Making Sense of math with tape diagrams Marisa Aoki

Goals Address what makes word problems difficult for students Experience strategies that support student engagement and understanding during word problems Explore tape diagrams as a sense-making and problem solving tool Discuss ways to help students connect ideas across various topics in mathematics

Age old question: Why do students struggle with word problems? - Robert Kaplinsky Video -

Student Hat

Facts, Inferences, and What is Relevant? Beth has some red beads She has 3 fewer yellow beads than red beads She has 4 more green beads than red beads What is the question? (Answer statement) Do we have all the information we need to solve it? 1 min: Quick sketch - NO OPERATIONS!  Share with partner – justify sketch and answers, partner critiques (switch roles) Make a number sentence to match your drawing Targeted share out Adapted from Steve Leinwand

Teacher Hat

Strategies that slow answer-getting Deleting numerical values (words only) Leaving off the question (students can create questions) 3 Reads/Math Stories (will demonstrate) Notice and Wonder from Annie Fetter (if time) Giving the answer in context and having students create the word problem(s) that produce it Teach math comprehension like you would reading comprehension AVOID: Key words and “follow these easy steps” techniques.

Why not key words?

Umm…Why haven’t we done tape diagrams yet?

Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE Math Stories – 3 Reads Problem-Solving Recording Sheet

Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE Math Stories – 3 Reads Problem-Solving Recording Sheet

Umm…Why haven’t we done tape diagrams yet? Just a tool Not the ONLY way to draw out thinking Without comprehension, tape diagrams just become another senseless procedure to students Problem-Solving doesn’t progress in stair-like steps

Examples: Addition and Subtraction Problem Types 9 boys and 8 girls were in the class. How many children were in the class altogether? 17 children are in the class. 9 are boys and the rest are girls. How many girls are in the class? 17 children are in the class. There are some boys and 8 girls. How many of the children are boys?

Student Hat

Math Stories – 3 Reads 30 seconds Remember! Tell Back to me

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

20 seconds to reread and check accuracy Math Stories – 3 Reads Chart response 20 seconds to reread and check accuracy

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

Final check – leave in view Math Stories – 3 Reads Chart changes Final check – leave in view

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? QuestionAnswer Statement

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? QuestionAnswer Statement

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? Total? Part? Comparison?

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? 30 second sketch

Partners: Justify - Critique Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? Partners: Justify - Critique

Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? Number Sentence

Share out-complete chart Math Stories – 3 Reads There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity? Share out-complete chart

Teacher Hat

Process: Present word problem (pick strategy that slows answer- getting and focuses on comprehension) Write answer statement What are we looking for – Total? Part? Comparison? Who/what has more/less? Sketch and label diagram/model Use diagram to solve problem Check reasonableness/justify Write expression/equation (justification good here too – often multiple correct answers) Compare/make connections

Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE Math Stories – 3 Reads Problem-Solving Recording Sheet

Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE Math Stories – 3 Reads Problem-Solving Recording Sheet

Pg. 5

Pg. 7

Pg. 8 - COMpare

Pg. 13 #3 Alan bought a bag with 29 jelly beans. He gave 13 to his little brother. How many jelly beans did Alan keep for himself?

Pg. 13 #4 Carl has 13 games in his collection. Daniel has 7 more than Carl. How much do they have altogether?

Pg. 14 #7 Seven friends went out for a nice dinner. They decided to split the bill evenly amongst themselves and paid $21 each. What was the total money left by the seven friends?

Pg. 14 #8 The grand prize for a contest was $270. Five winners came forward to claim the prize. Their claims were legitimate and it was decided to split the prize amongst the five winners. How much did each winner take home?

Pg. 14 #9 A box containing 96 pencils is opened and shared equally among some children. Each child receives 8 pencils. How many children shared the box of pencils?

Pg. 15 #10 Eric has saved $13.25. His sister, Fiona, has saved 3 times as much. How much has Fiona saved?

Pg. 15 #11 Gabriel harvested 124 lemons from the large tree in his yard. This was four times as much as he harvested from the small tree in hi yard. How many did he collect from the small tree?

Pg. 15 #12 Hermione was able to catch 90 fireflies. Ingrid was able to catch 18 fireflies. How many times as many fireflies did Hermione catch compared to Ingrid?

Pg. 16 #13 Jerry bought a large gummi bear weighing 64 ounces. He and his friends ate ¾ of it. How many ounces did they eat?

Pg. 16 #14 Kendra bought a batch of cookies, 2/3 of which were chocolate chip. If 30 of them were chocolate chip, how many total cookies did Kendra buy?

Pg. 16 #15 Lily spent 2/5 of her cash on a CD which cost $15. How much money did Lily have to begin with?

Notice and Wonder Pg. 21

Need support? I am more than happy to meet with/explain further/help plan lessons using these strategies during the “unconference” times Interest in this??? Email: marisa_aoki@sanger.k12.ca.us

Citations and resources Based on information presented by TCOE (Kim Webb) Book: Bar Modeling A Problem-solving Tool (Yeap Ban Har) Information and Strategies from Robert Kaplinsky: http://robertkaplinsky.com Steve Leinwand: http://steveleinwand.com Annie Fetter: http://mathforum.org/blogs/annie Article: ”Solving Word Problems” (Randall I. Charles) Problem-Solving Recording Sheet (shown in article) Problem Set Packet (TCOE) Math Stories Instructions (TCOE)