Number sense

Rounding and Number Lines

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by C. Elkins, OK Math and Reading Lady 

I get requests from many teachers to help with instructional strategies regarding rounding, so I am happy to share my thoughts (and freebies) with you. Difficulty with rounding usually means students lack number sense. The essential goal of rounding is: Can you name a benchmark number (whole, tens, hundreds, thousands, tenths, hundredths, etc.) that a given number is closer to? I have found the more experience a student has with number lines, the better they will be with number sense, and the better they are with rounding to the nearest ___.  Then this rounding practice must be applied to real world problems to estimate sums, differences, products, or quotients.

When doing a google search for tips on rounding (ie Pinterest), you very often find an assortment of rhymes (such as “5 or more let it soar, 4 or less let it rest”) and graphics showing underlining of digits and arrows pointing to other digits. These steps are supposed to help children think about how to change (or round) a number to one with a zero. Many students can recite the rhyme, but then misunderstand the intent, often applying the steps to the wrong digit, showing they really don’t have number sense but are just trying to follow steps.

My answer (and that of other math specialists) is teaching students how to place any number on a number line, and then determining which benchmark number it is closest to. Continue reading to see examples and get some free activities. And watch next week for some new rounding activities for grades 2-6 (whole numbers and decimals).

Continue reading →

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 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 →

Addition and Subtraction Part 2: Part-Part-Whole Models KG-2nd

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by OK Math and Reading Lady

In Part 1 I focused on a numerical fluency continuum, which defines the stages a child goes through to achieve number sense. After a child has a firm grasp of one-to-one correspondence, can count on, and understands concepts of more and less, he/she is ready to explore part-part-whole relationships which lead to the operations of addition and subtraction. That will be the focus of this post. Read on for free number bond activities and a free number bond assessment!

One way to explore part-part-whole relationships is through various number bonds experiences.  Number Bonds are pairs of numbers that combine to total the target or focus number. When students learn number bonds they are applying the commutative, identity, and zero properties. Do you notice from the chart below that there are 4 number bonds for the number 3; 5 number bonds for the number 4; 6 number bonds for the number 5, etc? And . . . half of the number bonds are actually just the commutative property in action, so there really aren’t as many combinations for each number to learn after all.

  • KG students should master number bonds to 5.
  • First graders should master number bonds to 10.
  • Second graders should master number bonds to 20.Teaching Methods for Number Bonds

  • Ideally, students should focus on the bonds for one number at a time, until mastery is achieved. In other words, if working on the number bond of 3, they would learn 0 and 3, 3 and 0, 1 and 2, 2 and 1 before trying to learn number bonds of 4. See the end of this post for assessment ideas.

  • Ten Frame cards: Use counters to show different ways to make the focus number. (See above example of 2 ways to show 6.) Shake and Spill games are also great for this:  Using 2-color counters, shake and spill the number of counters matching your focus number.  See how many spilled out red and how many spilled out yellow.  Record results on a blank ten-frame template. Repeat 10 times.
  • Number Bond Bracelets: Use beads and chenille stems to form bracelets for each number 2-10.  Slide beads apart to see different ways to make the focus number.
  • Reckenreck: Slide beads on the frame to show different combinations.
  • Part-Part-Whole Graphic Organizers:  Here are two templates I like. Start with objects matching the focus number in the “whole” section. Then move “part” of them to one section and the rest to the other section. Rearrange to find different bonds for the same focus number. Start students with manipulalatives before moving to numbers. Or use numbers as a way for students to record their findings.

    Once students have a good concept of number bonds, these part-part-whole organizers are very helpful when doing addition and subtraction problems (including story problems) using these structures: Result Unknown, Change Unknown, and Start Unknown.  Children should use manipulatives at first to “figure out” the story.

  • Here is an example of a change unknown story:  “I have 5 pennies in one pocket and some more in my other pocket. I have 7 pennies all together. How many pennies in my other pocket?” To do this, put 5 counters in one “part” section. Count on from 5 to 7 by placing more counters in the second “part” section (2). Then move them all to the whole section to check that there are 7 all together.  Students are determining “What goes with 5 to make 7?” 5 + ___ = 7
  • Here is an example of a result unknown subtraction story:  “Mom put 7 cookies on a plate. I ate 2 of them. How many cookies are still on the plate?” To do this start with the whole amount (7) in the large section. Then move the 2 that were eaten to a “part” section. Count how many are remaining in the “whole section” to find out how many are still on the plate?  7 – 2 = ____.
  • How are number bonds related to fact families?  A fact family is one number bond shown with 2 addition and 2 subtraction statements.  Ex:  With number bonds 3 and 4 for the number 7, you can make 4 problems: 3 + 4 = 7;  4 + 3 = 7;  7-3 = 4;  and 7-4=3.

Continue reading →

Daily Math Meeting Part 5: Using the 100 Chart and “Guess My Number”

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by C. Elkins, OK Math and Reading Lady

This post will focus on ways to use a 100 chart to teach or review several math standards in the number sense and number operations strands (all grade levels). Each of these strategies can be completed in just a few minutes, making them perfect for your daily math meeting. Choose from counting, number recognition, number order, less/greater than, odd/even, addition, subtraction, multiplication, number patterns, skip counting, mental math, 1 more/less, 10 more/less, etc.

You can use a 1-100 chart poster on the smartboard, in poster form, or as a pocket chart. The pocket chart is the most versatile. See an example here: enasco.com pocket chart   Here is also a link to little colored transparent pieces that can be placed in the pockets to highlight chosen numbers: enasco.com pocket chart transparent inserts   I often show students that a 100 chart is actually just a giant number line all squished together instead of spread out across the room. To do this, I print off a chart, cut it into rows, tape the rows together, then highlight each multiple of 10. Second concept is that the lower numbers are at the top, and the higher numbers are at the bottom.

 Counting, Number Order, and Place Value

  • Instead of starting with a full 100 chart, start with an empty chart. Add 1 number per day in order, building toward the 100th day of school. This would be suggested for KG level. 
  • For other grade levels: Start with the numbers 1-10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. Put the rest of the number pieces in a jar, baggy, or container. Draw one or more numbers at random each day and assist students in placing the number where it belongs. Example:  If you draw out 45, let’s look at the one’s place (5) and know that it belongs in the same column as the 5. Let’s look at the ten’s place. We know it is greater than 40, but less than 50 so this helps us know which row it belongs in. As you progress, start using the currently placed numbers to help locate the new numbers. “I need to place 67.  I see 57 is already on our chart and know that 67 is ten more, so I place it directly underneath.”
  • Number Thief Game:  After your chart is filled, try this game. After the children have left for the day, remove a few of the pieces. Then during your math meeting the next day, the children try to identify the missing numbers. Read how this blogger describes it:  “Swiper” at petersons-pad.blogspot.com
  • Number locating: Just practice locating numbers quickly. If asked to find 62, does the student start at 1 and look and look until they find it? Or can they go right to the 60s row?
  • Place Value Pictures:  You can’t do this on your hundred chart at meeting time, but there are dozens of picture-making worksheets available for free on TPT in which students follow coloring directions to reveal a hidden picture. Students get much better with locating numbers quickly with this type of practice.

Guess My Number: This is great for reviewing various number concepts. Here are a variations of guessing games. You can use with 1-100 chart, or 100-200, etc.

  1. Teacher writes a number secretly on a piece of paper (ex: 84). The teacher gives a single clue about the number, such as: “My number is greater than 50.” Then let 2-3 students guess the number. Confirm that they at least guessed a number greater than 50. Redirect if not. If you have the little colored inserts, place one in each of the incorrect numbers so students will know what was already guessed. If you don’t have those, just write the guessed numbers somewhere where students can see.  Give a new clue after every 2-3 guesses until someone guesses the number.  After guessing correctly, I always show the students the number I had originally written down so they will know I was on-the-level. Here are some example clues for the secret number 84: My number is even.  In my number, the one’s place is less than the ten’s place.  My number is less than 90. My number is greater than 70. If you add the 2 digits together, you get 12.  The one’s digit is half of the ten’s digit. Again, affirm good guesses because at first there may be several numbers that fit your clue.
  2. Yes or No:  This is almost a backward version of Guess My Number. Try this one after students are well-versed with the above game. It starts out the same though. Teacher selects a number. Then students have 10 tries to guess the number. They ask you questions, which can only be answered “yes” or “no.” Keep track on a chart paper of their questions and your answers. Some sample questions students could ask:  Is your number even? Is your number greater than 50? Is your number in the sixties? Is your number less than 90? Are both of the digits even? Some higher level questions could deal with multiples (Is your # a multiple of 2? Is your number divisible by 4?)

Continue reading →

Daily Math Meeting Part 4: Number of the Day/Week and Fun Facts

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by C. Elkins, OK Math and Reading Lady

This is part 3 of my “Daily Math Meeting” posts. I will share several different fun and motivational math activities that can be done in just a few minutes on a daily basis — all of them building number sense and reviewing concepts of subitizing, number bonds, addition, subtraction, less, greater, even, odd, etc.

Number of the Day / Week

You can look on Pinterest or TPT and see many good resources on this topic – from daily review sheets to bulletin board products. Here’s my take on it (depending on your grade level).  If you are KG, then I suggest a number of the week, building from 1-10 at first (for the first 10 weeks). Focus on #1 the first week, #2 the second and so on. Really go in depth with each number, revealing a little bit each day. Then after the 10th week, repeat. This will give students adequate time to focus on each number in depth. See the attached PDF for some of my slides regarding this topic. daily-practice-to-build-number-sense-pdf

Monday:  “Our number this week is one.” Here’s what it looks like (show the numeral 1).” Students say the number and make it in the air. Teacher shows how to write it. Then show a representation of the number (such as putting something in a jar or posting on the board).

Tuesday-Thursday: Review the above and then show another way to represent the number (maybe 1-2 more each day). Examples:  Five or Ten frame, dice, domino, fingers on a hand, place on the number line, word form, tally mark, random dot. Talk briefly about how the patterns help you remember the amount without counting them (which is subitizing). When showing the 4 on a dice, notice that “if you connect the corners, you make a square.” Then when showing 5, notice that, “it’s like 4, but with a dot in the middle.”

Friday: Quickly review previously posted information about your number. Share a problem involving the number.  “I had nothing in this jar, and then I put 1 marble in it. How many marbles are in there now?” Along with this type: “Look, I have a marble in my jar. That means I have how many? (Students answer with “one.”). “What if I take this 1 marble out? How many will there be in the jar?” Share other concepts of this number such as (uno, single for one; or double, twin, duet for two, etc.)

When working with numbers 2-10: You will also start focusing on number bonds. Using 2-color counters on a ten frame, show (and let students think of) different ways to make the number of the week. Example for #5: 1 red, 4 yellow; 2 red, 2 yellow; 3 red, 2 yellow; 4 red, 1 yellow; 5 red, 0 yellow; 0 red, 5 yellow. You don’t even need to make an equation yet. Just say “1 and 4 makes 5; 2 and 3 makes 5 . . .”

For first or second grade: I have two thoughts on this. You could do a number of the day utilizing the calendar date as your number. This means if it’s the 14th of the month, you are focusing on #14. This also means you would repeat these numbers each month – thus giving more exposure to the numbers students are most likely using on a regular basis. You could add the following concepts to your discussion: place value with tens/ones (in straw bundles, stick bundles, or posting sticky dots on ten frames); expanded notation (14 = 10 + 4); concepts of odd and even, and how to make the number using coins.

Second thought is this:  Keep track of the number of days of school (for those of you who like to celebrate the 50th and/or 100th day of school), but choose a number of the day or week to focus on so you can review those very important number concepts and number bonds with numbers from 0-20. Part of your board could have a whole/part/part section to show a way to break apart your number. Continue reading →

Daily Math Meeting Part 3: Days of the week, patterns, graphing

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by Cindy Elkins, OK Math and Reading Lady

In Part 1, I focused on subitizing practice during your meeting time (for PreK-1st grade classes). This week I will focus on days of the week and graphing opportunities.

Days of the Week

  • Rather than posting the whole month at once, post the current date piece each day. Show different ways to write the date (in words, with numbers).
  • Discuss the day before and the day after.
  • Find the day (Monday, Tuesday, etc.). Sing a song or watch a video about the days of the week and months. See list below.
  • Use the number as a focus for the day: If today is the 5th, let’s look at dot cards with 5, ten frames with 5, dice with 5, count to 5, count backward from 5, tally of 5, spelled form, and number bonds of 5.
  • Consider making patterns with your calendar pieces. For example, September could be red apple, green apple, red apple, green apple . . . for an AB pattern. October could be pumpkin, pumpkin, ghost for an AAB pattern. Or use different colors or shapes (circle, square  . . .). Or make patterns based on odd / even numbers, counting by 3’s, 4’s . . . the possibilities are endless.
  • Discuss the pattern, predict what will be next once the pattern is established. Introduce clap patterns which match your chosen calendar pattern. If you are working on AB, then do clap, snap . . . If you are working on ABC patterns, do clap, snap, touch  your knees . . . Have children make up patterns to follow.
  • If you have an upcoming activity, predict what the date will be. Example: We are going to the library in 3 days. Today is Monday, so when is our library day?
  • After the calendar is mostly complete for the month, you can emphasize ordinal numbers. Model how to find the first Friday, the second Tuesday, the third Wednesday, etc. Then have students practice.
  • Consider having a student in charge of the calendar each week as one of the class jobs. This student would post the new calendar piece and then get to lead the class in saying the date and other features of the daily calendar.

Days of the week / months songs (Click on link to go there fast!)

https://www.youtube.com/watch?v=3tx0rvuXIRg (Learning Station)

https://www.youtube.com/watch?v=yIvQOab00OQ (To Adams Family tune)

https://www.youtube.com/watch?v=5enDRrWyXaw (Months)

Graphing Ideas:  The calendar board is a great place to introduce graphing or review it on a regular basis.  You can make graphs or charts using bars, tallies, yes/no, or Venn diagrams. Continue reading →

Number Lines and Rounding

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by C. Elkins, OK Math and Reading Lady

I get requests from many teachers to help with instructional strategies regarding rounding, so I am happy to share my thoughts (and freebies) with you. Difficulty with rounding usually means students lack number sense. The essential goal of rounding is: Can you name a benchmark number (whole, tens, hundreds, thousands, tenths, hundredths, etc.) that a given number is closer to? I have found the more experience a student has with number lines, the better they will be with number sense, and the better they are with rounding to the nearest ___.  Then this rounding practice must be applied to real world problems to estimate sums, differences, products, or quotients.

When doing a google search for tips on rounding (ie Pinterest), you very often find an assortment of rhymes (such as “5 or more let it soar, 4 or less let it rest”) and graphics showing underlining of digits and arrows pointing to other digits. These steps are supposed to help children think about how to change (or round) a number to one with a zero. Many students can recite the rhyme, but then misunderstand the intent, often applying the steps to the wrong digit, showing they really don’t have number sense but are just trying to follow steps.

My answer (and that of other math specialists) is teaching students how to place any number on a number line, and then determining which benchmark number it is closest to. Continue reading to see examples and get some free activities.

Continue reading →

Number Talks Part 1: Subitizing and Number Bonds KG-1st grade

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By Cindy Elkins, OK Math and Reading Lady

A Number Talk is an opportunity to review number sense and operations by making it part of your daily math routine — so that what has previously been taught is not easily forgotten.

In this post I will expand on 2 methods for conducting a Number Talk session for KG-1st grade students (Subitizing and Number Bonds). Refer to a previous post (Sept. 10 – Daily Practice to Build Number Sense), in which I mentioned several other ways to review math concepts on a daily basis such as calendar topics, weather graphs, counting # of days of school, using a 100 chart, Choose 3 Ways, etc. Continue reading →

Daily Math Meeting Part 1: Ways to Build Number Sense K-5

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To build number sense, students need frequent exposure or review of concepts you have previously introduced. There are many ways to build number sense on an on-going, informal basis – especially when you can squeeze in 10-15 minutes daily:daily-practice

  • During morning meeting time
  • During a Number Talks session
  • At the beginning of your math lesson
  • At the end of your math lesson
  • End of day closure time

I have included several of my power point slides on this topic as a PDF file (daily-practice-to-build-number-sense-pdf). Continue reading →