problem solving strategies

Set Up Your Best Classroom Yet: Part 2

July 19, 2016By astutehoot

Yesterday as part of my blog series, Set Up Your Best Classroom Yet, I gave you a sneak peek into my second grade classroom with a focus on my guided reading area. I use the district prescribed curricula along with our reading, writing, and math strategy animals to help my students learn, apply, and transfer critical strategies across settings. My classroom décor centers around Hazel Hoot, an adorable green screech owl, and her special strategy friends. See how I integrate the Problem-Solving Pond along with our hands-on tools to support and enhance the required Saxon math curricula.

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Special Spaces

Problem Solving Pond

In our sequel, Hazel Meets the Math Strategy Friends, Hazel swoops down to catch her dinner at the local pond when she grabs Upton, an enchanted fish. Upton oversees Problem-Solving Pond and promises to introduce Hazel to his animal friends, all who teach a special problem-solving strategy. Using these strategies and Upton’s guidance, Hazel blossoms into an accomplished mathematician who is able to tackle problems with ease.

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In order to recreate the Problem-Solving Pond, I covered a bulletin board with fadeless blue water paper and added green tulle and silk pond stems to border the pond. Upton’s Solving Word Problems Poster and Strategies Banners are prominent features of Problem-Solving Pond; I reference them throughout each lesson. I printed our Problem-Solving Pond Bulletin Board Set added Velcro to the back of each strategy animal allowing me to detach to use during lessons.

pond I found this stuffed animal on Ebay that looks just like Upton and hung it with fishing wire and a plastic hook. During guided practice, I toss Upton to students and he helps us complete the problem-solving steps. Students LOVE solving problems with him!

Problem-Solving Pond Upton with student I also found inexpensive jars at Hobby Lobby to hold our hands-on tools such as Max’s Counters, Brian’s Slide and Learns, and Fiona’s Fact-Fluency Pencils and added these adorable labels.

During center time, students solve their Saxon story problems using the strategy animals and our Problem-Solving Journals. They also use our hands-on tools such as Problem-Solving Mats, Brian’s Slide and Learns and Fiona’s Fact-Fluency Flashcards to reinforce learned strategies and concepts.

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Students enjoy using the Astute Hoot rug to discuss their journal samples. They stand on the strategy animal that they used to solve the story problem and then discuss the strategies, process, and thinking they used.

breaking_badger_mat Read tomorrow’s blog to see my Writing in the Wild West classroom space and accompanying hands-on tools.

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Create Write-On, Wipe-Off Problem-Solving Journals

January 3, 2016By astutehoot

Problem-solving plays an important role in my daily math instruction. Students use pre-made journals to help them complete the problem-solving steps, solve the problem in 2 ways, explain their thinking and rate themselves on a learning scale. These journals track students’ progress with mathematical understanding, strategy selection and application. They also serve as an effective assessment tool. I decided to make a write-on, wipe-off version for students to use during math centers. Follow these 4 easy steps to make them for your classroom, too!

1. Gather materials: You will need a class set of manila folders, problem-solving journal templates, glue sticks, a laminator and dry erase markers.

2. Prepare folders: Glue on the front cover, problem-solving pages on the inside, and the discussion prompts on the back. Laminate and cut out (a perfect job for a parent volunteer).

Journal front 1.5 Inside of problem solving journal Back of problem solving journal mat

3. Select appropriate story problems: I use differentiated story problems during math instruction and color code to keep them organized. An extensive story problem bank is included in our Problem-Solving Essentials Bundle.
Word problems

4. Model procedures and provide practice: Explain how to use the write-on, wipe-off problem-solving journals. Model how to use a dry erase marker to complete the journal. Select a partner to use the discussion prompts, thinking aloud as you go. Practice using the journals during whole group instruction, roving to monitor student understanding. As students demonstrate understanding, incorporate these journals into math center time, either at an adult-led center or an independent math center.

Page 1.5 Inside of journal

Download our Math Intervention Problem-Solving Essentials Bundle for over 200 pages of lessons, activities, worksheets, printables, everything you need for comprehensive problem-solving instruction during math intervention, special education and general education.

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Presenting Brian Breaking Badger

April 3, 2014March 20, 2015By astutehoot

Hi, I’m Brian Breaking Badger, and I love to break numbers apart.
Separating place value is considered my art!
I break numbers into ones and tens with my teeth,
Then I work with the place value underneath.
I’ll add or subtract the tens, then the ones.
Before you know it, the problem’s all done!

WHAT is breaking apart? Students use place value knowledge to decompose or break each number apart into hundreds, tens and ones. Depending on the problem, students will either add or subtract each place value (first hundreds, then tens, and finally ones). Students will then add or subtract all numbers to solve the problem. Read more about Brian’s strategy below or download the complete unit here.

WHY is breaking apart important? When students use the breaking apart strategy, they are decomposing numbers by place value. This help helps strengthen mental computation, builds number sense and solidifies foundational place value skills. It also serves as an efficient method to double-check solutions as students.

HOW do I teach breaking apart? Teach breaking in isolation first so that students become familiar with the process of decomposing numbers. After proficiency is demonstrated, students can apply this strategy with story problems.

WHEN should I use breaking apart? This is an ideal strategy for developing mathematicians who have a solid place value and number sense foundation. It is most effective to introduce the breaking apart strategy after students are proficient with the hopping strategy since hopping requires place value identification and decomposition skills.

Helpful Hints:

Provide place value and expanded notation practice. Students need a strong place value foundation to decompose or break apart numbers. Provide regular practice through center games and kinesthetic activities. Simple games such as “Race to 100” where students roll dice and add numbers using place value manipulatives are engaging and effective. This game is the perfect addition to weekly math centers.

Act out the problem. Increase students’ understanding of the mathematical context by acting out the story problem. Students also love to show their badger fangs when they break apart the numbers.

Presenting Tallying Toad

March 13, 2014March 20, 2015By astutehoot

Hello, I’m Tallying Toad.
I get you started on the problem-solving road.
A tally mark is a straight line to show one;
Group tallies into five is how it’s done.
First make four tallies, nice and straight;
Then make a diagonal fifth tally and you’re doing great!

Todd Tallying Toad is our newest animal in our Problem-Solving Pond: A Common Core Math Strategy Unit. The Problem-Solving Pond was created to help teachers overcome Common Core math challenges and employ problem-solving strategies with confidence and fidelity. Read more about Todd’s strategy below or download the complete unit here.
WHAT is tallying? Students use tally marks to show the numbers represented in the story problem.

WHY is tallying important? When students use the tally strategy, they learn to count and notate groups of 5, strengthening number sense in the process. Tallying is an easy, quick way to double-check solutions for kindergarten and first-grade students.

HOW do I teach tallying? Teach tallies in isolation first so that students become proficient making neat, organized tally marks. After proficiency is demonstrated, introduce tallying as a problem-solving strategy and teach students to apply within a mathematical context.

WHEN should I use tallying? This is an ideal strategy for beginning mathematicians who are learning to count and record numbers. Tallying is a great way to represent smaller numbers in story problems. Students get comfortable with tallies and will try to apply to larger numbers, making some teachers cringe. Refrain from discouraging use of tallies for larger numbers; students must independently develop understanding that tallying is not an efficient, effective strategy for story problems with larger numbers.

Helpful hints:

• Supply models and provide kinesthetic practice. Beginning mathematicians often lack dexterous fine motor skills, which can impede formation of neat, straight tally marks. Provide craft sticks, Wikki Sticks or pipe-cleaners (cut in half) and have students make a model of the tallies before drawing them on paper. Allow students to practice kinesthetically in salt or Jell-o trays or trace on bumpy paper. Students can also practice making tallies with Play-Doh.

• Include visual support. As beginning mathematicians start to use tally strategy, they need visual support to ensure that tally marks are straight neatly organized into groups of 5.

• Practice counting by 5’s. Some students struggle with skip counting and could benefit from repeated practice. Chanting 5’s while walking in line, calendar time, even clean-up time all serve as opportunities for fun skip counting practice.

Introducing Clark Counting Crocodile

March 3, 2014March 20, 2015By astutehoot

I’m Clark the Counting Crocodile. Use me to help you count.
Start with the largest number, and draw lines for the remaining amount.
Count on for addition, count back for subtraction;
Then circle the answer as your final action.

Clark Counting Crocodile is the second strategy animal in our Problem-Solving Pond: A Common Core Math Strategy Unit. The Problem-Solving Pond was created to help teachers overcome Common Core math challenges and employ problem-solving strategies with confidence and fidelity. Read more about Clark’s strategy below or download the complete unit here.

WHAT is counting?As students build their number sense and fluency, they are able to solve a story problem with counting. In this strategy, students will learn to count on for addition and count back for subtraction using a 100’s chart for support as needed.

WHY is counting important?Counting is a crucial strategy because it helps students explore the relationships and patterns between numbers. Students need to recognize the order of numbers so they can understand that it is more efficient to start with bigger number. For example, in order to solve “4+27,” they should start counting from 27 and progress to “28, 29, 30, 31” instead of starting from 4 and progressing to 31, because in the latter case, they would have to count much more, increasing the possibility of errors. Proficient counting lays the foundation for number sense and place value.

HOW do I teach counting? Explain that Clark helps mathematicians solve problems by counting on to find the total or counting back to find the difference.

Counting on for addition: Students start with largest number in the problem; they put that number in Clark’s mouth and then draw the number of lines for the second number in the problem (if the second number is 14, students would draw 14 lines). Students then label the lines (below the line) and count on, writing each number above the line. Students circle the answer and write equation below to solidify understanding.

Counting back for subtraction: Students start with the largest number in the problem; they put that number in Clark’s mouth and then draw the number of lines for the second number in the problem (if the second number is 14, students would draw 14 lines). Students then label the lines (below the line) and count back, writing each number above the line. Students circle the answer and write equation below to solidify understanding.

WHEN should I use counting? This strategy isideal for problems that include smaller numbers. Most teachers use this strategy with K-2 mathematicians, but this is also beneficial for older students as it works for money, multiplication and division (included in unit).

Helpful Hints:

Create counting bags. Create counting bags with different numbers of objects in each bag and a set of appropriate number cards. Use common manipulatives such as cubes, beans, tiles for bags. Students also love seasonal items such as conversation hearts, acorns, pumpkins, shamrocks, etc. Have student count objects in each bag and then select the number card to name that amount. Students can simply place the objects and number card back into the baggie for checking. Mark the bags with letters or shapes for easy checking of student work.

Provide opportunities for strategy exploration. Allow students to build conceptual understanding by having them solve a counting problem in multiple ways. Students can solve the problem starting with the big number first and double-check solution by starting with the smaller number first. This exploration will guide students to recognize that while it is more efficient to start with the larger number in the problem, number order does not affect the sum. Provide templates with larger numbers; this will help students observe that the counting strategy is not efficient for larger numbers.

Meet Max Modeling Mouse

February 23, 2014March 20, 2015By astutehoot

Greetings I’m Max the Modeling Mouse.
I solve problems by using things from my house.
Beans, cubes and counters are useful math gear;
Use them to model the problem so it’s clear.

Max Modeling Mouse is the first strategy animal in our Problem-Solving Pond: A Common Core Math Strategy Unit. The Problem-Solving Pond was created to help teachers overcome Common Core math challenges and employ problem-solving strategies with confidence and fidelity. Read more about Max’s strategy below or download the complete unit here.

WHAT is modeling?: Students use manipulatives, counters or drawings to model, or represent the mathematics of the story problem.

WHY is modeling important?: By making a visual representation, students are able to see the situation presented in the problem. Modeling is critical to student understanding as it allows students to see, feel and process math in a concrete way.

HOW do I teach modeling?: Select appropriate manipulatives (beans, cubes, coins, place value rods) and make a visual model of story problem. Write equation below the model to solidify understanding.

WHEN should I use modeling?:

This strategy is ideal for presenting a new mathematical operation. Most teachers use this strategy with K-2 mathematicians, but this is also beneficial for older students as it works especially well with money, fractions, ratios and percentages. Modeling is a great way to double-check solutions because the visual representation increases understanding of the problem.

Helpful hints:

Create rules and expectations. Before introducing manipulatives, establish rules and expectations for use. Explain the mathematicial purpose of them as well as how and when to use them. Practice essential routines such as getting out manipulatives, freezing at teacher’s signal (with hands-off manipulatives) and cleaning up quickly and quietly.

Prepare manipulative bags. Count out specific manipulatives and store in individual Ziploc bags or small Tupperware containers so they are ready to use at any time. These individual units can be stored in student desks or in a large container.

Store manipulatives in a common area. Purchase an inexpensive storage container with shelves and house manipulatives here. Label each shelf and include a picture or glue on an example for student reference.

Allow time for student exploration and play. Before students use the manipulatives as mathematicians, provide time for exploration and play. This will help students stay focused and use them correctly during math time.

Check out our other Problem-Solving Pond strategy animals coming soon:
–Drawing Dragonfly
–Tallying Toad
–Counting Crocodile
–Hopping Hare
–Tabling Turtle
–Break-Apart Badger
–Equating Earthworm
–Fact Fluency Fox

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