ten frames

Multiplication using Ten Frames or Base Ten

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by C. Elkins, OK Math and Reading Lady

Yes, you can even use ten frames to teach multiplication concepts! Here are my mini ten-frames with dot cards from 1 – 10:  Click HERE to get a free copy. These are helpful to use, especially if you don’t have enough tens/ones blocks . . .  or you prefer manipulatives that are slightly easier to manage. These provide a strong connection to place value, and the commutiative and distributive properties.

I recommend two sets of the cards (1-9) per student. Each set has multiple copies of the same number. They can be laminated, cut, and placed in a baggie for ease in handing out and storage.

Multiplication Examples:

  1. Single digits (basic facts): 
    • For the problem 3 x 6, the ten frame is really helpful for the student to see 3 x 6 is almost like 3 x 5 with one more group of 3 added on (by being familiar with the fact that the top row on a ten frame is 5).
    • Because of the commutative property, I know these two facts will have the same answer. But which of these below do you think might be “easier” to solve? Students don’t often know they have a choice in how they can use the numbers to their advantage!
      6 x 3 (six groups of 3)
      3 x 6 (three groups of 6)
  2. Double digit x 1 digit:
    • Use of these also provides a strong connection of place value and multiplication. Notice how students can see the breakdown on the 4 x 12 problem (4 groups of 12 = 4 x 10 plus 4 x 2). Great introduction to the distributive property of multiplication!
    • Here is where application of the commutative property also comes in handy. Which of the methods below would you rather use to solve: count by 4’s or count by 12’s? Again, show students how to use their strengths to decide which way to think about solving the problem.
    • Even though the number of total pieces might seem to be a little overwhelming, it definitely is worth the effort for a few lessons so students get a visual picture of the magnitude of the products.
  3. Here are other ways to model multiplication problems with manipulatives like base ten rods or base ten disks.

After students get practice using these manipulatives (concrete), then proceed to pictorial models to draw them as simply as possible.  This will give them a good foundation to apply to the abstract (numbers only) problems.  I always pitch for the CPA progression whenever possible!!!

I will pause a while for the summer and just post once a month until school starts up again.  Take care, everyone!  But please don’t be shy.  Post your comments, ask your questions, etc.

Interactive math lessons and activities on NCTM

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Review by C. Elkins, OK Math and Reading Lady

Resource – http://illuminations.nctm.org

This is a math resource I absolutely love! It is a product of the National Council for the Teachers of Mathematics (NCTM).

This site includes lesson plans and interactive activities. Search in several ways: by topic, by standard, or by grade level. Need some strategy games? Check out “Calculation Nation” (some of which can be played against other players), and “Brain Teasers.” I have just added this link to my Resources page (on my blog home page).  Pass this along to parents for them to use with their children at home!

Many of the lessons connect to exploration projects and literature. The interactive features are outstanding!! These are perfect for the smartboard, on laptops, or tablets. Doing Zoom lessons? Then these are also wonderful for sharing the screen to introduce or review concepts. Once you are on the home screen, click the Interactives box (right side) and then the desired grade level. There are dozens of great applets, but here are a few you might really like. I have linked them for easy reference, so just click on the  title and you’ll be there:

Dynamic Paper: Customize graph paper, number lines, spinners, nets, number grids, shapes (to include pattern blocks, color tiles, and attribute blocks), and tessellations. You can also choose inches or cm. These can be customized, saved and printed as jpeg or pdf. I created the spinner shown here from this application.

Five Frame and Ten Frame tools: Geat activities to build number sense using five or ten frames. These may take 1-2 minutes to load.

Cubes: Build a rectangular prism one cube, or row, or layer at a time and then compute the volume or surface area.

Coin Box: Drag and exchange coins. There is also a feature I like (the grid at the bottom right corner), which puts coins in blocks (by 1s for pennies, 5s for nickels, 10s for dimes, and 25s for quarters). This really helps see the value of the coins. Want more info about coin blocks? Once on the Coin Box page, click on the “Related Resources” tab.

Try these for fractions: Fraction Models (which includes decimal and percent equivalencies) and the Fraction Game.

Geometric Solids: Create a shape (either transparent or solid) and swivel it around to see all of the faces, vertices, and edges. It has a cube and pyramid as far as basic 3D shapes are concerned. I wish it had more that 3rd-5th students would encounter.

Here’s a nice multiplication game:  Product Game  Two players (or a player vs. the computer) choose factors from the bottom bar to create products shown on the game board grid to get 4 in a row (and try to block your opponent from getting 4 in a row).  Be sure to see the directions included.

Some of the interactives require an NCTM subscription.  The ones I have listed above should be okay to access without membership. I have subscribed for years and just paid $94 for this coming year. Well worth it if you plan on using their site extensively.  This subscription also entitles you to a print and and online journal, blog capabilities, and more.

Enjoy these and so many more!!! Let us know if there are others you recommend.  I’ll highlight more on my next post.

 

Number Talks with Dot Cards: Subitizing, Number Sense, Facts (Part 1)

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by C. Elkins, OK Math & Reading Lady

Do you see 3 + 4 =7 or perhaps 5 + 2 = 7? Maybe you see 3 + 2 + 2 = 7.

I have been using dot cards for many years with K-2 students as part of my Number Talks routine. I’d like to share some ways to follow this routine using both ten frame dot cards and random dot cards.  These are also easy to use via distance learning situations.

If you haven’t tried this before, you are in for a treat!  It is so nice to listen how students process their thinking. I never cease to be amazed at how developed a child’s thoughts can be expressed . . . and how many children take this as a challenge to see how many ways a dot picture can be explained.  I often feel I learn so much about my students capabilities (or sometimes the deficits) during this type of Number Talk session.  Look for my recommended links below (FREE).

What are the benefits?:

  1. Students gain the ability to subitize (tell a quantity without physically counting).
  2. Students gain number sense by noticing more dots, less dots, patterns aid counting, the same quantity can be shown different ways, sequencing numbers, skip counting, and many more.
  3. Students gain the ability to see many different ways a number can be composed or decomposed which assists with addition and subtraction facts.
  4. Students gain practice with strategies such as counting on, add/subtract 1, doubles, near doubles, adding 9, adding 10, missing addends, and equal groups.
  5. Teachers are able to observe students’ processing skills in an informal math setting.

Materials needed:

  1. Ten frame dot cards:  This set is FREE from TPT and includes ten frame cards as well as random dot cards. Great find!!  https://www.teacherspayteachers.com/FreeDownload/Number-Talks-Early-Level-Starter-Pack-10-Frames-and-Dot-Cards-4448073
  2. Random dot cards (not on ten frames)

General procedures:

  1. Decide how you are going to show the cards:
    • Show to students who are seated near the teacher?
    • Show to students via a document camera projected to a screen?
    • Show to students online with a split screen?
    • Show to students via a ppt?
  2. Depending on the grade level, you may want to flash the card quickly to encourage subitizing or shorten/extend the time the card is shown.
    • To encourage subitzing to 5, I recommend flashing the card for a couple of seconds for dots from 1-5 for all age groups.
    • Depending on the number of dots and the complexity of the dots, you may choose to shorten or extend the time you display the card for amounts more than 5.  The goal is for the students to look for patterns, equal groups, doubles, dots making squares, rectangles, or triangles, determine a quantity, and then explain how they arrived at that amount.
  3. Students put a quiet thumbs up when they have decided the quantity.  They should not say the amount outloud at this point. This shows respect for others who are still processing.
  4. The teacher observes to see who is counting, who is participating, who uses fingers, who is quick /slow, etc.
  5. Teacher asks random students, “How many dots?”
  6. Teacher asks random students, “How did you see them?”
  7. Results can be stated verbally or written down by the teacher.

Here are some examples with sums less than 10:

Here are examples using 2 ten frames to illustrate quantities greater than 10:

Next post:  I will feature ways to use the random dot cards for your Number Talk sessions.

Do you need professional development for yourself, your team, your school?  Please contact me and we can work out a plan that fits your needs.  I can provide personal help via email or Zoom all the way up to custom made webinars or power point presentations.  Let me know!

Do you know students who need extra help at home via online tutoring?  See my link for Varsity Tutors and mention my name. 

Do you want to do some online tutoring yourself at a time that works with your schedule? See my link for Varsity Tutors and mention my name.  Feel free to ask me questions as well.  

 

 

 

Ten Frames Part 4: Multiplication

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by C. Elkins, OK Math and Reading Lady

Yes, you can even use ten frames to teach multiplication concepts! Here are my mini ten-frames with dot cards from 1 – 10:  Click HERE to get a free copy. These are helpful to use, especially if you don’t have enough tens/ones blocks . . .  or you prefer manipulatives that are slightly easier to manage. These provide a strong connection to place value, and the commutiative and distributive properties.

I recommend two sets of the cards 1-9 per student. Each set has multiple copies of the same number. They can be laminated, cut, and placed in a baggie for ease in handing out and storage.

Multiplication Examples:

  1. Single digits (basic facts): 
    • For the problem 3 x 6, the ten frame is really helpful for the student to see 3 x 6 is almost like 3 x 5 with one more group of 3 added on (by being familiar with the fact that the top row on a ten frame is 5).
    • Because of the commutative property, I know these two facts will have the same answer. But which of these below do you think might be “easier” to solve? Students don’t often know they have a choice in how they can use the numbers to their advantage!
      6 x 3 (six groups of 3)
      3 x 6 (three groups of 6)
  2. Double digit x 1 digit:
    • Use of these also provides a strong connection of place value and multiplication. Notice how students can see the breakdown on the 4 x 12 problem (4 groups of 12 = 4 x 10 plus 4 x 2). Great introduction to the distributive property of multiplication!
    • Here is where application of the commutative property also comes in handy. Which of the methods below would you rather use to solve: count by 4’s or count by 12’s? Again, show students how to use their strengths to decide which way to think about solving the problem.
    • Even though the number of total pieces might seem to be a little overwhelming, it definitely is worth the effort for a few lessons so students get a visual picture of the magnitude of the products.
  3. Here are other ways to model multiplication problems with manipulatives like base ten rods or base ten disks.

Continue reading →

Ten Frames Part 3: More addition, subtraction, and place value

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by C. Elkins, OK Math and Reading Lady

Welcome back to Part 3 of my Ten Frame series. This will continue with some more ideas on using ten frames for addition and place value. Be sure to grab my free set of mini ten frame dot cards and Place value mat with ten frames to use with these activities.

Add 9:

How often do you see students counting their fingers, drawing tally marks, or other figures to add 9? But what if they could visualize and conceptualize adding 9 is almost like adding ten, but one less? This is where the ten frame comes in handy.

  • To be most efficient with adding 9, help students to add 10 (or a multiple of 10) to any single digit.  Example: 10 + 7, 20 + 4, 50 + 8 . . .
  • Show a problem such as 9 + 7 as part of your daily Number Talk. Observe and listen to how students are solving.
  • Introduce this strategy by showing two ten frames – one with 7 and the other with 9. Check for quick recognition (subitizing) of these amounts on each ten frame.
  • Move one counter from the ten frame with 7 to the ten frame with 9. This will complete it to a full ten frame. Then add 10 + 6 mentally.
  • The purpose is for students to visualize that 9 is just one away from 10 and can be a more efficient strategy than using fingers or tally marks.
  • Practice with several more +9 problems.
  • For 3rd and up try mental math problems such as 25 + 9 or 63 + 9.  Then how about problems like 54 + 19 (add 20 and take away one)?
  • Can students now explain this strategy verbally?

Subtract 9:

  • Let’s say you had the problem 14 -9.  Show 2 ten frames, one with 10 and one with 4 to show 14.
  • To subtract 9, focus on the full ten frame and show that removing 9 means almost all of them. Just 1 is left. I have illustrated this by using 2 color counters and turning the 9 over to a different color.
  • Combine the 1 that is left with the 4 on the second ten frame to get the answer of 5.
  • Looking at the number 14, I am moving the 1 left over to the one’s place (4 + 1 = 5). Therefore 14 – 9 = 5

Use of the ten frame provides a concrete method (moving counters around) and then easily moves to a pictorial method (pictures of dot cards). These experiences allow students to better process the abstract (numbers only) problems they will encounter.

Place Value Concepts: Continue reading →

Ten Frames Part 2: Addition and subtraction

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by C. Elkins, OK Math and Reading Lady

Last week’s focus was on using ten frames to help with students’ number sense and conceptual development of number bonds for amounts 1-10. This post will feature ways to use ten frames to enhance students’ understanding of addition and subtraction. Look for freebies and a video!

There are many addition and subtraction strategies to help students memorize the basic facts such as these below. The ten frame is a very good tool for students of all grade levels to make these strategies more concrete and visual. I will focus on some of these today.

  • add or take away 1 (or 2)
  • doubles, near doubles
  • facts of 10
  • make a ten
  • add or sub. 10
  • add or sub. 9
  • add or sub. tens and ones

Doubles and near doubles (doubles +1, -1, +2, or -2): If the doubles are memorized, then problems near doubles can be solved strategically. 

  • Show a doubles fact on a single ten frame (for up to 5 + 5).  Use a double ten-frame template for 6 + 6 and beyond.
  • With the same doubles fact showing, show a near doubles problem.  This should help students see that the answer is just one or two more or less.
  • Repeat with other examples.
  • Help student identify what a doubles + 1 more (or less) problem looks like. They often have a misconception there should be a 1 in the problem. Make sure they can explain where the “1” does come from. Examples:  7 + 8, 10+11, 24+25, 15 +16, etc.
  • For subtraction, start with the doubles problem showing and turn over the 2-color counters or remove them.

Facts of 10: These are important to grasp for higher level addition / subtraction problems as well as rounding concepts. Continue reading →

Ten Frames Part 1: Number Sense

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by C. Elkins, OK Math and Reading Lady

The focus in this post will be an introduction to ten frames and ways they can help your students gain number sense. Then stay tuned because ten frames can also be a great tool for addition, subtraction, multiplication, and division.

Subitizing: This is the ability to recognize an amount without physically counting. Looking at the picture of red counters: If the top row is full, does the student automatically know there are 5? Doing a Number Talk is a great way to practice subitizing using a ten frame:

  • Use your own or pre-made dot cards. Flash the card for 1-2 seconds. Observe students. Are any of them trying to point and count? Or do they seem to know right away? Here’s a great video I recommend: KG Number Talk with ten frames
  • Tell students to put their thumb in front of their chest (quietly) to signal they know how many there are.
  • Ask a few students to name the amount.
  • Then ask this very important question, “How did you know?”
  • For the top picture you might hope a child says, “I knew there were 5 because when the top row is full, there are 5.”
  • For the bottom picture, you might hope for these types of responses: “I saw 4 (making a square) and 1 more.” or “I saw 3 and 2 more.” or “I pictured the 2 at the bottom moving up to the top row and filling it up, which is 5.”

The idea is to keep building on this.

  • What if I showed 4 in the top row? Can the student rationalize that it was almost 5? Do they see 2 and 2?
  • What if I showed 5 in the top row and 1 in the bottom row? Can the student think “5 and 1 more is 6?”

Here are some resources you might like to help with subitizing using ten frames.

Number Bonds: Using ten frames to illustrate number bonds assists students with composing and decomposing numbers. Students then see that a number can be more than a counted amount or a digit on a jersey or phone number. Here is an example of number bonds for 6:

  • 6 is 5 and 1 (or 1 and 5).
  • 6 is 4 and 2 (or 2 and 4).
  • 6 is 6 and 0 (or 0 and 6).
  • 6 is 3 and 3.

Teaching strategies for number bonds using ten frames: Continue reading →