In my last blog post, I suggested a vertical number line as one way to help your students connect numerals to number words.

Unfortunately, the only ones I had handy to show you were ones to 12 or 20 that I used to teach addition and subtraction strategies.

Eventually, I located the 0 to 100, floor to ceiling, vertical number line I made for my classroom on an old thumb drive. Then it was easy to create a new and improved free version for you based on the old template.

Still wondering about the benefits…

Vertical number lines can help your kindergarten, first, and second-grade students:

1. visualize the pattern of increasing tens and ones in two-digit numbers. They can easily see the sequence and repetition of the digits.
2. understand the value of numbers faster and easier. They are able to see the numbers increasing or decreasing in value. 24 is lower or less than 25 and 48 is higher or more than 38.
3. grasp the concepts of counting up and counting down when adding or subtracting. It is evident that sums increase and differences decrease in value.
4. make a connection between the terms rounding up and rounding down to the nearest ten to what they see.

While I taught rounding with a number line, I never thought to use a vertical one, even with it right there on the wall!

You can also create empty and interactive vertical number lines.

How to Prepare Your Vertical Number Line

Of course, this is technically a number path and not a number line. A number path is an effective counting model as opposed to a length model. Each number is clearly marked with a rectangle. Each rectangle can be counted.

I added stars in rectangles to make counting even easier. The stars are also color-coded for counting by 5’s and 10’s.

This number path is approximately 93 3/8 inches or 7 foot 9 3/8 inches tall.

• Start by choosing color or black/ gray/ white.
• Print the selected pages. Use cardstock and laminate (consider glare) for durability.
• Cut each strip carefully along the outside edge of the solid and dotted black lines.
• Put the strips together with tape. Start with zero and one. Place tape in the blank spaces. Align and overlap the ends of each strip, covering up each blank box.
• Or you can create one that folds up accordion-style for storage. To do this, cut off the empty boxes. Lay the strips face down so the ends abut. Then, tape across the edges.

Now you’re all set to post it on your wall!

More Ideas for Vertical Number Lines

Find ideas and resources for using an interactive vertical number line to develop number sense (Mr. Elementary Math) and using vertical number lines for adding multiples of tens (What I Have Learned).

Looking for More Resources…

• Frog Hopping Count Down (blog post with a freebie that includes a vertical number line to 12)
• Piggy Bank Count Up (a resource to purchase with a vertical number line to 20)
• Candy Bag Count Up (same as above with a different theme)

Click the highlighted words to download your free copy of the vertical number line 0-100.

I’d love to hear your ideas for using vertical number lines in the comments below!

Photo in title image by Coffee Beans and Children’s Dreams.

The post 4 Beneficial Reasons for Using a Vertical Number Line appeared first on Just Ask Judy.

Here are 6 math resources, great for first and second grades, which include those amazing birds.

Dress a Penguin

Let’s start with an easy to prepare freebie!

Here’s a color, cut, and glue activity for applying mental computation strategies to the basic addition and subtraction facts. Try it for morning work or as a math station.

Your students need to be familiar with the strategies. They will look at equations and determine the best of two strategies to apply. The two strategies for addition are Make 10 and Doubles Plus One while the two for subtraction are Count Back and Count Up To.

There is one set of pages for addition and one for subtraction. The first page in each set has two penguins, each labeled with a strategy. The second page has items of clothing with equations on them.

Select and print a set of pages. Add crayons, scissors, and glue. Now, you’re all set!

Your students will:

• Look at each equation.
• Choose the best strategy.
• Apply the strategy.
• Write the sum or difference.
• Color the clothing.
• Cut out the clothing.
• Sort the clothing by strategy.
• Dress each penguin in the correct clothing.
• Glue the clothing on the penguins.
• Color the penguins.

Be sure your students have the background knowledge and the fine motor skills required for this task. You want it to be fun and relaxing, not frustrating.

Scroll to the bottom of this post to download your free copy.

Featured next are my newest resources.

Winter Cover-Up Addition and Subtraction Facts to 20

While penguins are included in these resources, there are polar bears and snowmen too. I just couldn’t resist this adorable clipart created by Violet and Thistle!

You’ll love this winter-themed activity, with both digital (for use with Google Slides^TM) and print versions, that is designed to help your first and second-grade students practice, review, and develop fluency with the basic addition and subtraction facts to 20.

Use this engaging resource to support your instruction in mental computation strategies. Assign one or two slides/ mats at a time. Give the same ones to all students or assign them to individual students based on instructional needs. Try them with your small instructional groups, as a math center, or as a virtual activity.

Give Me the Details

There are 16 addition fact activity slides/ mats and 18 subtraction fact slides/ mats, sequentially organized by mental fact strategies. These activity slides/ mats coordinate perfectly with my other addition and subtraction fact resources.

The slides/ mats alternate between ones, generally, focusing on a single strategy with ones providing a cumulative review.

The print and digital versions follow the same sequence and have the same format. However, the equations in each grid are in random order so you can use both versions with the same students.

Each slide/ mat has 9 addition or subtraction equations. Students look at each equation and apply a fact strategy to determine the sum or difference.

With the printed format, students will place number tiles on top of the equations. In the version for use with Google Slides^TM, they will drag and drop a snowball or snowflake number on top of the equations.

Where Can I Find Out More?

Click on any of the highlighted words to waddle on over to my TpT store. Read the descriptions and check out the previews for more information. You’ll find three options for purchasing Winter Cover-Up; to print, for use with Google Slides^TM, or as a bundle.

Find more blog posts about teaching addition and subtraction facts. You’ll discover more information and yes, freebies!

More Penguin Themed Math Resources From My Store

Get up and moving on a cold, winter day with these two roam the room activities.

Telling Time With Playful Penguins

Here’s a set of 72 task cards for telling time to the hour, half-hour, hour and half-hour, quarter-hour, five-minute intervals, and one-minute intervals. You can easily mix and match sets to meet the instructional needs of your kindergarten, first, second, and third-grade students.

Penguins at Play Tens and Ones

Use this place value activity for first and second-graders to reinforce representing two-digit numbers in different forms; base ten, standard form, expanded form, and number word.

And finally, spend some time playing a game or collecting some data.

Make Ten Waddling Penguins

Get set to play three small group games (penguin collection game, memory match, and go fish) for learning the Make 10 addition facts with this resource that’s ideal for kindergarten, first, and second grades.

Play these games after you have introduced the Make 10 addition fact strategy, for either further development of the concept or to help acquire fluency with the facts.

It’s in the Bag for Winter – A Data Collection and Graphing Activity

Engage your first, second, and third-grade students with this seasonal activity. They’ll collect data by picking and replacing the letters of a word in a paper lunch bag until all the letters have been picked. Afterward, they’ll use their data to complete a bar graph and answer questions.

And of course, one of the words included in this set is penguin!

Click on the highlighted titles above to learn more about each resource.

Focus on Penguin Facts

Here are a few links to get you started with facts about penguins.

10 Facts About Emperor Penguins (National Geographic Kids)

5 Fun Facts About Penguins (CBC Kids)

Macaroni Penguins (Folly Farm) (They also want you to visit!)

African Penguin (San Diego Zoo) (Click the link for more detailed information.)

Click the highlighted words to download your free copy of Dress a Penguin.

I’d love to hear about your favorite fiction or nonfiction book about penguins in the comments below!

Photo credits: Volodymyr.Goinyk and Coffee Beans and Children’s Dreams

The post 6 Cool Penguin Resources to Energize Your Math appeared first on Just Ask Judy.

Popcorn Photo by etorres69

There are two prerequisites for mastering the subtraction doubles facts. First, students need to be fluent with the addition doubles facts. (Keep scrolling for help with this.) Secondly, they need to understand the inverse relationship between addition and subtraction.

As we all know, most students find learning subtraction facts more difficult than addition. The strategy for learning the subtraction doubles facts is to “think addition”. So, what’s the problem?

While pondering this, it struck me that the dilemma is these students simply don’t recognize the subtraction doubles facts for what they are.

One way to develop this recognition is more work with the parts and the whole. These kiddos easily recognize the parts and then recall the whole for addition. Why not work on deriving the parts from the whole?

Popping Doubles for Subtraction is a free resource for first and second-grade math. This resource is for students who’ve mastered the prerequisites but aren’t making the connection. The focus is on matching the parts to the whole to increase familiarity with the subtraction doubles. Use it during small group instruction or as an independent math center.

There are two versions, each in color and black/ white. Students match the whole and the parts for each double and place them on a popcorn mat, for the first open-ended version. The whole is given and students match the parts in the second version.

How to Prepare Popping Doubles for Subtraction

• Choose to print in color or black/ white.
• Pick the mat that is open-ended or the ones with the whole given.
• For the open-ended mat, decide if you want your students to use one mat (place the matches, record, and clear) or multiple mats.
• Print the mats and the popcorn numbers (parts). Use card stock and laminate for durability. Cut each page of mats in half. The popcorn numbers can be cut around the outlines or as rectangles.
• For the open-ended mats, print the bucket number ovals (wholes). Cut as ovals.
• Print copies of the recording sheet, if using.

How to Use This Subtraction Fact Resource

Seriously, this is a simple matching activity! Give your students the mats and the numbers. Tell them to find the parts that match the whole to create subtraction doubles facts. Have them record the corresponding equations. They can write these on plain paper, whiteboards, or the optional recording sheet. The recording sheet has spaces to write both the addition equation and the related subtraction one.

Add a little fun! Use a popcorn box or bag to store the number cards. Go ahead and pop some popcorn, too!

Looking for a way to provide concrete and visual support for learning the addition doubles facts with sums to 20? Recently, I updated my Dazzling Doubles resource, designed for students who need more than a rap to develop fluency with these facts. Click on the highlighted words or the photo to check out Dazzling Doubles, available for purchase in my TpT store.

While you’re there, download my Addition Fact Strategy- Doubles Free Sample!

Need more ideas to teach and practice subtraction fact mental strategies?

Read more blog posts.

• 1 Winning Way to Introduce the Count Down Strategy
• How to Start Teaching Subtract All and Subtract None
• Toss It! How to Actively Engage Your Students
• Subtraction is NOT Just Take Away

Purchase a Subtraction Fact Mental Strategy resource.

• Anchor Wall Charts
• Flashcards
• Worksheets
• Bundle

Find another freebie.

• Subtraction Fact Mental Strategy Count Up To Free Sample

Be sure to leave a comment sharing ways you have discovered to help students “think addition” to subtract!

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The post Free Fun With Popping Doubles for Subtraction appeared first on Just Ask Judy.

As part of my teaching past, I used a now defunct, oft-criticized supplemental math program that had high engagement, hands-on activities for developing an understanding of math concepts. This idea is a twist on one that introduced subtraction as taking away a quantity from a given set. While this activity could be implemented in the same manner, I’ve modified it to introduce the subtraction fact mental strategy for counting down or counting back. (I also changed the theme.) It’s a winning way to get your students involved in role-playing as active participants. Personally, I found the concepts of counting up or down, rather than counting on or back, to be easier for my students to grasp. I have, however, included both so you can choose.

For this introductory whole class activity, your students will role-play frogs hopping off lily pads. Designate an area of your classroom as the pond. Prepare 12 lily pads. You can easily google free printable lily pad templates. You can also freehand draw one. Print on colored paper or card stock. Then, laminate and cut. In addition, you could try green paper plates, carpet squares, or sit spots to represent the lily pads.

Kids Graphics by Educlips

Select a count down basic fact subtraction equation. I have included a list in the Frog Hopping Count Down resource. Place lily pads to represent the total number in your “pond”. Choose students (or rather well-behaved, listening frogs) to stand on or by each lily pad. Have your class state the total number of “frogs”. Pick 1, 2, or 3 “frogs” to hop off their lily pad and out of the pond, one at a time, as the class counts down. Demonstrate counting down with a number path, as needed.

Use the structure of a simple word problem while your students are acting it out. For example, 8 frogs were sitting on lily pads. Two frogs hopped off. How many frogs are still sitting on lily pads? Model how to write the corresponding subtraction equation. Repeat with different equations. Your students will eagerly wait for their turns to participate!

Follow up with this Frog Hopping Count Down practice activity. Just click on the highlighted words or a photo. This activity may be used in small groups or as an independent math station.

Materials for Frog Hopping Count Down

• task cards– count down or count back, color or black/ gray/ white
• number paths (optional)- display or individual size, color or black/ white, count down or count back
• optional small counters (frogs, gems, buttons, pompoms, etc.)
• recording sheets or whiteboards

Choose, print, and cut your materials. For durability, use card stock and laminate the task cards and number paths.

Each task card has a frog with a number and either 1, 2, or 3 lily pads. Depending on your students’ readiness, they can place a counter on top of each lily pad, use a frog counter to hop on each lily pad, touch each picture with a finger, or eye each picture to count down or back from the given number. Students can record the corresponding subtraction equations on whiteboards or one of the recording sheets.

Happy hopping! Share your favorite way to teach a subtraction fact mental strategy by leaving a comment.

Still looking for ideas to teach and practice subtraction fact mental strategies?

Check out these blog posts.

• How to Start Teaching Subtract All and Subtract None
• Toss It! How to Actively Engage Your Students
• Subtraction is NOT Just Take Away

Find a freebie.

• Subtraction Fact Mental Strategy Count Up To Free Sample

Purchase a Subtraction Fact Mental Strategy resource.

• Anchor Wall Charts
• Flashcards
• Worksheets
• Bundle

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The post 1 Winning Way to Introduce the Count Down Strategy appeared first on Just Ask Judy.

Photo by peterzsuzsa

Is This Subtraction Activity Suitable?

Using this activity will help you fulfill the first step in a concrete, pictorial, abstract (CPA) progression of instruction. Moreover, it will also give your students the opportunity to develop a deeper and lasting understanding of the underlying concepts.

Use this versatile resource as an introductory lesson for your whole class or small groups or as an intervention lesson with small groups or individuals. You can also utilize it as a follow-up activity in a math station. When working with a large group, you may want your students to work in pairs to reduce your material requirements and preparation.

At its most basic level, this resource can be used to develop a conceptual understanding for subtraction of the words all and none. Additionally, it will be helpful for introducing the subtraction fact mental strategies for subtracting zero (none) and subtracting all from a given number.

What You Need to Teach Subtract All and Subtract None

To get started, you will need a big-mouth rabbit mat and 10 counters for each student or pair of students. While carrot erasers are adorable and engaging, the cost makes them an impractical choice for larger groups. Use buttons, pom-poms, the printed carrot counters included in this resource, or any counters you have handy.

You also need a set of task cards. There are four sets to choose from, subtract all (word and number) and subtract none (word and number). Choose the set which best matches your instructional purpose. Create your own set of eight task cards by mixing and matching task cards with the same letter.

The ten frames mats are optional. They can be used to organize the number of carrots Rabbit has. Likewise, using a recording sheet is also optional. Plain paper and whiteboards work just as well for recording the subtraction equations.

How to Use This Subtraction Resource

Read the problem on your first task card step by step. Students show the number of carrots Rabbit has with their counters. These can be organized on ten frame mats. Students take the number of carrots Rabbit eats and place them in Rabbit’s mouth. Then, they write the corresponding subtraction equation on a recording sheet or whiteboard. Those students working as partners can take turns by task or by problems.

Additional Subtraction Resources

Be sure to read this previous post, Subtraction is Not Just Take Away, which includes a freebie for teaching the count up to strategy for subtraction facts. Find additional resources for teaching subtraction facts, including a free one, in my Teachers Pay Teachers store.

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The post How to Start Teaching Subtract All and Subtract None appeared first on Just Ask Judy.

Recently a teacher left a comment about one of my resources that had me pondering the possibilities. She was searching for “something to inspire struggling” learners. Granted, pencil and paper games and activities are certainly more motivating than practice with flash cards and worksheets but I always find incorporating physical activity into practice and review to be the bee’s knees of motivation!

Imagine the pure joy exuded by a little fellow, new to our school and repeating first grade, when my co-worker and I set up a jungle walk complete with props (think river, rocks, trees, and stuffed animals) through the classroom as a review of positional concepts!

Thinking along these lines, I crafted an activity, Toss It!, for practicing or reviewing adding and subtracting basic facts or multiples of ten. For the do-it-yourself version, you will need paper plates, a marker to write numbers, an object to toss, and number cards.

I chose green paper plates to represent apple trees and blue plates for ponds but you are only limited by your imagination! Dinner-sized plates stayed in place better than luncheon/ dessert sized.

Be sure to try tossing your object beforehand as some will be too bouncy. Beanbags, Koosh balls, Tossimals, and balled-up paper all worked well. You too may find yourself in a toy aisle tossing a few on the floor to see what happens! Lindsy at Preschool Alphabet has directions for creating felt apple beanbags.

This activity is perfect for an individual or small group of students. You can also set up multiple stations (to reduce wait time) so your whole class can participate.

Decide on the equations you want your students to practice. Since I teach facts by mental strategies this is how I did mine. Here are a few examples to get you thinking.

To practice the addition fact strategy of counting up (or on), use number cards 1 to 9. Pick a card. Number one or two sets of plates 1, 2, and 3. Place your plates on the floor or a table. Toss it! Use your two numbers to say or write the addition equation.

You can make this activity as physically easy or challenging as you like by changing the distance between the tosser and the plates. Also, decide if the object must land directly on a plate (or close is good enough) and the consequences if it doesn’t, toss again or lose your turn. Take turns tossing.

Use number cards 3 to 12 to practice the subtraction fact strategy of counting down (or back). Pick a card. Number one or two sets of plates 1, 2, and 3. Toss it! Say or write the subtraction equation.

Choose any numbers between 0 and 10, label your plates, toss it, and double your number to review the addition doubles. You can also say or write the corresponding subtraction doubles equation. If you teach this as halves; label your plates with even numbers between 2 and 20. Toss it! Say or write the equation to subtract half of your number.

Additionally, you can add and subtract two-digit numbers and multiples of ten. You will need a set of commercial or self-made flashcards for the numbers 11-99.

Use number cards 11 to 49 for addition. Pick one. Number your plates with multiples of ten, 10 to 50. Toss it! Say or write your numbers. Add. Substitute number cards 50 to 99 for subtraction.

You can find a complete version of Apple Tree Toss It! for adding and subtracting basic facts and multiples of ten in my Teachers Pay Teachers store.

I’d love for you to share your favorite ways to incorporate physical movement into practice and review activities in the comments below.

Check out this Pinterest board for more apple-themed ideas!

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Background Information

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