to neighboring schools’ maps? How are we the same? How are we different?Divide curriculum map into sub-units. Each new content gets its own “sub-unit”.
Where would KEY TERMS go?
Be aware of using the proper terminology of NYS standards language when creating your skills, content, and essential questions.
Color-coding and bold facing is helping us to organize our maps.
BOLD à any key terms that has been taught that year in previous units.
RED à review taught in previous years.
PINK à things that have been changed and want to check with math cabinet
PURPLE à things that need to be looked at (notations were made in parentheses)
GREEN à high frequency words
TOMORROW:
2nd grade: finish updating key terms, content, skills, standards (start with February)
Then get to work on assessments.
Math Mapping
July 14, 2010
8:00 am - 3:00 pm
Present: Katrina Rubino, Heidi Racioppo, Robin DePew, Christine Williams, Angela Rion, Michelle Donlon, Sue Gillis
Good resource: http://nylearns.org/
PROBLEM SOLVING:
2nd, 5th, 7th grade is going to need to add in problem solving skills throughout the map. 3rd grade has been putting in problem solving strategies in the content, skills, and included PS standards.
All of the other strands also need to be put into maps… Reasoning and Proof; Communication; Connections; and Representation Strands.
We need to look at the specific problem solving strategies and when they’re going to be introduced throughout the year as well as across grade levels. (act it out, draw a picture, use a number sentence, find a pattern, trial and error, guess and check, process of elimination, logic, etc.)
How do we progress from simple facts to more complex larger numbers?
How do we help the students decide which math computation to use.
How do we build the skills to multiple step problem solving at the end of 3rd grade?
Each time a new operation is introduced, the problem solving strategies that are best used need to be reviewed with that new operation.
GEOMETRY:
This was a tricky topic… We had a big discussion about geometry as to when and where we should have particular skills at each grade level, specifically between 2nd and 3rd while relating it to skills in K, 1, and 4.
2nd grade NYS standards do not mention 2-D shapes… However, 3-D figures are on NYS standards for kindergarten and 1st grade. So these are all review in 2nd grade. Concepts that are new for 2nd grade: regular figures, irregular figures, compose, decompose, line symmetry, & properties.
CONTENT STATEMENTS vs. BIG IDEA
What are we calling
2nd Grade:
When using Math Connects as a resource… SKIP chapters 9, 10, & 14. These chapters could be used as enrichment.
Finished tweaking each month… relating content, key terms, skills, and standards… Even added in the corresponding chapters from the Math Connects program.
Next steps: Need to add in problem solving skills and eventually the other process strands. Need to add content statements to most units.
5th grade… finished vocabulary for whole school year. Physically realigned the maps
3rd grade… Dec-June… went through key terms, organized them and color coded them; added content statements to most months.
Kindergarten… began to update mapping. Will do more work.
Math Mapping
July 15, 2010
8:00 am - 3:00 pm
Present: Christine Williams, Robin DePew, Katrina Rubino, Michelle Donlon, Jackie VanNosdall, Elizabeth Turner
Tech Paths is down this morning… So… Robin and Christine are working on problem solving strategies in 2nd & 3rd grade. Katrina decided to leave.
Problem Solving: **
All grade levels should adopt the 4-step plan from Math Connects. (Understand, Plan, Solve, Check) It’s a common plan with common vocabulary. There should be a chart and it should be posted in the room.
Problem solving is MORE than just looking for key words. There are multiple strategies that could be used for solving problem solving.
Possible format for problem solving assessment:
- Underline the question sentence. (1/2 point)
- Circle the important information with labels. (1/2 point)
- Name the strategy. (1 point)
- Show their work. (2 points & needs to match the stated strategy)
- Put a box around the answer. (1 point for correct answer)
Have an area with manipulatives out for the students to use if needed. JWe feel there should be a quarterly problem solving assessment. We went through and updated a 1st quarter 3rd grade problem solving assessment. Next Steps: develop benchmark problem solving assessments for each grade/each quarter.
Why do we need to learn computation?
To help transition to larger numbers in word problems… First, use single-digits in word problems. Then have the students replace the single-digit, with 2-digit numbers and have them solve it again with bigger numbers.
Talk to students about how certain strategies are quicker and more efficient than others. Act it out and draw a picture may not work because it is too time consuming and allows for more error… Where using a number sentence will solve that problem.
We are matching language from state standards with the state’s list of vocabulary words and cross referencing that with the Math Connects program to make a list of problem solving strategies for each grade level K-4.
Problem Solving Strategies
Kindergarten: {Possible Skills: Explore Guesses}
- Act it Out
- Use Manipulatives
- Draw a Picture
1st Grade: {Possible Skills: explore guesses, use trial and error, model with manipulatives}- Act it Out
- Use Manipulatives
- Draw a Picture
2nd Grade:- Logical Reasoning
- Act it Out with Manipulatives
- Draw a Picture
- Guess & Check (Trial and Error)
- Use a Number Sentence
- Look for a Pattern
3rd Grade:- Logical Reasoning
- Act it Out with Manipulatives
- Draw a Picture/Diagram
- Guess & Check/Trial and Error
- Write a Number Sentence
- Look for a Pattern
- Make a Table/Chart
- Make an Organized List (combinations)
- Process of Elimination (multiple choices)
4th Grade:3.CM.1 “Understand and explain how to organize their thought process.” This is the reason we kept Logical Reasoning as a problem solving strategy in 2nd grade and up.
NYS says “Chart”… Math Connects says “Table”
Common vocabulary is good, but not always appropriate… The vocabulary has to grow with the kids. It’s not age appropriate for little kids to say those big words. When new terms/vocabulary is introduced, it should be noted what the “younger” term is and now what the “older” term is. Language needs to grow with our children.
2nd Grade: Looking at the problem solving strategies list above… Go through math map and take out certain problem solving strategy lessons from math book. (Problem Solving Lessons to take out: 1-3, 4-4, 5-3; Remember, we are not using Chapters 9, 10, nor 14 at all.)
Conclusion:
Tech Paths did come back on line, however, we had a much richer discussion through the process of looking at the problem solving strategies. We took a lot of time to look at the NYS Standards, NYS vocabulary, and the resources from the Math Connects curriculum. This process helped us to develop the problem solving continuum K-4.
Next Steps:
Add the problem solving strategies, skills, and standards into the maps.
Work on common benchmark assessments for each unit and quarter in each grade level.
We need to discuss… Skills based unit assessments as well as quarterly problem solving assessments. The skills based assessments could include problem solving questions, but the quarterly problem solving assessment would be more specific to the problem solving strategies that are being used. The focus of the quarterly assessment could be problem solving strategies. The focus of the unit assessment could be more skills based, specific to the content of the unit.
We should also talk about the type of assessments we use. (pencil and paper, performance task, etc.)