# Activities and Instructional Ideas for counting & number value & sense as

Transitions to addition & subtraction &
place value

*Overview*:

Activities by concepts

## Classification

Before anything is counted an act of classification must take place. A person must group or classify the objects in the set to be counted. Cookies on a plate, fingers on a hand, toes in a shoe, toys on the floor, and so on. See classification concepts & misconceptions.

- Toys, classify by type color,
- Letters of the alphabet, classify by shape: straight lines (A, E, F, H, I, K, L, M, N, T, V, W, X, Y, Z) curved (B, C, D, G, J, P, R, S, U) circles (O, Q). Some letters might go in to groups for those more experienced (G, J, D).
- Pattern blocks, sort by color, shape, number of sides.
- Geometric shapes
- Animals and their parts, noses, eyes, legs, ...

## Counting

Counting begins with the memorization of numerals in their counting order. However, concepts such as: sequence, one more, one less, more than, less than, one-to-one-correspondence, cardinality, and conservation of number are developed slowly as children think about what numbers are and their relationships. See prenumber sense, counting, and number sense.

*Echo count*, listen and repeat number names in order.- Sequence of sounds, words… & objects
- Recognition activities of numerals, words …
- Count orally, from memory, by ones forward and backward
- Count stop and have child say next number: 1, 2, 3, ___ (4, 5, 6 ) ___; starting with numbers not one: 2, 3, ___6, 7, 8 ___
- Count visible objects
- Count objects with motion.
- Count and move hand up or down,
- Count and show number value on fingers, (rate student moves finger helps the teacher to visualize the student’s understanding)
- Count pointing to numerals or write a numeral and count
- Count pointing or writing number words
- Make a
*number roll*: A roll of paper with five or ten big dots evenly spaced on it, roll it up. Ask a student to unroll the number roll with you and have them count the numbers as each appears. - Count without starting on one
- Count items not visible, but with sensory input hear (claps, beat of drum ... ) , feel (items in a sock ... )
- Count clap patterns. Vary the rate and pattern of clapping. (See hierarchical inclusion)
- Count items hidden from view. Show five hide three ask how many hidden. Or told three in box and two in other box, how many in both boxes. Or have count items, place them in a container with a lid and ask to count how many are in the container (object permanence, conservation of number).
- What is the next number? What comes next? 1, 2, 3, _.
- What was the number before 5 …?
- What is the number after 5 …?
- Count and turn, Counting off in a line, Counting off in chairs, Counting in the circle game,
- Pendulum count
- Jump rope count
- Ball bounce count
- Polka-dot numbers in a line count
- Silent count to rhythm, _ _ 2 3 4 5 _ _ 2 3 4 5;
- Snap and clap
- Stand up sit down count ...
- Double circle, walk in opposite directions, count with hand slaps
- 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).

## Counting Backward

Counting backwards is more difficult for children. Use same ideas above. Provide enough thinking time, hints, visual prompts, whatever, and patience.

Ideas from above only alternate/ take turns… teacher one student two….

All above going up and down….

Count stop and have child say next number (in order: 1, 2, 3, ___ 4, 5, 6 ____; out of sequence 1, 2, 3, _____ 6, 7, 8 ______ )

All above only do backwards.

(Use variations of all above)

## Numeral and number recognition

- Point to a numeral and ask what the number is.
- Give students a randomized set of cards, have them turn a card over and say read the numeral.
- Have students point to numbers and tell their numeral name. Have a partner point and tell.
- Dice bingo (junior version) role a die and match the die to the numeral on a 2x3 grid (1, 2, 3, 4, 5, 6).
- Match dot cards with numeral cards, word cards…
- Match dot plates with numeral, ordinal, & number cards for students.

## Number sequence & ordinality

- Put these cards in order. Give students a set of cards. Numerals, words, combination and ask them to put them in order. Source of cards for students.
- Put plastic numerals in order.
- Deal a deck of number cards, one card to each child and have them line up according to the numbers. Have different groups do it at the same time…
- Not playing with a full deck: Form decks of cards (or hands of cards) with numbers missing from a sequence (3, 4, 7, 9, 11, 13), randomize the deck, give a deck to a student or pair and have students arrange them in order.
- Roll six dice and arrange them in order without counting, how fast can you do it?
- Roll a die and air draw it
- Show a plane figure 1 – dot, 2- line, 3 – triangle, 4 – square or rectangle, 5 – star (okay it’s not a plane figure, but it’s more fun air drawing than a pentagon), and 6 a hexagon.
- Make
*number roll*. A roll of paper with numbers 1 – 10 (20) on it evenly spaced, roll it up. Ask a student to unroll the number roll with you and have them count the numbers as each appears. *Screened number roll*. Show students a number roll and as it roles hold a screen to block a few numbers as they roll past.- FLASH any of the above and have students hold up a card with the numeral that represents the number. (let a student FLASH the class while the teacher talks to individual students to see if there is a strategy they can use to better recall certain patterns and numbers (composite groups, connecting die with others or dominoes with die…)
- Sort and classify all of the above into groups with 1, 2, 3, 4, 5, …
- Ten strips 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…?
*Number cover up*: Cut a 12x18 piece of construction paper in half length wise (6 x 18) and fold one of the pieces in half length wise. Divide it into ten equal rectangles. Inside the folded part with the crease on the top write the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 for beginning students and 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 for more experienced students. Then numbers will be on the bottom so that top will fold down and cover them. Cut slits so a flap can be lifted and the number below can be seen. Use this*number ten*or*number teen*chart by calling out a number and have students find the number.- Number cover ups can be made for larger numbers. Make
*covered number lines*for higher numbers ( 41, 42, 43, 44, 45, … 50) and do as above. *Dots with numerals on the wall*. Have students close their eyes, say a number that is on a dot, ask students to point to where they think it is, have them open their eyes and see what numbered dot they pointed at.*Dots in a row*. Put a number of dots in a row without numbers on them. Say a number and have students point to a dot in a row that could represent that number.*More dots in a row*. Put a number of dots in a row without numbers on them. Point to a dot and assign it a value (8), ask students to point to a dot two away. Ask what that dot might be. Repeat before after, could also do with skip counting.*Dots on a number roll*. Students can count each number or skip count as the numbers roll past. Can point to the dots or not point. Can screen some of the dots as they roll past. Could challenge students even more by asking them to wait and point to a specific dot when its number rolls to the center. Could challenge more by adding a screen.

## Zero

- Use bags of objects to sequence numbers starting with an empty bag for zero. Ask students to put the number of objects in the bag that is written on the bag. Ask how many objects are in the zero labeled bag.
- Later combine objects in one bag to zero objects in another bag. Suggest several problems with zero as an addend and include both kinds of problems 3 + 0 = 3 and 0 + 3 = 3. Have others make and share problems.
- Have students snap Unifix cubes together to make towers, trains, … for numbers (1-10). Call out a number and have them hold the tower or what ever up. Ask students to hold up zero.
- Ask how many elephants are in the room… zebras…

## Subitizing

*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.

- 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,
- FLASH dot plates or electronic dots or any of the above, have students air count, visualize without air counting …

## Skip Counting or alternate counting

- Skip counting or counting in multiples. Arranged objects (eyes, legs, dog legs ... ) ten strips, number dots, 100 squares, shapes: triangles, rectangles and squares (count sides or angles). Count orally and written. Add a cover to help students remember patterns through visualization or voice pattern or other mnemonic device. Most ideas from counting can also be used for skip or alternate counting forward and backwards.
- Arrange those cards: Make decks of cards for different multiples (2, 4, 6…; 5, 10, 15…; 10 , 20, 30…) Randomize a deck of multiple cards and have students arrange them in order.
*Composite group*: (unitize and composite) – recognize a group of three as a group of three and a group of one. Six groups of three can be thought of and worked with as six groups and multiply 6*3 as well as 6 collections of three Watch me count… arrange in a pattern (objects into six rows with three in each row) and count by ones and skip count by threes.*Unitary group*, is when a group of three is recognized or worked with as one (unitary) group (three). Repeated addition or repeated subtraction (skip counting…) can be thought of in two ways: single groups of objects and groups of groups. This becomes important when students get to the operations (addition, subtraction, multiplication & division).- Every one make bunny ear fingers, how many bunny ears are there?
- Make a W with your fingers, how many w’s? …
- Count objects in different groups in different multiples.
- Counting-on with a screen cover, 8, 9, 10, 11. (8+3) Teacher count students repeat (1…3; 4..6…) forward and backward starting and stopping with different numbers, can have student repeat again in their head or out loud. All together, or out loud by self…
- Arrange manipulatives with a recognizable pattern one color and rest another pattern. Ask how many in recognizable pattern and see if they will count-on.
- Use number strips, ten frames….
- Provide larger groups and ask to find five, 10, 15, 21… Watch me count… arrange before counting and count by touching, or not touching but pointing, not touching or pointing, arrange in a pattern and count.

## Counting-on

- 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).
- Counting on game put out 5 blocks cover up two, count on, Silent count to rhythm, _ _ 2 3 4 5 _ _ 2 3 4 5;
- Counting-on use screen cover, 8, 9, 10, 11. (8+3) Teacher count students repeat (1…3; 4..6…) forward backward starting and stopping with different numbers, can have student repeat again in their head or out loud. All together, or out loud by self…
- Arrange manipulatives with a recognizable pattern (one color) and additional similar manipulatives in a random pattern (a different color). Ask how many in the recognizable pattern and see if they will count-on.

## One-to-one-correspondence & matching

*Matching*, would seem to be a natural procedure for students to determine if groups are equal. However, it is rarely used.

- Use different sets of objects and determine if each sets matches a second or not. start with objects that are identical in size, shape, color ... and change them with the size being a later attribute to change. Younger students have difficulty thinking the number of large objects equivalent to the same number of smaller objects (which group has more animals? A group of 2 elephants or a group of 2 mice.).
- Use sterile egg cartons and collections of similar objects (that fit in the egg cells of the carton) to use as markers for counting. Have the child put one object into each part and count how many are in each group or set of objects. Record in math log.
- Sort the mail. Envelopes, student work for mail, mail boxes or students' desks. Have each address or put labels on envelopes and have students deliver them ...
- Set the table. How many forks, spoons, knives, plates, glasses are set for ...
- Numbered squares and rectangles. Show students different matrices (1x1, 1x2, 1x3, 1x4, 2x1, 2x2, 2x3, 2x4, 3x1, 3x2, 3x3, 3x4, 4x1, …) with and without numbers written in the cells (1; 1, 2; 1, 2, 3; 1, 2; 1,2,3,4; ... 1,2,3,4,5,6,7,8,9; ... ) have students look for patterns of numbers and ones that have the same number of squares.

*One-to-one-correspondence*

Connect each counting numeral with a one-to-one-correspondence to a cardinality.

- Use a flip ring with cards numbered 0, 1, 2, through the number you want to use in the game. Have students start at zero. Then when the bell rings have them flip a card and place a cube. As students flip and add ask them to point to the cubes represented by the current number.
- Giant number line: Have students play the preceding game. As they go through the chart have them record all numbers on a class grid and place the number of Unifix cubes beside it. Look for patterns (inclusion).
- Repeat the above and put the numbers on a matrix (4 - 4X4, 5 - 5X5 ...).
- Matrix patterns: Have students arrange chairs in a grid. Have them put students on the matrix in a pattern. How do they compare to the numbered squares?
- I’ll say a number you FLASH a pattern (1x1; 1x2; 1x3; 2x2; ... )
- Move on the grid. Have students stand on a grid. Have them take steps from one square to the next by telling them how many squares to move relative to two points marked at two different points on the grid. For example move 3 from the x, 2 from the polka-dot. Background for hundred chart and arrow math.

### Cover - up one

*Materials*: Large foam die, path with squares or other shapes
or grid of shapes, and collection of objects to use as markers to place on the dots of the die.

*Procedure*

- Roll the large foam die.
- Match one of the objects to each dot on die by placing an object on each dot of the die.
- When all the dots are covered transfer each object one at a time to the squares on the path or grid.
- Repeat the steps until the path or grid is completely covered.

### Cover - up two

*Materials*: Die, staircase of squares from one to ten (55
squares in all), 55 multilink cubes, that will fit on the squares in the
staircase.

*Procedure*

- Roll die
- Select the number of cubes that matches the number on the die.
- Place the cubes on the staircase.
- Continue until the staircase is filled.
- Students could use large foam die for one-to-one-correspondence like in Cover-up 1. Students that can count can place the squares and tell how many more are needed for each stair (hierarchical inclusion and addition).

### Snacks for all?

*Materials*: snacks and two colors of objects, one to represent
students and another to represent snacks (multilink cubes green and yellow,
or cutouts of children and milk cartons…).

*Procedure*:

- Ask the students if there are enough snacks (milk boxes, juice containers, cookies, crackers…) for every person in the class.
- Have them match yellow cubes to students and green cubes to snacks.
- Then ask them how they can tell.
- Could line up the blocks or snap them together and measure to see if there was enough.
- Same activity can be used to help students construct an understanding of odd and even.

## Cardinality with one-to-one-correspondence

- Use number strips, ten frames….
- Randomly place students and have them find how many were placed by: Count and turn, Counting off in a line, Counting off in chairs, Counting in the circle game,
- Count objects. Objects in the box game, piggy bank game, spill the beans game, Pendulum game, Jump rope count, Ball bounce count,
- Number in a polka-dot line ,
- Counting backwards. (Use variations of all above),
- Put pictures in sequence (baking cookies,...), Snap and clap, Stand up sit down count...;
- Double circle, walk in opposite directions, count with hand slaps; Put number words in order on cards together, in groups, by self on desk, one card to each child have line up according to the numbers. Have different groups do it at the same time…
- Have students snap Unifix cubes together to make towers, trains … for numbers (1-5) or (1-10). Call out a number and have them hold the tower or whatever up.
- Make number books. Records of toothpicks, tiles, pattern blocks
- Concentration: Take some boxes of the same size and put pairs of different amounts of objects under all the boxes. Have the students turn a pair of boxes over, if the pairs match they can remove the boxes and the objects. If the pairs do not match they cover the objects with the boxes and it is the next person's turn.
- Object cost grid. Make a grid with numerals from 1 - 50. Challenge students to locate an objects that cost the amount as each numeral on the grid. Pictures of the object or the object itself can be added to the grid.
- Bean toss and record results in Bean book and on a class chart.
- 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.
- 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.

## Conservation of number

The activities below are often assigned as counting activities. However, young students will not conserve number as they learn to count. To be able to conserve number a host of concepts related to prenumber sense and counting must be conceptualized before number sense can include conservation of number and then other conservation skills.

- Arrange [(1-5), (1-10), or (0-20)] objects (toothpicks,pattern blocks, tiles, jewels, wooden blocks, beans, junk box objects, unifix cubes, pattern blocks, ... ) in different patterns to find patterns with equivalent values (cardinality) and record quantities by gluing squares, toothpicks, or other objects into a learning log.

## Greater Than and Less Than

Young students are easily confused with the less than (<) and greater than (>) symbols. This does not mean they have not conceptualized a concept of more, greater, less, and equal. It is more likely they have not memorized which symbol is which and become skillful in their use.

It is helpful to have students invent a rule and nemonic. Then, display it so they can refer to it from time to time. Example:

- You might start with the
*=*sign and mention it is two parallel line segments where both ends of the line segments are equal distances apart to communicate equality. Which, is used to compare two numbers, or values in equations such as 7 = 4 + 3. - Then ask. If it is used correctly in the equation 6 = 4 + 3?
- Hopefully, the answer is no.
- Comment that the lines can not be parallel, because each side isn't equal and it isn't an equality.
- Then ask. How the symbol might be changed to a less than symbol?
- If need a hint, suggest.
- Maybe the two parallel lines could be tilted.
- Verify there are two ways they could be tilted.
*<*&*>*and when they are tilted one end is closer together and the other is farther apart. Not equal. One end is less farther apart (actually zero apart) and the other is more or greater apart. - Then ask. Which way would make more sense for less than?
- Then ask. Which way would make more sense for greater or more than?
- Then ask. What happens if they are used? For example as 3 > 4; 4 < 5; 1 + 2 < 3 + 4; ...
- Have them conclude it is easy to remember, because you can look at the shape to see if the ends are less, equal, or greater and then just read it. Like, 10 > 2, is read as 10 is greater than 2. And When it is like, 2 < 10, it is read as 2 less than 10.
- Lastly check to make sure they understand that if the smaller (tilted down or pointy) end points to the smaller number, then the other greater (tilted up or not pointy) end will always point to the larger number. This may seem obvious to older learners, but I have had younger learners question. How do you know the other end is right and not backwards? Use plenty of examples and review often.
- Repeat with several other examples until the learners conclude:
Obvious for some, not all.

If given two numbers that are not equal, then one is always greater than the other and the other is always less than the other.

When the < & > symbol is placed correctly between two unequal numbers (or in an unequal equation), such that the little number is at the little end, then the big number will always be at the big end.

I like this because it uses reason and is based on mathematical ideas. Not artificial like *hungry greedy alligators like to eat large numbers*.

See also equality.

- Make a more or less book. More pencils less windows.
- Comparing length of names on graph paper (first, last).
- Record height, compare each child, use cord arrange in height
- Compare mass with teeter totter (one to another)
- Compare handfuls. How little is a handful?
- Play tic-tac-toe and keep score with Unifix cubes
- Play squares and keep score with Unifix cubes
- Compare one jar’s capacity to another jar and pair as greater and/ or less..
- Put objects on a balance and mark pairs as greater and/ or less
- Order by volume: Put progressive amounts of rice in a collection of jars and mark each jar with a marker.

### Ordering sets

Have the students grab a handful of objects (selected so the numbers would range 15-30) and put them on a tray so that they could convince another person how many there are without counting them by ones. Have all students in the class bring their tray to the front and set it on tables or the floor. Without talking each student will place their tray so that the trays are in order according to the number of objects on each. If a tray has the same number of objects as another, then the tray will be placed perpendicular to the others. If students question the placement of a tray have them convince each other how they know where it belongs. Students should settle disputes without counting or simply referring to numbers.

### Activity two

Have students grab another handful of objects and place them on trays. This time place the students in pairs and have them decide which tray has more or less. Have them come to the front of the class and share their trays and tell how they know which has more or less (again without counting or just by referring to numbers). Repeat until all students have convinced each other which of the pairs is more and which is less or equal. Then have students place number and word cards to write a mathematics sentence to tell what they showed. (24 is greater than 22) or (Twenty-four is greater than Twenty-two). Students draw pictures and write a sentence of their inequalities into their journal.

### Activity three

Have students repeat activity one and have them put word cards (less than, equal to, and greater than) between the trays. Either during or after completing the activity the students will notice that only the cards less than and maybe equal to were used (if the trays were placed in sequential order from small to large). Challenge them to tell you what could be done so that greater than cards could be used. Rearrange or re-grab and repeat. Then challenge students to figure how to put the trays so both greater than and less than cards could be used. Do so.

### Activity four

Repeat activity one-three with the use of symbols <>= (could have students invent eat larger rule).

### Activity five

Have students grab a handful and make a right or wrong equality on the trays, share with the rest of the students, and let the other students tell how they know if it is right or wrong.

### Making five and using five as an anchor

- Dot plates with two colors: five all one color and all the rest another color to visualize five as an anchor.
- Dot cards include some cards with five as an anchor.
- Dot flash
- Use sequences like later in later sequences

### Activity six

Give students number cards and ask them to stand in line in order (ascending, descending) use numbers 0-110, could use random numbers or multiples of 5, 10, or others.

### Activity seven

Worksheets with equality problems

## Hierarchical inclusion - counting - on and skip counting

*Clap patterns*clap a 1-2 pattern and have students count (1, 2,3) also for same 1-2 clap pattern count (1, 1,2). Or reverse it. Clap 1-2 pattern and students count (1, 1,2) and ask them how claps first (1), how many second (2) and how many all together (3) Other patterns 2-1, 2-2, 3-1, 1-3, 2-3, 3-3, 3-2.- Have the student count a specific number of beans into your hand. Hide some in the other hand, show the student how many are left and ask how many am I hiding?
*The hand game*: Take a known amount of beans and shake them in two hands, then open one hand and ask how many beans in that hand, then ask how many beans in the second hand, and slowly open it.*Peek through the wall game*: Put a specific number of beans in a line. Then take a piece of cardboard cut like a picture frame and insert it somewhere in the line and say how many are on either side of the frame. 3 and 2.*Lift the bowl game*: Put a specific number of beans under a bowl. Take some out and put them on top. Ask or say how many are on top. Then ask how many beans are under the bowl and slowly lift the bowl. Also Cave or cover up game.- Put a row of objects on a card. Say the total of objects on the card and take away a number. The teacher then covers that number with another card and asks, How many are left?
- Two handed FINGER FLASH two fingers on left hand and three on right…
- Two colored dots (3 red and 2 black)
- Put (1, 2, or 3) counters or blocks on a table for students to see, cover them with a card, put another group of (1, 2, or 3) counters or blocks in a line next to the previous and cover them. Ask how many? Repeat adding more … Start over and use different amounts… Can vary by covering some and leaving some uncovered.
- FLASH ask how many dots or other… they saw. Can anyone describe it another way? Another way?

### Card game More (war)

*Materials*: Deck of cards with the suit symbol beside the
number blacked in so that only the numeral remains and the face cards removed,
ten bags with matching numbers 1 - 10 on the outside.

*Procedure*

- Deal all 40 cards to two students face down one stack for each player.
- Have each turn over a card.
- Both cards go into the bag with number of the largest card. (six beats four, so goes into the six bag).
- Continue until all cards have been turned over.
- Then explore the bag to see what is in each.
- Could also play by turning two cards and adding them.

### Cave or cover up game

*Materials*: Blocks that equal the largest number to Cover-up

*Procedure*:

- Set the number of blocks that you want the student to count up to in a row on a table.
- Ask them how many blocks there are (five blocks).
- Cover up an amount of blocks with your hand (three) or butter dish (see two).
- Ask how many are under your hand or dish.
- Then lift your hand or the cave and repeat the combination (3 + 2).
- Repeat with the same amount of total objects, but different amounts in and out of the hand.
- The teacher can vary the game by saying how many to hide.
- Must be able to count on and have hierarchical inclusion.

### Roll to empty the bowl

Put a number of objects in a bowl that you want students to count back from.

Have them roll a die or dice, count or subitize the number of dots, and remove that many objects from the bowl. Continue to roll till all objects are out of the bowl.

Record number of rolls.

Record in pairs and save so the class can discuss results. ...

### How many ornaments fit in a box?

What kinds of boxes and different
assortments could be made?

Cubes, packages, and boxes.

## Activities to go beyond ten &

## Connect number value to operations

Use a non-counting strategy to count. Additive, (construct, combine) subtractive, (destruct, partition) compensation, use a known result, use multiples, five or ten as an anchor, commutative property, inverse property, or a, combination of these.

### Hundred chart

- Have students place the number cards onto an
*empty chart*and ask them to explain why they placed it in that particular pocket. - Start with a a
*partically completed*hundred chart, hand students one number at a time, and ask them to complete it. Later for review, numbers can be passed out to all students and they can insert them in by as many as can comfortably fit at the cart. - Make hundred chart puzzles with numbers missing and let students complete them by writing the missing numbers. Laminate and use water based marker.

### Hundred square

- 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.
*Number cover up*with a completed 100 chart cover one number and ask students what number is covered.- 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.
- Hundred squares or hundred charts puzzles complete and incomplete with one number to start.
- Hundred squares or hundred charts
- 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.
*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 < < )

### Body Parts Investigation

*Materials*: Multilink cubes, sticky notes

*Procedure*: Ask students how many noses are in the classroom. Ask for suggestions on how to find out and prove the answer. If students don't suggest to model the problem by using objects the teacher should when the time is appropriate. Pass out one object (cube) to each student to represent the noses. Try different ways of arranging the cubes to show the number of noses. Discuss and illustrate each.

Ask. How many eyes? Again let students make suggestions. If necessary suggest that each student use a small piece of paper or sticky note to draw two circles. Try different ways of arranging the sticky notes to show the number of eyes in the class. Discuss and illustrate each.

Open the investigation by asking them to figure out in pairs or for themselves and in their own ways how many mouths, legs, hands, fingers, toes, and other body parts are in the classroom. When completed discuss and illustrate each.

### Apple Packaging Investigation - Combinations to make 10

*Procedure*: Tell the following story to the students:

I went to the store and wanted to buy some apples. The store had green, yellow, and red apples in containers of ten of each color. The grocer had individual apples but only the boxes of ten identical colored apples were on sale. Curious, I asked why she only had boxes of one color. The grocer answered there were too many different possibilities. I asked how many and she said she did not know. I said, maybe I would ask my students and see if they could tell me how many different combinations of apples could be made to fit in a box of ten.

Have students draw and label different combinations fo sums for ten (different colors of apples in a box).

### Bean Toss

Materials: the number beans (different colors on each side (green and white))equal to the sum that is to be investigated for each student (5), record sheet or small book with an outline of five beans on each page or section

Procedure:

Give each student five beans and a record sheet.

Have them drop the beans on their desk.

Record the number of beans on their record sheet by coloring in the outline green or leaving it white for each roll.

Have them repeat the procedure for the number of entries desired (10 or more).

When the students are done tossing their beans ask them how many different ways there were for the beans to land.

Tell them that you want them to identify all the different ways the beans could land. Discuss and list the ways until students are satisfied they have all the possible ways represented.

Create a chart with all the different possibilities.

Have students record the results on the class chart. There are several ways students could do this. One would be to have each student write the results on a sticky note and have them attach their notes to the chart.

Discuss the chart results.

### Bus Driver Dilemma

A bus driver wants to know how many people are on the bus at all times. She is tired of counting the passengers to find out how many. The bus holds 12 people. Tell me how she can know without counting. Can have students act it out, draw a bus, label stops, then create problems + - 3… record each step, and model the numbers. A number line is too abstract for students to use for operations at the primary level.

Blocks in a city. Friend walked from 16th street to 34th street, how many blocks? Use measurement model?

### Ten frame

Have students show numbers or do problems on a ten frame or two - twenty strips

### Rekenrek or calculating frame

A Rekenrek is a devise that has 20 beads. Ten beads one of two rods. Five white and five black on each rod. (Use like ten frames).

Can hide from group like 6 + 5, then show briefly (like dot plates). Ask how many? How know?

Use frame to make problems like a double - decker bus, slumber party on bunk bed …

Make pocket chart for students and group as tens with five and five so can use everyday.

### Tens Concentration

*Materials: *40 cards from a deck with the face cards removed. Aces count as one.

Procedure

- Deal all 40 cards in a 5 x 8 array.
- Have players take turns turning over two cards at a time.
- If the two cards add to ten, then they can remove them.

Variations - Go fish same way, Dominoes Ten play so that combinations need to add to ten…

### Learning Strategies of addition and subtraction with sequences

### See bean toss and Apple packaging investigation (could be altered for 5 apples)

See also

Addition and subtraction

Sequences

## Place Value