Tens and Ones with Bundled Paper Strips

The skill: understand a ten as a group of ten ones

In the base-ten system, ten ones can be grouped as one ten. For a physical model, ten individual strips are bundled together. The bundle represents one group of ten strips; it does not become one individual strip when a band is placed around it.

Fourteen can be represented by one bundle of ten and four loose strips. Counting all the individual strips would still give fourteen. The spoken and written number describes the total, while the tens and ones describe how the objects have been grouped.

The child can point to the bundle, count loose strips, direct an adult to move materials, or use a communication device. The activity does not require independent cutting, banding, or writing. The important relationship is between the group and the objects it contains.

Prepare strips and a workspace

Cut or tear at least fourteen similar paper strips, with adult assistance for cutting when appropriate. Count out ten for the first bundle and keep four loose. A paper sleeve, reusable band, or another suitable holder can keep the group together. Use materials appropriate for the child and setting.

Mark two areas on a table: one for tens bundles and one for loose ones. Labels can help, but the child can also point to each area while the adult names it. Keep space available to open a bundle and count its contents.

A pencil and paper can record 10 and 4, or the numeral 14. If manipulating a band is difficult, the adult can secure and open the bundle according to the child's directions. A flat group of ten strips under a paper label is another option if a band is unsuitable.

Make a verified bundle of ten

Place the loose strips in a row and agree that each strip represents one item. Move and count ten strips into a separate group before securing them.

1. Count the strips one at a time from one through ten, separating counted from uncounted strips.
2. Keep the ten counted strips together and place a sleeve or band around them.
3. Say, ‘This is one bundle of ten strips.’ Point to the one bundle and explain that it contains ten individual strips.
4. Open the bundle and count its contents again if the child wants to check. Reassemble it without adding or removing a strip.
5. Place the bundle in the tens area and four loose strips in the ones area.
6. Describe the whole collection as one ten and four ones. Count all fourteen strips if needed to verify the total.

A conversation when a bundle is counted as one strip

Adult: ‘How many strips are represented by this bundle and these four loose strips?’ Child: ‘Five,’ counting the bundle as one item and the four loose strips. Adult: ‘There is one bundle, and there are four loose strips. Let's open the bundle to see how many strips it contains.’

Together they count ten strips in the bundle and four outside it. Adult: ‘The bundle is one group, but it contains ten strips. Ten and four make fourteen strips.’ The child can point to each part as the adult counts.

The answer five accurately counts the visible groups and loose pieces as five separate units, but it does not count the individual strips inside the bundle. Naming the unit makes the distinction clear.

Represent fourteen in tens and ones

Place one verified bundle in the tens area and four loose strips in the ones area. Ask how many tens bundles there are and how many loose ones. The answers are one ten and four ones.

Write 14 and explain that, in this two-digit number, the 1 is in the tens place and the 4 is in the ones place. The 1 represents one group of ten, not one individual strip. Point between the written digits and the physical areas.

Unbundle and count all strips if the child wants to check the total. Reassemble the ten strips afterward. The same fourteen individual strips remain throughout, provided none was added or removed.

Compare a bundle with ten loose strips

Prepare one verified bundle of ten and, separately, ten loose strips. Count the loose strips and open the bundle to count its contents. Both groups contain ten individual strips, though one group is packaged together.

The bundle and the loose group are equal in the number of strips, not necessarily identical in their physical arrangement. A sleeve may add material but is not counted as a strip. Keep the counted objects and the holder distinct.

Ask the child to choose which arrangement is easier to count quickly and why. The bundle is useful because its size has been verified; without that agreement, a wrapped group could contain an unknown number and should be opened or checked.

Exchange ten loose ones for a ten

Place ten loose strips in the ones area. Count them, then gather those exact ten into one bundle and move the bundle to the tens area. The representation changes from ten loose ones to one ten; the number of individual strips remains ten.

Ask what changed: the arrangement and the number of visible groups changed. Ask what stayed the same: the ten original strips are still present inside the bundle. Open it if the child wants to verify.

Do not add a prefilled bundle while leaving the original ten loose strips in the collection. That would create twenty represented strips rather than exchange one group for another. An exchange must replace the ten loose ones with a bundle containing those same ten strips or an agreed equivalent group.

Exchange a ten for ten loose ones

Place one verified bundle in the tens area and no loose strips in the ones area. Open the bundle and move its ten strips to the ones area. There are now zero bundles and ten loose strips, but the total remains ten strips.

This arrangement is useful for understanding an exchange even though ordinary two-digit place-value notation normally regroups ten ones into one ten. The same quantity can be represented physically in more than one grouping.

If the child counts the empty sleeve as an extra strip, move it aside and identify what the question asks to count. The sleeve is a tool for holding the group, not one of the ten paper strips.

Build several two-digit examples

Use one bundle and two loose strips to represent twelve; one bundle and seven loose strips represent seventeen. Count the loose ones and use the verified bundle as ten. If enough strips are available, compare both arrangements side by side.

For twenty-three, prepare two separate bundles of ten and three loose strips. The tens area contains two groups, each with ten strips; the ones area contains three individual strips. The total is twenty plus three, or twenty-three.

Check each bundle before relying on it. A bundle of nine and a bundle of ten are not interchangeable merely because both are wrapped. Open and count a questionable group, then repair it before using it as a ten.

Understand zero in a place

For twenty, place two verified bundles in the tens area and no loose strips in the ones area. Write 20. The 2 describes two tens and the 0 indicates zero ones in this standard grouping.

Zero ones does not mean that the whole collection is empty. The two bundles contain twenty strips. Ask separately how many loose strips there are and how many strips are represented altogether.

For ten, one bundle and zero loose strips correspond to 10. Open a bundle if the child wants to verify that ten individual strips are present. The written zero records an empty ones place, not an absent tens group.

Compare fourteen and forty-one

Build fourteen with one bundle and four loose strips. If enough materials are available, build forty-one with four bundles and one loose strip. Compare the tens areas first: one ten and four tens are different quantities.

Write 14 and 41 beside their models. The digits are the same but their positions differ. In 14, the 1 represents one ten and the 4 represents four ones; in 41, the 4 represents four tens and the 1 represents one one.

If forty-one strips are not available, draw four clearly labeled groups of ten and one individual mark as a representation. Explain that the drawing stands for the groups. Avoid saying four pictured bundles contain four strips; each bundle represents ten.

Build a number from a spoken instruction

Say, ‘Show one ten and three ones.’ The child selects one verified bundle and three loose strips. Ask how many strips are represented: ten plus three equals thirteen. A numeral card 13 can label the model.

Now say, ‘Show two tens and one one,’ if enough bundles are prepared. The model represents twenty-one. Count the bundles as groups and the loose strip separately, then connect both to the written numeral.

If the child places one loose strip in the tens area for the first instruction, compare it with the verified bundle. The area label indicates the role in the model, but a single strip does not physically contain ten strips. Offer the bundle or construct it together.

Read a model before writing the numeral

Place two tens bundles and four loose strips on the table. Ask the child to identify the number of tens and the number of ones before naming the whole. The model represents twenty-four.

Write 24 and point to the 2 in the tens place and the 4 in the ones place. If the child writes 42, compare each digit with the labeled areas. Four tens and two ones would represent a different collection.

The child can select numeral cards or dictate the digits while an adult writes. Keep the physical model visible. Writing the symbols from memory is a separate challenge from reading a supported model.

Add ones until another ten is formed

Start with one bundle and nine loose strips, representing nineteen. Add one loose strip. There are now ten loose ones as well as the original ten. Count the loose group and exchange those ten strips for a second bundle.

The result is two tens and zero loose ones, representing twenty. The exchange changes the grouping, while adding the one strip changed the total from nineteen to twenty. Separate these two actions when explaining what happened.

If the child leaves the ten loose strips visible after adding a second prefilled bundle, the model contains too many strips. Use the same ten loose strips to create the bundle or remove the equivalent group during the exchange.

Draw the model with a clear key

Draw a long rectangle labeled ‘10 strips’ for one bundle and four small marks for the loose strips. Write 14 beside the drawing. Explain that the rectangle represents ten individual strips; it is not a single strip in the total count.

A more detailed drawing can show ten short lines inside the bundle outline. Count them to verify the key, then count the four separate lines. The drawing can be simpler later if both participants remember what the bundle symbol represents.

If a child draws one bundle rectangle and four marks and says five, ask whether they counted symbols or represented strips. Both observations can be described, but fourteen is the number of strips represented under the stated key.

Make the first round easier

Begin with ten loose strips and count them together. Form one bundle while the child watches. Ask the child to point to the single group and then open it to see the ten strips. No written two-digit numeral is required for this first comparison.

Add one loose strip and compare one ten with one one. The child can indicate which area contains the larger group while an adult names the quantities. Use large paper pieces and a holder that can be opened safely and comfortably.

Keep the bundle's contents visible or available for checking. A child can direct an adult to gather the strips. The support makes the grouping accessible without changing the number represented.

Add challenge with a missing part

Show one bundle and ask how many loose strips must be added to represent fifteen. The child can add loose strips one at a time and count on from ten to fifteen. Five loose ones are needed.

For a different question, show fourteen strips as one ten and four ones, then ask how many tens bundles are present. The answer is one bundle, even though it contains ten strips. Keep the requested unit explicit.

If a child answers four to the first problem, add four loose strips and name the resulting fourteen. One more is needed for fifteen. Check the model rather than relying only on the written digits.

Play a partner exchange game

One person prepares a set of bundles and loose strips; the other names or indicates the total and checks the contents if needed. Swap roles. Begin with small two-digit examples that can be verified with the available materials.

A partner can offer ten loose strips and ask for an equivalent bundle. Count them before gathering and verify that no extra strip remains. The exchange preserves the total while changing its grouping.

If the prepared bundle contains nine strips by mistake, open it and count. Add one strip from a clearly identified supply to make a verified ten, explaining that this repair changes the number of strips in that particular group. Do not silently call an unverified bundle ten.

Observe the strategy and support

A useful note might say: ‘Opened one bundle, counted ten strips, and identified four loose ones in a model of fourteen.’ Another could record that the child matched 14 to a visible one-ten, four-one model after an adult named the areas.

One accurate model does not establish understanding of every two-digit number or exchange. One error does not establish a persistent difficulty. If questions continue, concrete examples can be shared with a teacher or appropriate professional.

The same strips can be reused for a later number. Verify the bundle's contents when needed and keep the physical grouping clear. A written record is optional.

Predict the result of adding one ten

Build fourteen with one ten and four loose strips. Show a second verified bundle and ask what the new model will represent when it is added. Place it in the tens area: there are now two tens and four ones, or twenty-four strips.

Ask what changed and what stayed the same. The tens count rose from one to two; the four loose ones did not change. The total rose by ten because the added bundle contains ten individual strips.

If the child predicts fifteen by counting the new bundle as one strip, open it and count its contents. The addition is one group but ten individual strips. Compare that with adding one loose strip to fourteen, which does produce fifteen.

Check an incorrect bundle before counting

Prepare a wrapped group with nine strips and a separate loose strip. Ask whether the wrapped group can represent one ten under the agreed rule. Open it and count nine. It needs one more strip to become a verified group of ten.

Add the separate strip, count all ten, and close the bundle. Explain that this repair changes the number of strips in the group from nine to ten. If the loose strip came from elsewhere in a larger collection, identify that source before claiming the larger total stayed the same.

A band alone does not guarantee ten contents. Once a group has been checked and remains intact, it can be treated as a ten in subsequent steps. If it opens and a strip may have fallen out, count again before using it as a known group.

Compare two models of the same total

Show fourteen as one bundle and four loose strips. Beside it, represent the same quantity as fourteen loose strips or as a drawing of fourteen individual marks. Count each model separately. Both describe fourteen, even though the grouping differs.

Do not combine the two representations and say there are fourteen objects across both physical collections. If both sets of strips are physically present, together they contain twenty-eight strips. Each model separately represents fourteen.

Exchange ten loose strips in the second model for a bundle and compare the resulting one-ten, four-one arrangement with the first. The exchange preserves the second model's total. The child can direct the grouping while an adult handles the sleeve.

Explain the units in a written record

Create a small table with headings ‘tens bundles,’ ‘loose ones,’ and ‘total strips.’ For fourteen, enter one, four, and fourteen after constructing the model. For twenty-three, enter two, three, and twenty-three if the necessary bundles are available.

Ask what each column counts. The number one in the first row counts bundles; it does not count the individual strips inside that bundle. The total column counts all represented strips. Labels make this distinction visible to a person who did not see the activity.

If a row says one bundle, four loose ones, and five total strips, open the bundle and revise the total after counting. Five can describe the visible groups and loose pieces as separate units, but the requested total is the number of individual strips.

Return to the fourteen-strip example

Place one verified ten bundle and four loose strips in their labeled areas. Ask the child to show a partner the tens group, the loose ones, and the entire collection. The partner can open the bundle and count its ten strips before combining them with the four.

If the child wants to represent fourteen again, gather the same ten into the sleeve and return the four loose strips to their area. Compare the physical model with 14. The 1 describes a ten and the 4 describes four ones in this grouping.

This final check gives both participants a way to revisit the original relationship. The bundle, loose pieces, and written numeral describe related aspects of the same quantity; they are not three separate collections to add together.

Continue with number parts

For exploring a smaller whole in two parts, see Making Five in Different Ways. For individual object counting, try One-to-One Counting with Snack-Time Supplies. The bundle activity builds on counting ten individual strips once each.

Numbers and counting offers an optional digital continuation. Paper strips and a way to hold ten together are sufficient for the activity.