Two%Step!Story!Problems!in! Operaons!and!Algebraic ... · PDF fileNCTM 2 step story...
Transcript of Two%Step!Story!Problems!in! Operaons!and!Algebraic ... · PDF fileNCTM 2 step story...
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Two-‐Step Story Problems in Opera5ons and Algebraic Reasoning Grades K-‐2
Na5onal Council of Teachers of Mathema5cs Annual Mee5ng
Thursday, April 18, 2013
Melissa Hedges K-‐8 Mathema5cs Teaching Specialist Mequon Thiensville School District Mequon WI
Beth Schefelker Mathema5cs Teaching Specialist Milwaukee Public Schools Milwaukee WI
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Study standard 2.OA.1 Structure of 2-‐step story problems Looking at student work Scaffolding instruc5on for 2-‐step story problems
Agenda
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Learning Inten5on & Success Criteria We are learning to… • Extend our understanding of story problem situa5ons as determined in 2.OA.1
We’ll know we’ve been successful when we can…
• Iden5fy the structure of two-‐step story problems and determine a solu5on strategy to solve them.
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Story Problem Situa5ons in Grade 2 2.OA.1
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2.OA.1
• Read standard 2.OA.1
• What is familiar about this standard?
• What are the expecta5ons for children in Grade 2?
• Be prepared to share out.
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Represent and solve problems involving addi;on and subtrac;on. Use addi5on and subtrac5on within 100 to solve one-‐ and two-‐step word problems involving situa5ons of adding to, taking from, puYng together, taking apart, and comparing, with unknowns in all posi5ons, e.g., by using drawings and equa5ons with a symbol for the unknown number to represent the problem.1
2.OA.1
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Two-‐step story problems
Read Progressions p. 18 paragraphs 1-‐4. Work with a table partner… Study the margin: Examples of two-‐step Grade 2 word problems.
What insights have you gained by reading and discussing the examples?
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Red Easy Problems Blue Middle Difficulty
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Structure of two-‐step problems
Two easy subtypes – same opera5on
Two easy subtypes – opposite opera5on One easy and one middle difficulty Two middle difficulty
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The zoo has 7 cows and some horses in a big pen. There are 15 animals in the big pen. Then 4 more horses ran into the pen. How many horses are there now in the pen? Looking at student work… • What misconcep5ons might you an5cipate? • What strengths do you no5ce in the student work?
• What instruc5onal next steps might the teacher take to support student learning?
Zoo Horses – A first adempt!
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Student B Student E
Student F
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A Scaffolded Approach
At the first bus stop there were 12 children on the bus, 8 boys and some girls. At the next bus stop, 6 more girls got on the bus. How many girls were now on the bus altogether? What do students need to understand and know to solve this?
What equa5on(s) would you expect them to write?
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A Scaffolded Approach
At the first bus stop there were 12 children on the bus, 8 boys and some girls. Intermediate ques5ons: How many girls are on the bus? 8 + ☐ = 12
At the next bus stop, 6 more girls got on the bus. How many girls were now on the bus altogether? 4 + 6 = ☐
There are 10 girls on the bus.
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What type of problem?
Tanisha has two packages of s5ckers. There are 20 s5ckers in one package and 24 s5ckers in the other package. David has 35 s5ckers. How many more s5ckers does Tanisha have than David? What types of problems were used to compose this two-‐step story problem?
What do students need to understand in order to solve this problem?
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Standards’ Progression
K.OA.2 PuYng together, adding to, taking from, taking apart within 10
1.OA.1 Represen5ng and solving with unknowns in all posi5ons with all 12 problem types within 20
2.OA.1 Represen5ng and solving with unknowns in all posi5ons with all 12 problem types with in 100 and 2-‐step problems
3.OA.8 Solve 2-‐step problems using all 4 opera5ons add & subtract within 1000; mul5ply & divide within 1000
4.OA.3 Solve mul5step problems using all 4 opera5ons having whole number answers, including problems in which remainders must be interpreted.
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Bringing it all together
• Read OA Progressions p. 20-‐21: “Summary of K–2 Opera5ons and Algebraic Thinking”
• How would you respond to a teacher who says, “Really? OperaBons and Algebraic Thinking in K-‐2? What’s the big deal?”
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Learning Inten5on & Success Criteria We are learning to… • Extend our understanding of story problem situa5ons as determined in 2.OA.1
We’ll know we’ve been successful when we can…
• Iden5fy the structure of two-‐step story problems and determine a solu5on strategy to solve them.