Math Strategies – Page 2

5 Secrets to Successful Test Prep

March 25, 2014April 1, 2014By astutehoot

Just the mention of standardized testing causes major anxiety for both students and teachers. These 5 secrets of successful test prep, along with our complete Standardized Test Prep Unit, will alleviate angst, strengthen skills, promote self-awareness and build confidence.

Create an engaging test prep theme. After spring break, my class is transformed into Test Prep Troops. I decorate the classroom with camouflage flair including a special sign on door and camouflage test prep bulletin board that displays learned test taking strategies. We learn a Test Prep Chant (to the tune of traditional military cadence) that we perform before each practice session. Students also use special camo pencils and wear personalized dog tags during testing. These inexpensive camouflage items can be found at your local party store.

Teach specific test taking strategies. Before I start test prep, I select the strategies I want to teach and the order in which to teach them. Since my second grade students are new test takers, I start with Bubbling Basics and have them practice making neat, bubbled answers on a bubble sheet. Listen and Learn is the second strategy I introduce because students have to listen carefully as most of the Stanford 10 standardized test is read-aloud. We play Simon Says and other games that focus on following directions to practice this skill. The rest of the strategies are taught while completing specific test prep practice. Be a Determined Detective and The Key is in the Question are perfect strategies to teach during reading comprehension practice passages. Show Your Solutions and Significant Signs are ideal for math computation practice. I post the strategies in a prominent place in the classroom and refer to them during test prep time. Download our complete Standardized Test Prep Unit here.

Encourage reluctant test takers. Testing can cause major anxiety for students; relieve this pressure with Tina Turtle, Troubled Test Taker. Introduce Tina with her rhyming poem; discuss her anxious feelings and help the class make connections to their own testing experiences. Explain that students have one important job— to teach Tina the test-taking strategies and tools needed for success. Each student gets a copy of Tina with blank scales; they are blank because she is lacking testing strategies. Students will teach Tina new strategies and record them on her scales; by the time Tina takes the test, her scales will be covered with strategies. Together Tina and the class will become confident, prepared test takers.

Store test prep in an important place. Create special test prep folders to house strategies and practice tests. Simply use 2 pocket folders with prongs; label one pocket “Reading” and one pocket “Math”. Put Tina and her poem in a plastic sleeve inside the folder; students can refer to her poem and fill out her scales during each practice session. Glue the Test Prep Chant and Test Taking Tips on the front and back of each folder.

Include motivational rewards. Since my class is the Test Prep Troops, I give a special ration at the end of each session. This can be a Smartie (for smart students), pencils, stickers, etc. Pick a reward that your students will enjoy; parents can help donate these items as well.

Say Hello to Hailey Hopping Hare

March 23, 2014March 20, 2015By astutehoot

I’m Hailey the Hopping Hare, I’m the skip-counting master.
This is a skill that helps to count things faster;
Learn to count up or down by a number other than one.
Quick like a bunny, you soon will be done.
Keep in mind that skip counting is repeated addition.
Moving swiftly through problems is my main mission.

WHAT is hopping? Students use place value and number sense to add or subtract numbers. Students first start with the bigger number in the problem; this number is the starting point for hopping. Then they decompose or break apart the second number by place value (into 10’s and 1’s). Depending on the problem, students will either add or subtract, hopping first by 10’s and then by 1’s. Students label numbers above hops to help ensure solution is correct. Read more about Hailey’s strategy below or download the complete unit here.

WHY is hopping important? When students use the hopping strategy, they are essentially skip-counting by 10’s and 1’s. This helps strengthen mental computation, builds number sense and solidifies foundational place value skills. It also serves as an efficient method for students to double-check solutions. Furthermore, hopping can easily be extended to larger numbers and multi-step problems because it tracks mathematical thinking and steps taken to complete problem.

HOW do I teach hopping? Teach hopping in isolation first so that students become familiar with the process of identifying larger number and decomposing smaller number by place value. Use patterned, pre-labeled or open number lines until students can proficiently count and track hops (see examples). After proficiency is demonstrated, introduce an open number line where students determine the starting point then draw and label hops without support.

WHEN should I use hopping? 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 hopping strategy after students become proficient with the counting strategy. When larger numbers are used, students quickly realize that counting becomes inefficient and laborious. Hopping allows students to employ counting skills they are comfortable with, but increases rigor and mathematical practice.

Helpful hints:

Supply models and provide kinesthetic practice. Select appropriate number lines according to students’ individual needs. Some students will easily grasp hopping and will be able to use the open number line while others will need the patterned number line to see and count the 10’s and 1’s. Make a large patterned number line for kinesthetic learners and have them physically hop the numbers. Students will not only love this activity, the multi-modal approach reinforces learning.

Make Hailey pointers. Cut out and laminate Hailey patterns and use a hot glue gun to adhere to craft sticks. Students can use a Hailey pointer to hop the numbers in each problem.

Practice skip-counting. Some students struggle with skip counting and could benefit from repeated practice. Chanting by 100’s, 10’s and 1’s while walking in line, calendar time, even clean-up time all serve as great practice opportunities. Be sure to vary starting points so to ensure that students aren’t just counting by multiples of 100’s, 10’s or 5’s. (For example start at 57 and count by 10’s, then switch and count by 1’s.)

Be flexible with students’ hopping methods. Remember, the whole point of teaching strategies is to help students become fluid, flexible thinkers with deep conceptual understanding. While Hailey teaches students to start with bigger number and hop by 10’s and then 1’s, do not insist that students need to only hop this way. It is imperative to allow them to experiment and try multiple methods in order to find the most meaningful and efficient hopping method for themselves. Some hop to the nearest multiple of 10 and then continue hopping by 10’s, while others hop by all of the 10’s in one hop. Accept all methods if students solve problem correctly, explain method and apply across settings.

Introducing Daphne Drawing Dragonfly

March 22, 2014March 20, 2015By astutehoot

Hi, I’m Daphne the Drawing Dragonfly.
Draw a mathematical picture to give my strategy a try.
Read the problem and draw what’s going on;
Then write a number sentence for what you have drawn.

Daphne Drawing Dragonfly 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. Daphne’s unit is perfect for general education, special education, RTI and math intervention. Read more about Daphne’s strategy below or download the complete unit here.

WHAT is drawing? Students make a visual representation of the story problem such as a picture, bar model, tens frame or array.

WHY is drawing important? When students use the drawing strategy, they are making a concrete representation, strengthening understanding of the mathematical concepts. Effective math classrooms include frequent use of pictorial representations to help students process and visualize mathematical concepts learned.

HOW do I teach drawing?Teach students to create neat, organized drawings with labels and numbers. Students will need to be taught the bar model and arrays, but it is best to let students create the pictorial representation that they see and works for them.

WHEN should I use drawing? 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. Drawing is a great way to double-check solutions because the visual representation increases understanding of the problem.

Helpful hints:

Create drawing guidelines. As a class, decide important components to include in a mathematical drawing. Possible components include:
- Simple drawings
- Appropriate spacing
- Neat labels (words or numbers)
- Easy to read

$Guidelines for math pictures$

Encourage students to use a variety of pictorial representations. Often students will get in a “strategy rut”, relying on one strategy for many different kinds of story problems. While drawing is an effective strategy for most problems, the type of pictorial representation used depends on the type of story problem.

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.

Huge SALE February 27 & 28!!!!

February 27, 2014By astutehoot

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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

$Math Animals with names$

Cooking in the Classroom

February 16, 2014By astutehoot

Cooking is a fantastic way to synthesize many skills and concepts. It promotes higher-level thinking skills such as analysis, synthesis and evaluation. Since we want our children to function independently as they grow, what better way to develop and foster this than through cooking? Here are some of the benefits cooking provides students:

–Builds math skills (use measurement, fractions, numeric properties, sorting and classifying)

–Strengthens reading skills (teaches recipes and directions; promotes vocabulary development, use of ordinal words and oral expression)

–Creates opportunities for science exploration (use of senses, make predictions, note physical changes, identify foods)

–Promotes social studies and collaborative skills (fosters teamwork and collaboration, recreates family experiences and promotes cultural awareness)

In order to start cooking in your classroom, simply download our Classroom Cooking: Recipes & Functional Text Activities. This unit contains 17 tried and true recipes tied to CCSS; all are connected to literature, focus on holidays or seasons and have accompanying comprehension questions. A parent letter is included to explain unit and request donations. Bon Appetit!

Why? The Simple, Yet Essential Question

February 2, 2014By astutehoot

As teachers, we are programmed to listen for the correct answer and are appeased when we hear it, assuming that students understand and are ready to move on. However, this is a serious misconception as students are missing out on a vital opportunity to explain and justify their thinking. Asking “Why?” provides critical insight to student understanding as students give the following responses:

A strong explanation that describes process to class
An inaccurate explanation that shows a student’s misunderstanding or inability to justify an answer

Besides assessing understanding, asking “Why?” provides students with opportunities to:

Notice mistake(s) and self-correct the answer
Reveal mistake(s) or misunderstanding shared by the class
Take risks and build confidence
Strengthen communication skills
Give alternate explanations
Summarize explanations given by other students

Including this simple question has major consequences: it promotes a language-rich classroom; supports inquiry-based instruction; and builds classroom community.

Asking good follow-up questions can open the door “why-d” to learning.

Download our FREE Essential Questions & Prompts, a sneak peek at our upcoming Common Core Problem Solving Unit.

Shopping for Standards: Setting Up a Classroom Shop

November 4, 2013December 2, 2013By astutehoot

Looking for a fun, easy way to strengthen students’ money skills? Set up a classroom market! This guaranteed favorite can be used throughout the year and modified according to instructional needs. Follow these easy steps to create your own classroom market:

1.Setting up shop: Visit your local dollar store for grocery baskets, cashier receipt pads, calculators and price labels. (Make sure each student in the center has a grocery basket so each has opportunity to shop.) Make a store awning using a cardboard science project trifold and cover it in fabric. A simple, inexpensive cash register can be found on e-Bay or local thrift shops.

2. Providing products: Bring in canned products, purchase plastic play food or pull out Treasure Box trinkets. My market is holiday-based to appeal to student interest so it changes regularly. Students can shop for Thanksgiving dinner, holiday gifts, school supplies, etc. Changing the product once a month promotes engagement as students are excited to see and purchase new items.

3. Pricing power: Price items according to students’ instructional needs. If you just introduced money, keep prices low and easy to count. This provides counting practice and builds number sense. As students become proficient counters, increase the prices and have students add more complex numbers. You can also add dollars and cents to increase difficulty.

4. Hiring help: For the first month or two, the teacher or parent volunteer will be the cashier, checking students’ totals and helping them make change. As students become proficient with these skills, allow students to be the cashiers. Students can partner up; one student will be the cashier, one will be the shopper and then they will switch roles. Another option is to allow one or two students can be the cashier(s) for the whole group.

5. Synthesizing standards: Add functional text forms to incorporate reading and writing standards into the market. Simple items such as shopping lists, receipts and inventory check-lists require students to read and write a variety of functional text, an important component of informational text.

Set up a shop in your classroom and you’re in store for endless instructional possibilities!

Top 3 Tips to Break the Ice and Build Community

August 12, 2013August 29, 2013By astutehoot

You know the horrible feeling when you walk into a room and you don’t recognize a single soul? Even worse, everyone else already knows each other, happily mingling together. Most adults shudder at the thought, yet as teachers, we fail to consider how these situations make our students feel. Many students come to school on the first day without knowing anyone, much less bathroom and cafeteria locations. We fill the first days with procedures, rules, and other endless explanations without taking any time to help students feel comfortable and safe, two basic conditions required for learning.

Here are my top 3 icebreaker activities:

Student Scavenger Hunt: Make a Bingo board and write an interesting fact in each (Went to Disneyland this summer). Students will hunt for a classmate who matches the fact and record his/her name in the box. This activity gets students moving and talking, both of which they are hesitant to do the first few days. It also allows time to practice important transitions and procedures such as freezing at teacher’s signal, cleaning up and active listening.
Friendship Web: Students and teacher sit in a large circle. The teacher starts with a ball of yarn, says his/her name and throws the ball to a friend. When the friend catches the yarn, he/she states his/her name and a fun fact about him/herself. Explain that we are building a class web where we are always here to help and support each other. We are all connected in learning. Take a picture and post.
Friendship Salad: Purchase 3 cans of fruit, bag of marshmallows, 1 large container of yogurt and an old, very rotten banana. Read a friendship book (Horace, Morris But Mostly Delores is a great choice) and stop right after friends get in a fight. Discuss possible strategies to solve the disagreement. Then make the Friendship Salad. Show the bowl and tell students this represents the classroom; it is empty and needs many things such as good friends, happy days and lots of learning. Pour in one can of fruit—these are kind kids in the room who help others (can elaborate). Pour in the second can of fruit—these are the hard workers in our room—they always give their best effort and complete their work. Pour in the third can—this represents students who share. Dump in the bag of marshmallows—these represent respectful, polite words used with each other. Add the yogurt—this is for smooth, happy days. Stir together and walk around to let the kids see and sniff. Then show, the secret ingredient—the rotten banana! Start to peel and put in and students will start to scream in disgust. Explain that it only takes one person with rotten behavior or a rotten attitude to ruin the whole classroom. Extend the explanation to the story (i.e., Horace and Morris were being rotten friends when they excluded Delores). The moral of the lesson—don’t be a rotten banana!

Like these ideas? Check out our Back to School Ice Breakers and Community Building Activities for 85 pages of engaging plans and exercises.

Test Prep Center

April 13, 2012July 27, 2013By astutehoot

Motivate students to prepare for upcoming standardized tests with the creation of a fun, engaging test prep center. I created “The Standardized Testing Swamp” in my classroom. Both Tina Turtle, Troubled Test Taker and Frankie, Fumbling Fox, are posted at the center, along with test-taking tips and strategies. Test prep centers, games and activities are also housed in this special center. For even more ideas, check out Astute Hoot’s comprehensive motivational test prep unit at http://www.teacherspayteachers.com/search?keyword=astute+hoot+test+prep&subjectarea=0&startsearch=1

Standardized Test Prep

April 5, 2012July 27, 2013By astutehoot

Standardized testing is now a major component of education. Yet, just the mention of a standardized test causes major anxiety for students, teachers and parents. Astute Hoot has the answer for this anxiety! Unlike other test prep units that focus on laborious drill and kill, our comprehensive test prep unit was specifically designed to alleviate angst, strengthen skills, promote self-awareness and build confidence.

In this unit, students meet Tina Turtle, Troubled Test Taker and Frankie, Fumbling Fox, both of whom struggle with major test taking anxiety. Each week, the students teach Tina and Frankie an important test taking skill or strategy; students help Tina and Frankie practice the strategy at a test prep center. Students can easily relate to the animals’ struggles and they feel empowered as they help these two troubled test takers.

This unit includes:
•Tina, Test Taking Turtle and accompanying poem
•Frankie, Fumbling Fox and accompanying poem
•Detailed instructions on creating Test Prep centers and folders
•10 test taking tips (on both individual pages and on one whole page)
•10 lesson plans to teach test taking tips
•5 test prep activities (with literature connections) to boost self-esteem and motivation
•Customizable parent letters
•Test prep award
•Several color pictures show test prep in action!

Check it out at http://www.teacherspayteachers.com/Product/Standardized-Test-Prep-Unit

Games That Teach: Part 4

February 28, 2012July 27, 2013By astutehoot

Use dice, playing cards and poker chips to practice number recognition, counting, and basic facts in a game-like format. This is great way to make math time fun, especially for kiddos (and maybe parents) with math anxiety.

Games That Teach: Part 1

October 23, 2011July 27, 2013By astutehoot

Turn Hopscotch into a fun learning game! Use chalk to draw a hopscotch and fill in the squares with a specific concept (numbers, shapes, letters, sight words, etc.). Kids will have so much fun jumping and moving while learning basic academic skills.