Instructional Ideas or Activities for Operations


Before any operation can make sense students must have number sense (prenumber sense, counting) and conservation of numbers.


  1. Count using counting-on or count-down. Place five objects on a tray or table, ask the student to count them, when the student counts three objects, stop, cover the three objects with a hand, ask how many are under the hand, then ask to continue and count the rest (two).

Skip counting. or alternate counting

  1. Dots on a number roll.
    • Learners count each dot as the dots roll.
    • Skip count as dots roll past.
    • If learners point to the dots, challenge them to sit on their hands as they count.
    • Use a separate piece of oak tag to screen some of the dots as they roll past.
    • Challenge students even more by asking them to wait and point to a specific dot when its number rolls to the center. Challenge more by adding another screen.


Subitizing is being able to identify the value of a group of objects by looking at it without actually counting the objects. See development & additional information and resources.

  1. Pattern recognition instead of counting display patterns from the following and instantly try to recognize a value: dominoes, die, ten frame, playing cards, regular plane figures, rectangles, arrays, finger patterns,
  2. FLASH dot plates or electronic dots or any of the above, have students air count, visualize without air counting …
  3. Bean toss and record results in Bean book and on a class chart.
  4. Estimate and count: Bring in bags of objects. Beans, M&M's, peanuts, safety pins, Q - tips, sugar cubes, crackers, cookies, macaroni ... Students estimate, out number on slip of paper, count items by putting them into cubs of ten.
  5. Count jars of objects. Use the same kinds of objects above, place them in jars, have the students guess and check. Switch jars, objects, and repeat.
  6. Blank hundred square or empty hundred pocket chart. Randomize a set of the numbers and pass one to each child. Challenge students to come one at time and place their number where they think it belongs on the chart.
  7. Number cover up with a completed 100 chart cover one number and ask students what number is covered.
  8. Can Use the hundred squares or hundred charts and the Number roll to do any of the counting, skip counting and point to the numbers. Make screens of different sizes to place to challenge students even more. Point to where the number is screened if a screened number is in the sequence.
  9. Hundred squares or hundred charts puzzles complete and incomplete with one number to start.
  10. Hundred squares or hundred charts
  11. Flash Arrays and have students tell the number of squares in the array. If students rely on counting squares in arrays, screen part of the array, but be sure to show at least two sides. Have students tell how many squares. Later show top and side separately.
  12. Arrow math problems give a starting number and then arrows as code to a secret number. (43 ٨ ٨ > > > ) find the number or (43 ٧ ٧ ٧ < < )

Combinations of addends

  1. Presto change O. Put two stacks of three, presto change O, to three stacks of two. Presto change O to six stacks of one...
  2. Packaging Red and Blue Candy Use several five frames for each student or pair of students and see how many different ways the red and blue candies (use chips or red and blue cubes) can be packaged.
  3. Line them up, group them up, cup them up. Put five groups of three, line them up, cup them up... How many cups should we use? Continue to line them up one group at a time, if there is one lined up for each cup then put them in the cup and repeat until all are used and there are none or some left over. If there are some left over ask if it worked?
  4. Unifix trains. Make four groups of three. Put all your cubes into a train. What size of trains can we break or big train into? Twos? Did it break into trains of two evenly? Yes. Put your train back together. What other way? Did it break into groups of five evenly? No.
  5. FLASH different rectangle and different strips that are empty and have students report the number of squares.
  6. FLASH ten frames with different arrangements in the frames. How many were occupied and how many were not. Fill with different colored counters (five blue on top, two red and three green on bottom) how many…?
  7. Frame move it Place chips on a frame so that a row is not complete ( 4 on top 3 on bottom) ask how many fives and more? Slide one up to see, how many left on the bottom? Do with other sums to develop five as anchor.
  8. Frames move it Place chips on two frames so that neither frame is complete ( 6 on one 7 on the other) ask how many tens and more? Slide them around and see. Do with other sums to develop ten as anchor.
  9. Plates for frames use plates to group anchor patterns to find sums. At first students will put groups of five or ten in a familiar pattern and in time they won’t care as they will recognize the group as a unit.
  10. FLASH different sizes of rectangles or strips like above.
  11. FLASH different sizes of rectangles filled with different colors to represent different multiples for each of the rectangle.
  12. Bean Toss Give each child five lima beans that are colored differently on each side (white and green) have them drop the beans and color the results on their bean log. Compile the class notes and discover all the different addends for five. Repeat for other numbers.
  13. Tower Making using cubes of two colors (red  and green) how many different towers can be made if only towers are aloud in the city that are five high?


  1. The shark game: Use fish crackers. Pick a certain amount, have the student eat some, and ask how many are left. The shark was still hungry and ate some more, eat the next one, and ask how many are left? Then say three more swam up, how many are there? And continue until all the fish are gone.
  2. Listen and count: Ring a bell a certain amount of times. Then turn over a card with a + or - sign.. If the sign is + add a number of objects that the bell rang to the card, if the card is - , then take that many objects from the card.
  3. What do you picture in your mind when I write this symbol? (numeral). How could you picture this? (3 + 4) (5 - 2)
  4. One student makes up a problem and another records it. Use the hand game, peek through the wall, lift the bowl, cave game, move off the grid game, concentration, whale game.
  5. Magic box, bag, house: If I put two cubes in the box (drop into hole in top) and you put three cubes (drop in top) how many cubes are hidden in the box? Check and see. Pair students…
  6. Toss dice and record results (sum) on chart.
  7. Five and Ten as Anchors many of the FLASH and counting ideas can be used by starting with a group of five or ten and FLASHING or START counting.
  8. Subtraction race: Build a train of Unifix cubes. Roll dice and may remove the number of cubes as rolled on the dice or pass. Must remove the exact number of cubes to go out. This adds the idea of probability.
  9. Crazy mixed up numbers. Students write random numbers on a strip of paper. Another student makes a set of objects for the first number and proceeds to tell what needs to be done to the first set to get a set equal to the second number on the list. This is continued for the rest of the numbers on the list.
  10. Add or pop balloons game. Students pick a number and put that many balloons on a bulletin board. The next student draws a number and either adds balloons to get the next number or pops balloons to get the equivalent number of balloons.
  11. Bell and student in the box: A student gets in a box with a bell. Rings the bell a number of times and other students tell the number of times the bell has rung.
  12. My turn your turn: Select two teams and one student to stand in the middle of a row of squares. Challenge students to find the middle square of a row (must have an odd number of squares.) The first team rolls a die, the child in the middle faces that team, the team calls out their number, and counts aloud while the child in the middle walks toward them the number of steps indicated by the roll of the die. The object of the game is to have the child in the middle step off the game board at your team's end.
  13. The magic box: Select a card, look at the red side, make the number of circles for the red number on your paper, put the card into the box with the red side up, when it flips over and comes out it has a blue six on the other side, put the number of X’s with the circles to make 6. Read the problem.
  14. To do subtraction have the students turn the cards over with the blue side up, make that number of circles on their paper, put the card in the box so it flips over, when the red number comes out of the box have the students cross out enough circles so they will have that number of circles left on their paper. Read the problem.
  15. Missing addends: Picture of a house with windows. Place a picture of three kids looking out a window (or three pictures of a kid looking out a window or draw three happy faces on windows). Ask the question. You can see three kids in the house looking out the window. If there are two more kids inside the house not looking out the window, how many kids are in the house?
  16. How many jumps: Tell the students that you will say a number (3) and then you will say another number (5) and ask how many jumps are from 3 to 5?
  17. How many jumps backwards: Tell the students that you will say a number (8) and then you will say another number (5) and ask how many jumps are from 8 to 5?
  18. Multiple jumps or skip jumps: Tell the students that you will say some numbers (4, 6, 8) and then you will say another number (12) and ask how many jumps are from 8 to 12?
  19. Skip jump backwards: 
  20. Subtraction with rows or 100 square if have a row of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, cover number four and five. What is the subtraction problem it represents? Okay, did you think of 5-2 = 3? Did you count back for the answer? Count back (4, 3) or (5, 4, 3) answer is three. What? How visualize? Are dots (numbers, lines) one or are spaces one?
  21. Draw both examples…
  22. Comparisons
  23. Here are four red hats (red cubes). Here are six children (blue cubes) how many children don’t have hats?
  24. Here are eight red hats (red cubes). Here are six children (blue cubes) how many hats will be left if each child takes a hat to recess?
  25. Arrays if students rely on counting squares in arrays screen the array and show top and side and see if they can tell how many squares.
  26. Place value as sets of ten
  27. Until about third grade students act as if a group of ten the ten individual objects in the group are two different entities. A group of ten straws and ten straws are not different they are the same thing. Students that persist in representing the two in 23 with two blocks instead of twenty blocks are demonstrating this phenomenon.
  28. Young learners inventory books in the classroom. Stack and put rubber bands around ten books, count the books as groups of ten, and extras. Young learners will probably not use place value to determine a total number of books, but they are thinking of each group of ten as a convenient collection of ten books, not one group of ten units simultaneously as ten units. If this idea is expanded to one group of hundreds can be unitized as one group (100’s), ten groups (10’s), or one hundred groups (1’s).


  1. Jar lids with nail hole in bottom, how long does it take to sink? Record time.
  2. Guess when the time is up game. Ten seconds, fifteen, thirty, one minute. Great to use to calm a class and reduce stress.
  3. Compare length of time. Ice cubes take to melt, lifesavers to be sucked, birthday candle to burn out, wind - up toy to wind down, tie shoe, sip zipper, paper plane to fly...
  4. Time trials. Students sit in a circle and pass an object around the circle, predict the time, have a counter count the number of times the bell rings (tape a bell ringing once every second) or the number of times a pendulum swings, before the object completes the circle. Change events and do another time trial.

Word problems

  1. The teacher reads word problems and the students act them out. Sue had a birthday how many candles on the cake. There were four chairs at the table, Juan put two more how many where there? ... Cardinal, ordinal (Jan, Meg, Molly lined up, who is second...), addition, subtraction, multiplication (Jon made six birthday cakes, each had two layers how many layers?) division (Jill had six pencils, she put two into three stacks, how many were in each stack?).

Pattern activities

  1. How many eyes do ___ number of people have. Past pictures of people on a page and record the numbers of different body parts beside each 2, 4, 6, 8 ...
  2. How many lines to make stars? Show on paper. Draw label 1 - 5, 2 - 10, 3 - 15, ...
  3. How many sticks on a Popsicle?
  4. Observe patterns on fruits and vegetables and creatively describe and draw the patterns. When students tire looking at the outside have them predict inside. Ask if seeds. How many? Cut open look at pattern, count seeds...
  5. Look at leaves on a branch ..., patterns, and number sequence …
  6. Clothing patterns: Have students copy the pattern. Collect the pattern copies and have student match the patterns with the materials.
  7. Money
  8. Shapes: triangle, squares ... see patterns - includes dots, v, w, triangle, square, & more
  9. Jump rope patterns and rhymes
  10. Three & four leaf clovers in different patches
  11. Join hands problems with different groups.
  12. Pyramids of people
  13. Chain reaction: Give a student a piece of paper, cut in half, give a half away, cut in half give away, continue... Repeat next day and record what happened. Try with more sheets of paper....
  14. Play London bridge. Each time a person is caught, they select a person from the line to start a new bridge, continue until all bridges, play next day record next, or if learners demand, record today.
  15. Apartment house interior designer, architect ... Build an apartment complex from milk cartons, put one cube for each sofa, or chairs, or sinks... count chart ...
  16. Two handed take away ... Start with a group, remove objects, two at a time by using both hands, each taking one together. Even number subtractions.
  17. Chip chop: Chop a board into x pieces how many chops? Draw a rectangle (board). Draw lines to make as many pieces as possible (one ine two pieces). As add lines, chops, how can the pieces increase the most?
  18. Milk carton clothes pin game. Use clothes pins to clip milk cartons together. How many clothes pins does it take to join two cartons? How many more are needed as more milk cartons are added?
  19. Pattern block puzzles. How many triangles to make a hexagon? Stack them on top record stack another layer...
  20. Make a tessellation: What is the pattern? write it...
  21. Geoboard nail patterns ...
  22. City planner Intersecting roads. How many intersections with one road? two? ...



Dr. Robert Sweetland's notes
[Home: & ]