How can I get started with Math Circles?
Part 1: General Preview of Math Circles
Generally pre-assess students knowledge of math vocabulary and problem solving strategies. This can be used as a post assessment at a later date to see if students are building general fluency in math vocabulary and internalizing basic D.I.C.E. problem solving strategies. Use this general fluency assessment.
Lesson 1: Introduce word problems
What is a word problem? (incorporate into morning message)
Can you think of a word problem?
How do you solve a word problem?
When do you need to solve word problems in your everyday life? In the classroom? (i.e. attendance – how many people are absent today?) Can you think of a word problem that you recently solved as a class?
Emphasize that math is a language that has a dictionary (math vocabulary words). Have students generate a list of math concepts that they have covered (either this year or in the past). If you are using a specific math program, use the given supplemental resource available (i.e. for Everyday Math the Student Reference Book, or a math glossary that accompanies the program).
Part 2: Introduce steps in problem solving
1. Predicting: what is this problem about? - Sometimes I will present the beginning of a word problem and cover the question, and then have students predict what the question may be. It is interesting to see how students identify clues to make strong predictions.
2. Questioning: what do I need to know to solve this? This speaks to the ability to infer what math concept is embedded in the language of the word problem.
3. Number model: How do students represent the words in abstract math symbols (numbers and signs)
4. Summarizing: double-checking the answer to make sure that it makes sense
** Note that these steps overlap with reading strategies that you may be using with your students - thus, another opportunity to help students understand that solving word problems requires focus, attention, and inferential thinking.
Part 3: Introduce Math Circles and the roles (one at a time)
Lesson 1: Whole group math circle - Detective
A conversation
Show the template (have it large to use with the class) - I like to make an actual template that I can place on my board and use to model whole group problems. You can also use this template on a smartboard, etc.
Start with vocabulary
- prepare sheets with math problems and multiple choice math vocab words and have them match vocabulary with the problems
- write down the clues that often accompany specific math operations
Lesson 2: Illustrator
Practice sheets - matching the illustration with the word problem to model the kinds of drawing that kids might use
Show how manipulatives can be used to help develop the illustration with hands on materials
Lesson 3: Calculator
Practice sheets - have students match number sentences with word problems
Talk about number sentences - how they are important and reinforce place value, math facts, etc. - key concepts in computation.
Lesson 4: Editor
Practice sheets - have word problems presented in D.I.C.E. that have an incorrect illustration, number sentence that does not match the word problem, or an answer without units and have the students locate and correct the mistake.
Part 1: General Preview of Math Circles
Generally pre-assess students knowledge of math vocabulary and problem solving strategies. This can be used as a post assessment at a later date to see if students are building general fluency in math vocabulary and internalizing basic D.I.C.E. problem solving strategies. Use this general fluency assessment.
Lesson 1: Introduce word problems
What is a word problem? (incorporate into morning message)
Can you think of a word problem?
How do you solve a word problem?
When do you need to solve word problems in your everyday life? In the classroom? (i.e. attendance – how many people are absent today?) Can you think of a word problem that you recently solved as a class?
Emphasize that math is a language that has a dictionary (math vocabulary words). Have students generate a list of math concepts that they have covered (either this year or in the past). If you are using a specific math program, use the given supplemental resource available (i.e. for Everyday Math the Student Reference Book, or a math glossary that accompanies the program).
Part 2: Introduce steps in problem solving
1. Predicting: what is this problem about? - Sometimes I will present the beginning of a word problem and cover the question, and then have students predict what the question may be. It is interesting to see how students identify clues to make strong predictions.
2. Questioning: what do I need to know to solve this? This speaks to the ability to infer what math concept is embedded in the language of the word problem.
3. Number model: How do students represent the words in abstract math symbols (numbers and signs)
4. Summarizing: double-checking the answer to make sure that it makes sense
** Note that these steps overlap with reading strategies that you may be using with your students - thus, another opportunity to help students understand that solving word problems requires focus, attention, and inferential thinking.
Part 3: Introduce Math Circles and the roles (one at a time)
Lesson 1: Whole group math circle - Detective
A conversation
Show the template (have it large to use with the class) - I like to make an actual template that I can place on my board and use to model whole group problems. You can also use this template on a smartboard, etc.
Start with vocabulary
- prepare sheets with math problems and multiple choice math vocab words and have them match vocabulary with the problems
- write down the clues that often accompany specific math operations
- addition: in all, altogether, sum
- subtraction: difference, fewer
- multiplication: product, in all, altogether
- division: share equally
Lesson 2: Illustrator
Practice sheets - matching the illustration with the word problem to model the kinds of drawing that kids might use
Show how manipulatives can be used to help develop the illustration with hands on materials
Lesson 3: Calculator
Practice sheets - have students match number sentences with word problems
Talk about number sentences - how they are important and reinforce place value, math facts, etc. - key concepts in computation.
Lesson 4: Editor
Practice sheets - have word problems presented in D.I.C.E. that have an incorrect illustration, number sentence that does not match the word problem, or an answer without units and have the students locate and correct the mistake.