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?
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
Start with 14 (red)
Turn over 9 (yellow)
Move the red together
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:
If you find you don’t have enough base ten blocks to go around, then the mini ten frames might be a good substitute for students to show their understanding of place value regarding tens and ones.
Provide individual students (or pairs of students) a baggie of prepared tens frames. You would need 10 complete 10 frames and then 1 of each of the others (0-9).
Using a blank tens/ones mat, state a 2 digit number such as 35. Show students the 3 represents how many 10’s there are (3) and the 5 represents how many 1’s (5). Place ten frames on the mat to illustrate.
35 — With mini ten frames
Vary how you ask students to show amounts: Sometimes say, “Show me 35.” vs. “Show me 3 tens and 5 ones.” vs. “Show me 30 and 5.”
Variation of using base ten blocks with this place value mat:
This place value mat (link above in opening paragraph) allows you to use your base ten blocks on the ten’s side and the units cubes on the one’s side, with one helpful difference.
The ten frame template allows students to organize their ones as opposed to random placement when no ten frame is present. This helps students with number bonds and it really helps you, as the teacher who is observing, to determine immediately if the student placed the correct # of units.*
With the examples shown (47), students can show the ones as 5 + 2 or 4 + 3.
47 = 4 tens, 7 ones
Another way to show the ones
*Even without the use of this mat with printed ten-frame, I insist students show some type of organized placement of units cubes any time they are being used for some type of counting. Students can be creative with patterns that resemble domino or dice dots, ten frame configurations, equal rows, etc. Try it!!!
The ones cubes are organized!
Adding or Subtracting 2 digit numbers:
Use a generic tens/ones mat and the mini ten frames so students can model problems such as these:
39 + 15
26 + 12
Use the tens/ones mat (with ten frames). Utilize both ten frames in the one’s place for adding two 2-digit numbers.
Students can use units cubes or counters for the one’s place for concrete experiences.
This shows 64 + 19
Utilize some of the previously mentioned strategies for working with doubles, near doubles, 9, etc.
Show regrouping: Example 82 – 7. Start with 82 (with all purple tens on the ten’s side). Since there aren’t enough ones to subtract 7, regroup by moving ten to the one’s place (shown in picture below). Critical step: Be sure to have students see that there are still 82 dots on the board (70 + 12). Now 7 can be removed (2 from the orange card and 5 from the purple card, which leaves 5). The answer would be 75.
For pictorial practice, laminate the mats and students can draw in the pieces with dry-erase markers.
Check out this free resource from one of my favorite math specialists (Math Coachs Corner):
Last week, we looked at some ways to gain number sense about decimals. This post will address using decimals in the operations of addition and subtraction . . . and how to model concretely and pictorially. You can also download the color grid pages along with a free decimal math game in this post. Part 3 (future post) will address multiplication and division of decimals.
If you missed last week’s post, please review it first before continuing with this one. Before performing various operations with decimals, students must have a basic understanding of how to represent them concretely, pictorially and numerically. Example: .8 = .80 can be proven with base ten blocks and with 100 grid drawings. This understanding should also be linked to fractions: 8/10 is equivalent to 80/100. Click here for pdf of Representing Decimals page.
For concrete practice, use a 100 base ten block to represent the whole (ones), the tens rod to represent tenths, and unit blocks to represent hundredths. Construct each addend and then combine them. Ten tenths’ rods become one whole. Ten hundredths cubes become one tenth. Continue reading →
Number sense regarding decimals usually starts with fourth grade and continues with more complex operations involving decimals in fifth grade and beyond. It is this extension of the place value system and then relating them to fractions and percentages that often perplex our students (and the teachers, too)! Read ahead to get your freebies (Decimal practice notes, anchor charts, and Discovering Decimals Number of the Day / Game activity).
Students must understand this base-ten value system extends in both directions — between any two values the 10-to-1 ratio remains the same. When using place value blocks in primary grades, students recognize the 100 square as 100, the tens strip as 10, and the units cube as 1. Then with decimals, we ask them to reverse their thinking as the 100 square represents 1 whole, the tens strip represents a tenth, and the unit cube represents a hundredth. This may take repeated practice to make the shift in thinking — but don’t leave it out. Remember the progression from concrete (hands-on) to pictorial to abstract is heavily grounded in research. Students will likely gain better understanding of decimals by beginning with concrete and pictorial representations.
I am sharing my decimal practice notes, which highlight some of the basic concepts to consider when teaching. Pronouncing the names for the decimals is not in these notes, but be sure to emphasize correct pronunciation — .34 is not “point three four.” It is “thirty-four hundredths.” Use the word and for the decimal point when combining with a whole number. Example: 25.34 is pronounced “Twenty-five and thirty-four hundredths.” I know as adults we often use the term “point,” but we need to model correct academic language when teaching. You can get also the pdf version of these notes by clicking here: Decimal practice teaching notes.
Anchor chartsare excellent ways to highlight strategies in pictorial form. Here are some examples of anchor charts to help students relate decimals to fractions, location on a number line, word form, and equivalencies. Get the free pdf version here: Discovering decimals anchor charts. It includes a blank form to create your own. Continue reading →
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.
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.
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?)