Concepts of Print Interventions:



Comparing Numbers Interventions:

|Skill- Comparing Numbers within 20 |

|Intervention – Find a Match |

|Source or adapted from - Developing Number Concepts – Bk 1 – Counting, Comparing and Pattern |

|By: Kathy Richardson |

Materials: Level 1: Counters

6-10 margarine tubs (or similar container)

Level 2: Same as level 1 + Small dot cards*

Level 3: Same as level 1 + Numeral Cards

Instructions for administration:

This intervention has three levels. Begin at Level 1 and progress through the levels as students are ready.

Level 1

In this activity children look for matching sets of counters (similar to Concentration)

1. Place paired of sets of counters under the margarine tubs (Make sure that there are two tubs for each number you want the children to work with.)

2. Arrange the tubs at random in a grid formation. Have the children take turns, first peeking under one tub and then under another, looking for matching sets.

3. When the student finds a match they should remove the pair of tubs and the counters from the playing area.

4. If the child does not find a match, they should replace the counters under the tubs in their original positions.

Variation 1:

After student lifts the first tub, instead of having them lift just one more tub in hopes of finding the matching set, allow them to lift as many tubs as necessary until they find the match.

Variation 2:

For each pair of matching sets, put loose connecting cubes under one tub and joined connecting cubes under the other.

Level 2

1. Hide dot cards under half of the tubs and matching sets of counters under the other half.

2. Have students take turns looking for the matches.

Level 3

1. Hide numeral cards under half the tubs and matching sets of counters under the other half.

2. Have students take turns looking for the matches.

Suggested Progress Monitoring Tool:

Provide the student with two groups of objects, group A and group B. Group B should have more than Group A (with neither group exceeding 20 objects).

a. “Can you tell me about these groups?

b. Which group is greater?

c. Which group has less?

d. Are they equal?”

This sentence frame may help: “Group A is ___________ (greater than, less than, equal to) Group B.” Students may use matching strategies, counting strategies, or equal share to determine whether one group is greater than, less than, or equal to the number of objects in another group.

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Progress Monitoring Date: ________________

|Student Response: |

|A. |B. |C. |D. |

| | | | |

| | | | |

| | | | |

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing Numbers within 20 |

|Intervention – Is It More or Is It Less? |

|Source or adapted from - |

|Developing Number Concepts – Bk 1 – Counting, Comparing and Pattern |

|By: Kathy Richardson |

Materials: Connecting Cubes

Directions for administration:

This intervention has two levels. Begin at Level 1 and progress through the levels as students are ready.

Level 1

1. Tell the children to build two “trains” of specific lengths.

(i.e. “Build a red train that is seven cubes long. Build a blue train that is three cubes long.)

2. Ask the student to compare the trains to see which on has more cubes and which has less. (i.e. “Show me the train that has more/less.”)

Variation

Have the student build several trains that have less than ten cubes. Give them a number and say, “Show me a train that has more.” or “Show me a train that has less.” Have the whole group state each relationship. Repeat with trains of various lengths.

Level 2

Have the student determine how many more cubes or less cubes one train has than the other. Depending on the language the children are able to interpret, choose questions that get them to compare two trains (i.e. “What can we do to the red train to make it just as long as the blue train?” or “What can we do to make the blue train the same length as the red train?”

Students ready to move ahead can consider these questions:

“Can you tell how many more cubes the red train has than the blue train?”

“Can you tell how many less cubes the blue train has than the red train?”

Suggested Progress Monitoring Tool:

Provide the student with two groups of objects, group A and group B. Group B should have more than Group A (with neither group exceeding 20 objects).

a. “Can you tell me about these groups?

b. Which group is greater?

c. Which group has less?

d. Are they equal?”

This sentence frame may help: “Group A is ___________ (greater than, less than, equal to) Group B.” Students may use matching strategies, counting strategies, or equal share to determine whether one group is greater than, less than, or equal to the number of objects in another group.

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Progress Monitoring Date: ________________

|Student Response: |

|A. |B. |C. |D. |

| | | | |

| | | | |

| | | | |

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing Numbers within 20 |

|Intervention – Two-Color Grab Bag |

|Source or adapted from - |

|Developing Number Concepts – Bk 1 – Counting, Comparing and Pattern |

|By: Kathy Richardson |

| |

Materials: Connecting cubes (of two colors)

Paper Bag

Instructions for administration:

Level 1

1. A student takes one or two handfuls of cubes from a paper grab bag.

2. The student then snaps together his or her cubes of the same color to form stacks.

3. Have the student identify the number in each stack.

4. Ask the student to compare the stacks to see which one has more and which one has less.

Level 2

Have the student determine how many more cubes or less cubes one stack has than another. Ask questions to get the children to look at the difference between two stacks. (i.e. “What would you have to do to make both stacks the same?”)

Ask children who are ready:

“How many more cubes (or how many less) are in one stack than in the other?”

Variation

You can provide smaller objects, such as buttons of two colors, so that the children will be able to take handfuls of more than 10.

Suggested Progress Monitoring Tool:

Provide the student with two groups of objects, group A and group B. Group B should have more than Group A (with neither group exceeding 20 objects).

a. “Can you tell me about these groups?

b. Which group is greater?

c. Which group has less?

d. Are they equal?”

This sentence frame may help: “Group A is ___________ (greater than, less than, equal to) Group B.” Students may use matching strategies, counting strategies, or equal share to determine whether one group is greater than, less than, or equal to the number of objects in another group.

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Progress Monitoring Date: ________________

|Student Response: |

|A. |B. |C. |D. |

| | | | |

| | | | |

| | | | |

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing Numbers within 20 |

|Intervention – Number Cards |

|Source or adapted from - |

|Developing Number Concepts Bk 1: Counting, Comparing and Pattern |

|By: Kathy Richardson |

Materials: Counters

Number Cards

Instructions for administration:

Level 1

1. Show the student two numeral cards.

2. Have the student use the counters to make a group of each size.

3. Have them then tell which group has more and which has less.

Level 2

1. Display two numeral cards, telling the student to make a group of counters to show the larger number.

2. Ask the student what they would have to do to change their group to show the smaller number.

3. Next, show another two numeral cards.

4. Tell the student to make a group to show the smaller number.

5. Ask what they would do to change their group to show the larger number.

Level 3

Present pairs of cards with numerals to 20. Repeat the process from Level 1 or Level 2.

Suggested Progress Monitoring Tool:

Provide the student with two groups of objects, group A and group B. Group B should have more than Group A (with neither group exceeding 20 objects).

a. “Can you tell me about these groups?

b. Which group is greater?

c. Which group has less?

d. Are they equal?”

This sentence frame may help: “Group A is ___________ (greater than, less than, equal to) Group B.” Students may use matching strategies, counting strategies, or equal share to determine whether one group is greater than, less than, or equal to the number of objects in another group.

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Progress Monitoring Date: ________________

|Student Response: |

|A. |B. |C. |D. |

| | | | |

| | | | |

| | | | |

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing & Ordering Numbers within 100 |

|Intervention – Bead Strings |

|Source or adapted from - NZ Maths website |

Materials:

- a string with 100 beads

- index cards (to use as tags)

- paper clips

Instructions for administration:

Show the students a piece of string. Use paper clips and index cards to label the beginning and end of the string as 0 and 100.

Ask the students to use grouping strategies to locate the multiples of 10, beginning with 50 (half way), 10, and 90. Tag these numbers on the string.

Now record other numbers in the range 0–100 on tags, and ask the students to find efficient ways to locate the numbers. Encourage grouping strategies. For example, 75 is found by identifying the position half way between 50 and 100.

As an independent activity, give the students bead strings and a set of tags with numbers already on them. The students place each tag in its correct position on the string. Partners check each others’ strings.

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Compare _____ and ____ using the symbols >, , _____ (Use 2 three-digit numbers like 123 and 321)

Progress Monitoring Date: ________________

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing & Ordering Numbers within 100 (can be adapted to numbers within any range lower or higher) |

|Intervention – Rocket-Where Will I Fit? |

|Source or adapted from - NZ Maths website |

Materials:

- Standard 1-6 dice

- 5-9 dice

Instructions for administration:

Each student needs to draw a “rocket” playing board like the one shown. The number of floors on the rocket can be increased where larger whole numbers or decimals are involved. The aim of the game is to fill every floor of the rocket with numbers in order.

If a player cannot place a number they have thrown, they miss that turn. Players take turns to roll a dice twice. From the numbers thrown, the students decide which two digit number they will use. For example, if five and three is thrown, the student could use 53 or 35.

The students then record the number on a level of the rocket where they think it best fits between 10 and 67. Once a number is written it cannot be moved.

Extension Activity

Repeat: The students can throw the dice three times to make a three-digit whole number and place that number between 110 and 667.

[pic]

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Compare _____ and ____ using the symbols >, _____ (Use 2 three-digit numbers like 123 and 321)

Progress Monitoring Date: ________________

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

|Skill- Comparing & Ordering Numbers within 1000 |

|Intervention – Who is the richest? |

|Source or adapted from - NZ Maths website |

Materials:

- play money

Instructions for administration:

Write this table of bank balances on the board. If necessary, the students model these amounts with play money. Ask who has the most money in the bank. The students need to realize that they start with the left-hand place value of each amount. For example, a person with any 100s in their amount will have more than someone whose largest place value is in the 10s.

Repeat with varying amounts of money.

|Matthew |$199 |

|Erica |$87 |

|Jose |$200 |

|Janice |$99 |

|Eli |$348 |

 

Activity

Move onto doing the same kinds of problems without money. Focus attention on the significance of starting from the left-hand digit when comparing numbers. Order numbers within these lists. The third list is particularly taxing because of the presence of numerous nines.

|List 1 |List 2 |List 3 |

|109 |740 |90 |

|345 |704 |909 |

|99 |119 |990 |

|677 |911 |999 |

|56 |747 |1090 |

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

Compare _____ and ____ using the symbols >, _____ (Use 2 three-digit numbers like 123 and 321)

Progress Monitoring Date: ________________

|Teacher Observation Notes: |

| |

| |

|Rubric Score (circle one): 1 2 3 |

|Not yet: Student shows evidence of misunderstanding, in either an incorrect |Got It: Student essentially understands the target|

|concept or ineffective procedure. |concept. |

|1  Unsatisfactory: |2 Marginal: |3 Proficient: |

|Little Accomplishment |Partial Accomplishment |Full Accomplishment |

| | | |

|The task is attempted and some |Part of the task is accomplished, but |Strategy and execution meet the content, process, |

|mathematical effort is made. There |there is lack of evidence of |and qualitative demands of the task or concept. |

|may be fragments of accomplishment |understanding and/or the learning may |Student can communicate ideas. May have minor |

|but little or no success.  Further |not be transferring outside of the |errors that do not impact the mathematics. It is |

|teaching is required. |intervention time back to Tier 1 time. |clear that the student is transferring this |

| |Further teaching is required. |concept to Tier 1 and in the regular classroom |

| | |setting. There is evidence to support this. |

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