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About Scottie Altland

Scottie Altland is a certified elementary educator with specialties in math and curriculum development. Previously, Scottie taught grades 5-8 in public schools and worked for a local non-profit organization, offering families and students a broad range of family life education programs. As a mother of two, she enjoys spending time with her family, is an outdoor enthusiast, and continues to love teaching and learning. For the past year, Scottie has served as the Elementary Math Editor for Demme Learning.

6 Fun Spring Spelling Activities


Spring spelling activities that are seasonal, easy, and play-based!

Talking, singing, playing rhyme games, reading aloud, and experimenting with writing and drawing with your child are great ways to establish a good literacy foundation. During the spring months, try some of these seasonal, easy, and play-based literacy activities to support and encourage your preschooler’s curiosity and confidence with spelling.

Spring Spelling Activities

1) Water Words

On a warm spring day take a bucket of water and a paint brush (a one-half or two-inch bristle-head brush works well) out to the sidewalk or driveway. Have your child paint letters and words with water on the concrete.

Variation: Take this activity a step further and create muddy messages: On a wet day find a stick and some space in the soil and practice writing words in the mud. A sunny day? Fill the watering can or grab the hose and create your own muddy canvas.

2) Air Spelling

Take some time to explore outdoors and talk together about the new things you see now that spring has arrived. A tree, bug, bird, or the sky may be just a few topics your preschooler wants to explore and discuss. “Write” these spring-related words together in the air with your finger, hand, arm, or a small stick.

Variation: Have your child write their spelling words on your back with their finger. Try to guess the word they are spelling.

3) Rhyme Anytime

Use phrases like ‘snug as a bug in a rug’ or make up nonsense rhymes together about things you are doing – for example, ‘see my feet walk to the beat’ or ‘put your glass from your drink into the sink’. Sing nursery rhymes with your child such as ‘Jack and Jill’, ‘Twinkle, Twinkle Little Star,’ or the Alphabet Song when you’re at home, in the car, or out and about. By doing this, you are teaching your child about language, rhyme, repetition, and rhythm. These activities also will help her understand the meaning of words as well as how words are created.

4) Carrot Pencils

Dip the tip of a whole carrot into some paint and have your child trace over words you have written (or typed) or practice writing his own words on paper.
Waxy Words: On a piece of white paper have your trace over or write his own letters or words with a candle (a white or light colored candle works best). Next, have him paint over the entire paper with watercolor paint. Let the paper dry completely and see the words appear.

5) Rainbow Spelling

Have your child trace over words in several different colors of chalk, crayons, markers, or colored pencils. This activity can also be taken outside and completed with sidewalk chalk or sidewalk paint (available online or at most craft stores).

6) Stick ‘n’ Spell

Gather some spring-related items such as seeds, dandelions, small sticks, small leaves, blades of grass, or feathers. Separate the objects into containers. Write words on cardstock, large enough for your child to trace over with a glue stick or some paste and a paintbrush. Next, have your child select an item to stick on to each letter, covering each as completely as possible. When the glue has dried, have your child trace over each letter with his finger and say each letter and then the word.

Spring Spelling Apps

On a rainy day or on the go, you and your child might like to try these apps recommended by KinderTown that promote early literacy skills.

Starfall ABCs App Review

Starfall ABCs brings each letter to life with pictures, animation, games, songs, and stories. Using a clear, articulated voice, the app identifies each letter by name, sounds, and words. Children interact with each letter by taping, sliding, sorting, and dragging as each letter takes them through five or more screens of engaging phonics learning.

Read KinderTown’s full review here.

Gappy Learns Reading App Review

Gappy Learns Reading supports young learners building words letter by letter and sound by sound. Poor Gappy gets lost from his home, and your child needs to build 10 words to get him to his house. After building 10 words, your child earns a prize to customize the house in uniquely creative ways. There are four levels in the app, so young learners who are just working on letter identification can build words, and early readers can work on spelling lists of their own. This is a well-designed app for learning about letters and sounds while building words.

Read KinderTown’s full review here.

Engaging in literacy activities sets the stage for your preschooler to get excited about spelling. Remember that the goal of these activities is to give your child in a variety of literacy-based activities and to feel more relaxed about learning how to spell. Keep in mind that, while these types of activities are fun ways to practice individual letters or words, you should not depend on them alone to teach spelling. As your child gets older, your regular spelling program should present words in context to help him develop a visual memory of the words through writing.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


4 Fun Spring Math Activities


Spring math activities for the whole family to enjoy! Going outdoors allows you and your preschooler to conduct active explorations of early math concepts.

It’s spring – time to get outdoors! Together the fresh air, sunshine, and change of scenery bring endless possibilities for exploration. In the excitement of a new season of growth the outdoor environment can be just what your young child needs to get excited about playing, practicing, and investigating math concepts. So sneak some math-related learning in some unlikely places such as your own backyard or the park.

Spring Math Activities

Counting Designs and Pictures

With your child, gather a specified number of small objects, such as small sticks, pebbles, dandelions, blades of grass, or leaves (at least 10 to 20). Challenge your child to make a picture, pattern, or design on a flat surface using all the objects. Together count the total number of objects as well as and the number of each type of object. (Counting, Problem-Solving) Extensions:

• Compare two or more groups of objects. Which has the greater number of items? The least?
• Compare two groups of objects. How many more would need to be added or subtracted so they were equal amounts?
• How many different ways can the objects be arranged to make a completely new design?

Size Seeking Activities

1) Collect a variety of items such as sticks, flowers, pebbles, or blades of grass. Have your child arrange them in order from longest to shortest or largest to smallest (or vice versa).

2) Introduce early measurement concepts and put your child’s comparison and problem solving skills to work by completing the activities on the Size Quest activity sheet together. [PRINTABLE] (Measurement, Comparing)

Introduce early measurement concepts and put your child’s comparison and problem solving skills to work with these activities.

Estimation Discussions at Home or on the Go

Discuss any (or as many) of the questions below. Ask your child to estimate first and then find the actual measurement, weight, or time. For young learners you can give the unit of measure when one is not indicated. Have older students determine the best unit of measure to use when one is not given. (Estimation)

• How long do you think it will take you to run 100 meters?
• How far you think you can jump?
• How far do you think you can throw a ball?
• How long do you think you can stand (or hop) on one foot?
• How many shots will it take you to make a basket? To make 3 baskets in a row?
• How tall do you think our front door is?
• How long do you think it will take you to fill up a watering can with water? (show them a specific size) How many plants do you think you can water with it?
• How long do you think it takes to drive to the grocery store?
• How much do you think (name of family member) weighs?

What’s My Value?

Collect a variety of small objects outside. Let your child assign a value to each to create math equations. Perhaps an acorn = 5 and a twig = 2. Next, he can choose an operation and write and solve an equation with sidewalk chalk, such as acorn – twig = 3. By doing this you are introducing your child to the algebraic concept that a symbol can represent a numeric value. (Algebraic Reasoning)

Spring Math Apps

Can’t go outside? KinderTown recommends the following apps for early learners who are practicing math skills on a rainy day or on the go.

Park Math App Review

Your child will have fun with Blue Bear and his friends as they play throughout the park and learn to count, add, subtract, compare and sort numbers and objects as well as create and investigate patterns together. This app includes two levels of play: Level 1 includes counting up to 20 and addition/subtraction with numbers up to 5. Level 2 includes counting up to 50 and addition/subtraction with numbers up to 10. Children enjoy completing the activities while listening to classic tunes such as The Muffin Man and Five Little Ducks.

Read KinderTown’s full review here.

Bugs and Numbers App Review

Young learners from preschool through early elementary school can learn their numbers, count money, tell time, and develop an understanding of fractions. Preschoolers will be most successful if they start at the beginning levels and work through the progression of the games. The realistic graphics help to make this app engaging. Parents have the option to set up separate accounts for multiple children.

Actively involving your child in conversations and observations and encouraging manipulation of concrete materials all invite your child to experience mathematics through play and explore the outdoor world!

Read KinderTown’s full review here.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


4 Outdoor Math Activities for Kids


These outdoor math activities may inspire your student to use his mathematical thinking skills while spending quality time together.

Teaching math can be much more than working problems from a textbook. You can turn outdoor activities and trips into opportunities to sharpen and teach math. Take advantage of backyard playtime, a walk in the woods, or a visit to a city or beach to talk about math.

The key ingredient to teaching math skills outdoors is to make the experience a positive one. In these instances, take the time for conversation, exploration, and extension of math concepts. Help your student develop awareness that math is everywhere. Encourage him to recognize shapes, patterns, and symmetry in his environment.

The following outdoor math activities may inspire your student to use his mathematical thinking skills while spending quality time together.

Outdoor Math Activities to Do Together

The Spectacular Spider Web

Geometry is the study of shapes and their properties. Spiders are born knowing how to design and spin a web. Each species of spider spins a unique design. Have your student research the geometrical parts of a spider web design and learn to identify components such as the bridge thread, radius threads, auxiliary spiral, and signal line. If your student is so inclined, he can try to draw or “spin” his own web using a wire coat hanger stretched into a circle and some yarn.

Seasons of Symmetry

When one half of an object is the mirror image of the other half, the object is said to have symmetry. Teach your student to look for different types of symmetry in nature to extend her knowledge and understanding of shapes and patterns. These may include wallpaper symmetry, fractal symmetry, and radial symmetry. During outdoor activities you can challenge her to search for examples of items in nature that have these types of symmetry. This activity can be continued throughout the year. Keep a running list of items she finds in the places you visit and as the seasons change. The list may include butterfly wings, sunflowers, tree leaves, honey comb, spider webs, snowflakes, nautilus shells, sea stars, peacocks, people, and even foods such as romanesco broccoli, pineapple, and the inside of a kiwi when sliced in half. Just be warned that, once your student is aware of it, she may begin to point out symmetry in everything she sees!

A Sphere of Activity

A sphere is a perfectly round, three-dimensional object. Have fun outside with a beach ball, blowing bubbles, playing kickball or playing with marbles. Ask your student to name examples of spheres in the natural world around him. His list may include a water drop, orange, or a sea urchin. Extend your student’s thinking by asking him to compare spheres that occur naturally and those that are manmade: what is different about them? For older and more mathematically-mature students, you may choose to introduce the term spheroid as a figure that is approximately spherical in shape. If your student wishes, he can research the mathematical definition and its relation to 3D geometry and applications in calculus.

Geometry around Town

The architecture of buildings and other manmade objects provide a wonderful setting for your student to look for shapes and geometric properties. Point out architectural features, such as windows, in the shapes of squares, rectangles, or parallelograms. Your student can probably find roofs made up of triangles, rectangles, and trapezoids, but can she find a roof that is shaped like a cone? Patios and walls often display a variety of brick and stone patterns that may tessellate (completely fill the plane with no spaces in between). Stop to admire the fountain in the center of town and notice that arching water may form the shape of a parabola. Encourage your student to look all around. Where does she see triangles, pentagons, hexagons, octagons, and other polygons? Can she identify three-dimensional solids such as triangular prisms, rectangular prisms, and cylinders? Challenge her to discover that different shapes put together can form a new object. For example, what different shapes make up a bridge, water tower, or lamp post? By looking around from different angles and perspectives (standing, sitting, or lying on the ground) you will be amazed what she can discover!

Remember that just because you want your student to learn math doesn’t mean he always needs to be inside following a structured math lesson. Outdoor math activities are a great way to have fun learning math together. Your child will appreciate the opportunity to experiment, investigate, and talk with you about the wonders of mathematics.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.


3 Ways to Make Student Mistakes Valuable


How can we help change the negative perceptions associated with mistakes so our children can more easily bounce back?

Our children are growing up in a world that emphasizes high standards for academic success. As parents, we want our students to put forth their absolutely best effort each and every time they attempt a task. In doing this, to some degree, we create academic learning conditions that discourage mistakes. Watching our children make mistakes is not easy.

Whether it’s misspelling a word or doing poorly on a math test, children learn important lessons from making mistakes and gain confidence when they spring back from them. An important part of the learning process is knowing what to do after a mistake has been made. The challenge is that mistakes are naturally associated with negative emotions such as feeling unintelligent, ashamed, or embarrassed. Alternately, when mistakes are perceived as being valuable assets in the learning process, students can learn to how use them constructively to guide their learning.

How can we help change the negative perceptions associated with mistakes so our children can more easily bounce back?

Communicate the Value of Mistakes

One way to encourage this attitude is to analyze mistakes together and be specific about the feedback. Knowing that the answer to problem #5 is wrong doesn’t suggest how he can improve. Pointing out to him that he substituted an incorrect value in a math formula gives him guidance for solving the problem the next time.

When you review work with your student, he will discover that a mistake that makes him feel inadequate is usually a simple error in computation or a single concept applied incorrectly to several questions. In either scenario, the “fix” is usually easier than how big the problem feels to him. The more accepting you are about the mistakes he has made and how they happened, the less significance your student will place on future errors. He will begin to understand that mistakes are opportunities from which he can learn and which will help him become more resilient.

Identify the Reason Why a Mistake Happened

Did the mistake happen because your student needs more practice with basic facts? Were the steps of a process properly executed? Did she misread the directions? A problem marked wrong simply shows that the actions he took to solve it did not work, but this can easily be adjusted for the next round of practice.

Sharing specific ways she can improve is an effective way to coach her in purposeful practice. Purposeful practice involves isolating what’s not working and then mastering the skill causing difficulty before moving on to the next concept or lesson. For example, a singer learning a new song does not sing the piece start to finish, rushing through tricky sections and trying to sing it “good enough” just to finish. The vocalist will pause in trouble spots, figure out how to make it sound better, and then continue to sing the section again, only moving on when it has been mastered. This same principle can be applied to mistakes in a school assignments by focusing on the specific type of practice that is needed, instead of how much.

Acknowledge What Your Student Has Done Well

Then give him a chance to correct his mistakes and redo his work. This helps him learn that you value his effort and accept imperfection. It also conveys that sometimes learning involves trying again or learning a new strategy. When improvement becomes a significant factor in the evaluation process, a student is more likely to show progress and develop confidence.

We know our children will make mistakes on their assignments, projects, and tests– some simple and some more complex. It is important to show them that their mistakes contain seeds of learning. It is not an easy task, but, over time, you can help shift your student’s mindset, even slightly, so she views mistakes not as incidents to be feared and avoided but as inevitable, and often valuable, opportunities for new learning.

We have the opportunity to minimize opportunities for student anxiety and make confidence and resilience a habit in the lives of our children.


4 Creative Activities for Reinforcing Place Value


Try supplementing and reinforcing the concept of place value with these creative activities.

Place value is a key mathematics concept for students to learn. The concept that numbers can be broken apart and put back together gives students a more solid understanding of how different operations work. Knowing when to exchange groups of units (ones) for tens, how to handle a zero in the hundreds place when subtracting, or correctly recording numerals in a quotient, for example, can be confusing for many students. The Math-U-See presentation of place value using Decimal Street and our color-coded pieces for units, tens, and hundreds helps students develop an authentic understanding of place value by helping them construct meaning through visual representations and hands-on practice.

Try supplementing and reinforcing the concept of place value with your Math-U-See curriculum with the following activities:

Place Value Activities

Build a Number

Materials:
Integer Blocks
• Decimal Street™ poster
• Paper and pencil

Set up:
Your student needs to have access to 9 unit blocks, 9 ten-blocks, and 9 hundred-blocks.

Note: Depending on your student’s understanding of place value you may choose to have your student work on single, double, or three-digit numbers at separate times or review them all in one activity session.

• Ask your student to place a mystery amount of unit blocks (0-9), ten-blocks (0-9), and hundred-blocks (0-9) on the Decimal Street™ poster.
• Once the number is built, have your student write the number on the paper and then say it.
• Verify the answer is correct and record the number on a sheet of paper.
• After five numbers have been built, review the record of the numbers that were built and discuss the following:

• Did your student create more single-, double-, or triple-digit numbers?
• Which number is the greatest number or the least number?
• Underline a digit in one of the numbers and then ask your student to tell you the value it represents. (ex., in the number 65 the six represents 60 or six tens.)

Digit Swap

Materials:
Integer Blocks
• 0-9 cards (green, blue, and red)

Set up:
Shuffle each set of cards and place them in three separate stacks facing down.

• Have your student select one card from the blue stack and the green stack to create a number. For example, he may draw a green 4 and a blue 5 to create the number 54.
• Have your student build the number with the Integer Blocks and say the number.
• Next, you select a card from any of the three stacks.
• If you select a blue or green card, replace the current digit of the same place value with the new card.
• If you choose a card from the red stack (for example, 7), place that card to the left of the 5 to create the number 754.
• Have your student build the new number with the Integer Blocks and say the number.
• Play continues with you and your student exchanging digits to create new numbers to build and say.

Listen for the Number

Materials:
Integer Blocks
• Decimal Street™ poster
• Dry erase board, marker, and eraser

Set up:
Sit with your student back-to back, so that you can see the dry erase board and your student cannot. Your student needs to have access to the Integer Blocks and the Decimal Street™ poster.

• Write a number on the dry erase board that contains up to 3 digits.
• Read the number aloud to your student.
• Your student builds the number that he has heard with the Integer Blocks.
• Next, compare his model with the number on the board and verify it is correct.
• Switch roles periodically so that your student has the opportunity to be the reader and builder.

Remodel the Number

Materials:
Integer blocks
• Decimal Street™ poster
• Dry erase board, marker, and eraser
• Paper and pencil

Note: This activity reinforces the concept of zero place holders.

• Write a two-digit number on the dry erase board (for example, 63). Ask your student to build, write, and say the number on the Decimal Street™ poster.
• Next, tell your student she is going to remodel the number. The new number will always have a zero in it. For example, you might ask her to remodel the number to become 603.
• Have your student build, write, and say the new number (603).
• Discuss how the number changed and how it remained the same. For the given example, the digit 6 moved to the hundreds place, and the 3 remained in the units place and the zero shows that there are no tens. The number still contains the numerals 6 and 3.
• This activity can be adapted to begin with a 3-digit number. For example, begin with 287 and ask your student to remodel it so it is 280.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.


Math Journal Examples & Ideas


Having your student record his math activities through writing and sketching in a math journal can help reinforce his mathematical understanding.

What is a Math Journal?

Whether you call it a notebook or journal, having your student record his math activities through writing and sketching can help reinforce his mathematical understanding.

Writing about math processes and creating diagrams and pictures stimulates different pathways of the brain, more than computation in isolation will do. A math journal provides students of all abilities and ages with the flexibility to examine and express their mathematical reasoning. This is especially useful when math concepts are too complex or abstract to keep track of mentally.

A math journal also benefits you, the instructor, by providing a glimpse into your student’s mind so you can address any misconceptions and applaud his successes. Also, along the way, you will have a record of your student’s math studies that can be used for a portfolio.

How you choose to use a math journal will depend on your purposes, preferences, and the particular age and needs of your student. Let’s review some frequently asked questions to help you decide how you can best implement a math journal in your current program.

What Should My Student Use for a Math Journal?

Consider your objective when choosing the materials to create a math journal.

Do you want your student to be able to categorize his work and materials? A binder or three-prong folder with labeled dividers that separate the different types of entries by chapter, skill, or concept may be appropriate.

Do you want him to use it to document his work throughout the school year? In this case, a spiral or composition notebook where he can keep track of all his entries might be more efficient. In this format, worksheets can be taped in and folded, if necessary.

If your goal is to add journal entries from time to time, you can staple plain paper together to make small booklets to showcase particular concepts, problems, or a math theme, such a problem solving.

How Should My Student Use a Math Journal?

There is not one right way to do math journaling, so feel free to pick a format or a combination of ideas that works best for your student and math program. Keep in mind that the math journal can be filled with a variety of math-related concepts, ideas, and experiences.

Some possibilities to get your started might include:

• Drawings, diagrams, or models to illustrate math problems or math concepts.
• Written explanations of mental calculations.
• Lists of math vocabulary or symbols.
• Math-inspired art (such as tangrams, tessellations, fractals, or symmetry).
An interview with an adult who uses math in a profession.
• Newspaper or magazine clippings of math-related current events.
• Photographs of your student doing a hands-on math-related project.
• Creative writing that features math within the story.
• An explanation of how a problem was solved.
• Biographical sketches of mathematicians.
• Personal reflections about how your student feels about math.

How Often Should My Student Write in a Math Journal?

The frequency that you use a math journal can be as routine or flexible as you would like it to be. Begin with an attainable goal.

For example, you might choose to have your student reflect on a topic before he begins a unit of study and then again after a few days of instruction.

Because of the variety of ways math journals can be used, entries can be generated as often as 1-2 days a week or as occasionally as 2-3 times per math unit. The time it takes your student to create an entry will vary depending on his writing skills, the topic, and guidelines you establish regarding the depth and quality of an entry.

Ten minutes is typically is sufficient for most students, but you will want to allow extra time for more complex topics or problems. Be sure to build in time every so often for your student to share and celebrate his work. Doing this will help keep him accountable and provide authentic practice expressing his thoughts and ideas verbally.

How Much Should My Student Write?

Writing about math may be difficult and strange to your student in the beginning. Be positive and encouraging with his efforts, even if he just writes a sentence or two. As the weeks pass he will become more comfortable with math journaling, and you will see improvement in both the content and amount of writing he can produce.

What Are Some Good Prompts for a Math Journal?

Open-ended questions create greater potential to stimulate mathematical thinking and reasoning than closed questions.

For example, “Round 36.67 to the nearest tenth” is a closed question because it requires your student to provide a single “right” answer.

This question can be modified to be an open-ended question, encouraging your student to “stretch” his thinking, by considering multiple strategies or solutions, as in, “Give three different numbers that when rounded to the nearest tenth results in 36.7.”

By incorporating open-ended questions into math journaling your student, will attain a healthy balance between trying to find the “right” answer and discovering how problem solving works.

Should I Review Math Journal Entries?

Math journals best serve as a record of a student’s progress and mathematical thinking. Whether or not you choose to grade it formally is up to you.

Routinely reading and talking about your student’s entries is probably the most meaningful and effective feedback he can receive. Talk to your student if he gets stuck and comment on what he has written to encourage his efforts.

Ask your student to read his response and describe any diagrams or pictures; then give verbal feedback or ask him questions to help guide or extend his mathematical thinking.

Some questions you might think about while reading or listening to your student’s journal entries might be: Is the answer correct? Does he include mathematical reasoning that supports the solution? If computation is involved, did he use an efficient method or mental math? If relevant, does his solution indicate the use of estimation or determine if the answer is reasonable? Is there other information you would still like to know about your student’s thinking after he has shared his entry?

If you are looking for a flexible component to complement or enhance your current math program, try incorporating a math journal. By reading and listening to your student’s entries, you can evaluate progress and recognize his strengths and needs. Overall, a math journal is a great tool for your student to process his understanding of mathematical concepts and a fun way for students of all ages and abilities to enjoy math beyond just working with numbers.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


What is the Sequence in Math?


Is there a sequence to helping students develop mathematical thinking skills?

Children tend to follow a developmental sequence in their learning as they grow and develop. As a very basic example, most children first begin to crawl (while some may scoot), which is then followed by learning to walk, run, skip, and jump, with increased speed and agility over time. As children gain more experience and practice with these skills, they may find some more challenging to master or that they excel in one particular area. Similarly, children follow developmental learning progressions in their mathematical thinking, constructing meaning in their own way with foundational concepts and applying and extending them to more complex ideas at their own pace. So, is there a sequence to helping students develop mathematical thinking skills?

Some math skills must obviously develop sequentially. A student cannot begin to add numbers until he knows that those numbers represent quantities. Mathematics encompasses a wide variety of skills and concepts. Although these skills and concepts are related and often build on one another, it is possible to meet with success with some and have difficulty with others. For instance, a student may struggle with basic computation but finds he excels in geometry or with logic concepts. We can help our students develop a deeper and more comprehensive understanding of mathematics if we think of the subject in in terms of clusters of concepts and skills, rather than a strict linear progression.

As early as prekindergarten through grade 2, children begin to develop beliefs about what mathematics is and what it means to understand and to “do” math. Keeping students actively engaged, demonstrating enthusiasm, and using activities that encourage curiosity will help set a positive tone for learning math. At this early level, students should develop a solid understanding of the number system, including place value. Students should begin to count aloud; recognize the number of objects in a group; follow a sequence of two- and three- step commands; understand relative size and sort objects by size and shape; perform addition and subtraction computations efficiently; and respond accurately to mathematical signs. Instruction should also encourage exploration and understanding of patterns and measurement concepts and begin to learn the concepts of time, money, and basic graphing.

Building on their inquisitive nature, children in grades 3 through 5 should be encouraged to investigate and solve real-world problems. Instruction should include problem solving in which students have the opportunity to explain how they arrived at a solution and to consider more than one way of solving a problem. Students should be able to recall basic math facts with ease and demonstrate the relationship between processes such as addition and multiplication and subtraction and division. Students should also begin to work flexibly with the concepts, strategies, and representations of multiplication (and division), equivalence, and estimating quantities; use a variety of methods for computation; and analyze data. In addition, developing competency with fractions, decimals, and percentages will prepare them for middle school mathematics.

By the time students reach grades 6 through 8, they are forming opinions about their mathematical abilities, interest, and motivation that will influence how they approach mathematics during their high school years. Instruction at this level should build upon their strong foundation of basic skills and strengthen their emerging capabilities to think critically, comprehend cause and effect, and demonstrate their reasoning in both concrete and abstract representations. The foundational concepts of algebra and geometry can be integrated into instruction to accomplish these goals. Students should perceive relationships and make conversions among fractions, decimals, and percentages. In addition, they should be able to use and apply a wide array of equations and formulae, use calculators (and computers) with ease, and self-monitor their thinking during multi-step problem solving, as well as summarize and describe data distributions.

Keep in mind that every student is different, especially when it comes to being ready for upper-level mathematics. Some students may be ready for an algebra course as early as seventh grade, while for other students it is beneficial to wait until early high school. No matter where a student is on the math continuum, students who are ready for an algebra course not only demonstrate a strong command of basic computation but also exhibit a level of “mathematical maturity” that includes a desire and readiness to understand abstract mathematical definitions; to work with abstract models, symbols, and representations; and to recognize and make connections among mathematical structures. The course and skill progression from this point would be determined by the student’s academic goals and projected career path.

Math is a learning progression of concepts and skills that build upon one another. It begins with fundamental concepts such as counting, addition, and subtraction and gradually builds and expands toward an understanding of more complicated ideas such as geometric theorems and factoring polynomials. We know that students who don’t have a strong base will inevitably encounter difficulty at some point. It’s important to help students remember what concepts they still can improve upon. We can promote students’ mathematical thinking and reasoning abilities through developmentally appropriate instruction and activities. Over time they will eventually “run” with those concepts and organize them into broader mathematical structures, becoming lifelong learners who enjoy and are proficient in math.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.


Teach Word Problems with a Graphic Organizer [Free Download]


A graphic organizer can help develop the habit of visualizing a word problem in smaller chunks. Download yours and learn more about it in the blog post.

Word Problem Challenges

Many students love to read stories, play with puzzles, and creatively approach problems in their everyday life, so why do they have such an aversion to math word problems?

Word problems often pose a challenge because they require reading and comprehending the text of the problem, identifying the question that needs to be answered, and finally creating and solving a numerical equation.

If your student answers a word problem correctly, you assume he has a grasp of the concept. However, if it’s incorrect, you are left with many questions:

• Does he realize the answer doesn’t make sense?
• Did he not understand the context?
• Did he simply compute all the numbers in some way just to finish?
• Did he truly not know where to begin?

Most importantly: How can I help?

If you are lucky, you can identify the mathematical misconception and work from there. Oftentimes, however, the student’s answer isn’t even reasonable, and it can be difficult to pinpoint the exact area of his confusion. Then what can you do? If you find it challenging to teach your child how to solve word problems, try one or more of the suggestions below to help your student gain confidence in his problem solving skills.

Word Problem Strategies

Be More Relaxed & Playful

If your student has anxiety about word problems, try approaching them in a more relaxed and playful way by presenting problems that have more than one right answer, like a math puzzle or game. This can relieve the pressure of having to find “the right answer” and place the emphasis on the problem solving skills.

For example, consider this word problem: Shawn had $156. He went shopping for new hockey skates and now has $12 left. Find the cost of Shawn’s new hockey skates.

You can revise the problem to something like: The answer to a subtraction problem is 12. Tell what the equation might be.

The second question gives your student a springboard to work from, since it already indicates the operation. It also allows her to begin at her level of numerical comfort. In addition, because there are many answers to this type of problem, you can discuss with her how she went about solving it and gain some insight to her conceptual understanding and the strategies she used.

As an extension, you can ask her to write a word problem to match the math problem she created. These techniques can help her build confidence in her problem solving abilities and provide insight to you as to how she approaches solving a problem. Gradually she can work up to solving more problems like the first one presented above.

Extract the Numbers

Another way to increase comfort with word problems is to extract the numbers – in other words, create “numberless” problems. This is a great way to help your student notice the relationships in a problem and to observe how the language can help him understand those relationships.

For example, think about a problem such as: There are 125 girls participating in a choral competition. Twenty-nine more boys than girls are participating. Find the number of boys in the choral competition. Extract the numbers so it reads: Some girls are participating in a choral competition. More boys than girls are participating.

Then discuss with your child how he could find the number of boys participating in the choral competition.

By doing this you are helping him to focus on the situation of the problem, which will lead him to the necessary computation. He can insert his own numbers, or you can slowly introduce the numbers back into the problem for him to work with when he is ready to test a strategy. This method can also help your student determine when a problem contains extra information that is not necessary for solving the problem.

Graphic Organizer Example

Representing the information in the math problem with manipulatives, a drawing, or a diagram can also help make sense of the situation.

For example: Sara has 15 grapes. How can she divide the fruit between herself and two friends evenly?

Your student can show the 15 grapes with cubes or other small objects to represent the grapes and move them into three groups to find the answer. Discuss with your child how the picture, diagram, chart, expression, or equation relates to the situation in the problem. Ask her to explain why she chose it or why she thinks it is a good mathematical expression to use for the problem.

A graphic organizer can help develop the habit of visualizing a problem in smaller chunks. This can help shape your student’s thinking strategies to begin to think about where to start the problem solving process. Graphic organizers can also aid in brainstorming different thoughts and ideas as well as analyzing and synthesizing the mathematical concepts and procedures he selects to solve a problem.

Free Graphic Organizer Download

Click on the sample graphic organizer to see how it can be used to solve a word problem.

A graphic organizer can help develop the habit of visualizing a word problem in smaller chunks. Download yours and learn more about it in the blog post.

A blank version is also available for you to use with your student.

Word problems help your student to see math applied in the real world, and they encourage and give a reason to learn the underlying concepts and operations.

You can help your student make sense of these problems by helping and encouraging them with the problem solving processes. As your student moves forward in his mathematical learning, he will need to apply problem solving processes to more complex situations. By practicing on a regular basis, your child can strengthen and develop confidence in his problem solving skills.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.


Make Math Fun with a Math Selfie


A math selfie can help improve problem solving skills, increase self-confidence, and showcase student work while learning math.

A math selfie can help improve problem solving skills, increase self-confidence, and showcase student work while learning math.

Whether showing a quizzical look or a wide-eyed, cheerful smile, selfies are a mainstay among today’s youth. Selfies (short for self-portraits), serve as a way for pre-teens and teens to express their mood and share important experiences. As technology continues to become more prevalent in daily life, selfies provide a way for young people to participate and affiliate with that world. Although taking selfies is a part of “growing up digital”, it does not mean that all self-portraits are acceptable. As parents, we need to help our students learn the limits and guidelines for the type of pictures that are appropriate and those that are not. By applying an academic lens to selfies, we can help our students engage in the selfie trend in a positive way. The best part is that it can be applied to just about any math problem!

Math Selfie: Part One

Begin with a word problem. Perhaps your student has learned how to calculate the circumference of a circle and is completing practice problems to work toward mastery of the concept. Let’s see how the math selfie could be applied to a practice problem from this lesson.

Sample Problem: A machinist made a metal rod with a diameter of 5.4 millimeters. What was the approximate circumference of the end of the rod?

First, have your student read through the problem. Next, introduce the interactive mnemonic device, SELFIE, to help your student work through the problem solving process.

#SELFIE
 
Show my work
Estimate the answer
Look for errors
Find a solution
Include math terms
Explain my thinking

Show my work: Create a visual representation. He may decide to build a model, draw a diagram, act the problem out, or record a list of information needed to solve the problem. One or more of these strategies may be used, or he might come up with his own unique way to show it.

Estimate the answer: Determine a reasonable range for the solution. She might say that 3.14 rounds to 3 and that 5.4 rounds to 5. Since 3 x 5 = 15, a reasonable final answer will be around 15 mm. She might also indicate that 3.14 is already an approximation; therefore, the final solution will be as well.

Look for errors: Encourage him to check his work. This may include reading through his computation, using a calculator, or having a sibling or peer review what he has done.

Find a solution: Perform the actual computation. Look to see that she substitutes values correctly in the formula, that her work is accurate, and the answer is labeled with a unit of measure. Refer to the example below.

math-example

Keep in mind that, for other types of problems, this step might include creating a chart, table, or graph; showing a pattern; forming a conclusion; or making a prediction.

Include math terms: Listen for accurate use of math terms as your student teaches you how he solved the problem. For instance, does he refer to 3.14 as pi? Did he use the term diameter instead of saying “the line drawn from the center of the circle”?

Explain my thinking: Allow your student to reflect on the accuracy of her answer and prove that her method for solving the problem works. For the circumference problem, she might share his computation, talk about the strategy she used, or describe what she understands conceptually about circumference. If your student has trouble getting started in this process, you can help her by asking open-ended questions such as “What made you decide to do it this way?”, “What questions arose as you worked?”, or “How would you rate your solution?” If your student is ready to extend her thinking, you might ask questions like “How could you solve the problem if you were given the radius instead of the diameter?” or “What other math concept can you connect with this?”

Note: You may choose to have your student complete one or several problems using the SELFIE mnemonic before moving on to part two.

Math Selfie: Part Two

Once the problem solving is completed and all work has been checked for accuracy, your student is ready to snap a real selfie! Using a smartphone, tablet, or webcam, your student can take a self-portrait showcasing his problem solving skills while being creative. Maybe, for the sample problem given, he will choose to include circular objects he finds around the house or include a copy of his written work in his self-portrait. Free photo editing apps such as Pic Collage or Photo Grid allow your student to create an instant collage of his work and add digital stickers, borders, or text. He can share his accomplishment with your family digitally or print out a copy.

Printable Math Selfie Chart

Click here to download a printable math selfie chart.

A math selfie can help improve problem solving skills, increase self-confidence, and showcase student work while learning math.

So the next time your student grumbles about word problems, try refreshing your math routine with a math selfie. The interactive mnemonic helps your student to build responsibility for making sense of mathematics, use precise vocabulary, receive feedback, and reflect upon on the problem solving process. It also helps you as a parent learn more about your student’s level of understanding and identify what your student needs next. By capturing and celebrating his work with a selfie or photo collage demonstrates how your student can participate in the selfie trend in a fun, positive, and safe way.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.


Outdoor Summer Math Games & Apps


Summer offers parents and preschoolers time to enjoy the outdoors while still “stretching the brain.” The outdoor environment provides endless rich opportunities to build upon your child’s mathematical skills. Together, you can explore numbers, shapes, measurements, and more by trying some of these fun and easy guided activities or by simply asking the right questions to engage your child in talking about math.

Explore numbers, shapes, measurements, and more with your children this summer with these math games and apps.

Outdoor Summer Math Games

Have a Ball!

Gather a variety of balls (football, basketball, soccer ball, golf ball, bouncy ball, ping pong ball, baseball, etc.) and place them in a box or laundry basket. Have your child sort, order, weigh, and count the balls. He can also experiment with positions (in, out, around, on, under, etc.) as he places the balls in relation to another object, such as a table or chair.

Number Walks

Write a number on an index card and stick it to a container, such as a wagon, bucket, or paper bag. The object of the game is for your child to place the same number of items in the container as the number on the card. When she has the correct number of items, she can show you and then replace the items back where they belong. When replacing the items, you might encourage her to try to count backward. As an extension, you can have your child look for groups of similar objects.

Spray It!

Learn math this summer with this sidewalk chalk math game. src=

Draw at least 10 numbers or shapes with sidewalk chalk in a designated area. The amount of numbers or shapes drawn can be increased or decreased given your child’s skill and comfort level. Give your child a spray bottle filled with water. To play, ask your child to find a particular number, shape, or to find the answer to a math fact. When he finds it, he sprays it! Variations of this might include finding even or odd numbers, skip counting, counting backward, finding shapes with the same number of sides, or finding a shape that has a given number of sides. As an alternative to using a spray bottle, your child might enjoy using a flyswatter, wet sponge, or duster.

Free Exploration

Let your child explore outdoors and see what he does on his own without offering suggestions of what he can do. Does he run? Build? Climb? Dig? Ask open-ended questions about his discoveries, such as:

• “What have you discovered?”
• “How did you find that?”
• “What shape is it?”
• “How many do you see?”
• “What is the same/different?”
• “Can you group these … in some way?”
• “Can you see a pattern?”
• “What would happen if…?”
• “How many ways can you find to …?”
• “What happens when we …?”
• “What could you make from…?”

You do not have to know all the answers! When possible, encourage your child to examine an object from all sides. Discuss what you see together—the shape of leaves, the pattern of colors, or the number of blades of grass, pebbles, or bugs.

Picture Walk, Then Talk

Let your child take some pictures outdoors. When you get home or on a rainy day, look at the pictures together. Let your child talk about what she sees. Ask her some of the open-ended questions listed for the previous activity. Encourage your child to make up a story problem for you to solve from what she sees in the picture.

Summer Math Apps

Can’t go outside? On the go? KinderTown recommends the following apps for early learners who are practicing math skills:

Gro Garden

Together you and your child can become virtual gardeners and learn about the cycle of sustainable organic gardening. Plant and care for crops, feed hungry animals, and make compost from the food scraps. Each activity generates something that is needed in the next step, activity, or scene. The exploratory play incorporated in this app encourages your child to solve problems as she plays using trial and error and critical thinking skills. Note to Parents: The game’s pace is slow at first, as players must wait for their crops to grow. You might need to encourage your child to be patient. Once the garden starts to grow, the activity level quickly picks up.

Bugs and Buttons 2

This app includes six games at three different levels, each covering early math, pre-reading, and critical thinking skills. Your young learner can practice his fine motor skills in a fun and engaging manner. Math games such as “Button Repair” address visual/spatial issues. Other math skills your child will practice include sorting, counting, and matching.

Spending time outdoors allows you and your preschooler to conduct active explorations of early math concepts. Actively involving your child in conversations and observations and encouraging manipulation of concrete materials all invite your child to experience mathematics as he plays in, describes, and thinks about his world.

Free Addition Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Mastering addition facts is a critical part of becoming a confident math student.