Concepts of Print Interventions: - Elementary Math



Rote Counting Interventions:

|Skill- Rote Counting within 20 |

|Intervention – “Before and After” |

|Source or adapted from - |

|NZ Maths |

Materials:

- Counters

- Before and After sheet

Instructions for administration:

1. This game can be played with the teacher and one student or with a small group of students.

2. Each student takes turns to draw a card from the stack of cards. The student chooses the number before or after the drawn number then covers this number on their game board.

3. If the student cannot cover a square the next student has their turn. The drawn card is replaced in the pile so it can be drawn again.

4. The game ends when a student covers all their numbers. 

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 1. I’ll tell you when to stop.” (Stop at 20)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Rote Counting within 100 |

|Intervention – “Clapping” |

|Source or adapted from - |

|NZ Maths |

Materials: None

Instructions for administration:

Activity: The students count from 1 clapping hands in time.

Examples. Repeat but start from numbers other than 1. Also do counting backwards from various numbers.

Activity: The students count from 1 clapping hands and slapping knees alternately in time.

Examples. Repeat but start from numbers other than 1. Also do counting backwards from various numbers.

Activity: The students count from 1 clapping hands and slapping knees alternately in time. However they do not say the numbers out loud when they slap their knees.

Examples. Repeat but start from numbers other than 1. Also do counting backwards from various numbers.

Activity: Count backwards and forwards from some number by slapping knees, then chest, then clapping hands

Examples. Repeat by varying the parts of the body used.

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 1. I’ll tell you when to stop.” (Stop at 50)

“Start counting at 34. I’ll tell you when to stop.” (Stop at 70)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Rote Counting within 100 |

|Intervention – “Counting” |

|Source or adapted from - |

|NZ Maths |

Materials:

- blank laminated hundreds board

- Flip Strip

- large Rekenrek

Instructions for administration:

Depending on the need and age of the student, you may choose to only use parts of this intervention.

Get the students to clap as they count in ones. Write the numbers on the hundreds board as they are said.

Practice the number sequences forwards and backwards.

Ask the students to identify individual numbers on the hundreds board from the sequence they have just counted.

Repeat with flip strips.

Activity

Use body “percussion” to skip-count in twos. For example, the students touch their knees and silently think “One”, then clap and say “Two”, then touch their knees and think “Three”, then clap and say “Four” ...

Repeat skip-counting by twos by writing every second number on the hundreds board.

Similarly skip-count by fives and tens.

Repeat skip-counting by twos by moving pairs of beads on the Rekenrek. Relate the counting sequence to sets of objects and ask the students to give the total number of beads.

Similarly skip-count by fives and tens.

 

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 1. I’ll tell you when to stop.” (Stop at 50)

“Start counting at 34. I’ll tell you when to stop.” (Stop at 70)

“Count by 2’s. I’ll tell you when to stop.” (Stop at 30)

“Count by 5’s. I’ll tell you when to stop.” (Stop at 110)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Rote Counting within 100 |

|Intervention – “How High Can You Count?” |

|Source or adapted from - |

|RTI & Math: The Classroom Connection |

Materials:

- blank 3” x 5” or 5” x 8” index cards

- markers

- paper

- pencil

- pens

- stopwatch

- HoverCam or large chart paper easel

- masking tape

- conductor’s baton or pointer or magic wand

Instructions for administration:

Part A: Counting forward from 1 to 100-Crank up the Band!

1. Explain to students that they are going to learn to rote counting or say numbers in order from one to ten. Demonstrate: Say, “One, two, three, four, five, six, seven, eight, nine, ten.” Tell them they are going to mimic count by repeating each number after you say it, just like you say it. Say, “You will respond when I point to you with my baton.” Compare this activity to playing an instrument in an orchestra or band. Demonstrate holding the baton up in the air and say, “one.” Point to them with the baton and they say, “ one.” Say, “two.” Baton back in the air and they say, “two.” Continue to ten. Incorporate variety by saying the numbers slowly, quickly, high pitched, low pitched, quietly, thunderously, etc.

2. When students can mimic count without error, challenge them to synchronize count or say the numbers simultaneously with you. Continue to use the baton to establish the synchronization of the choral response.

3. As students become adept at synchronized rote counting, tell them that is time for them to synchronize count themselves with you playing the role of conductor. Challenge them to rote count without cues.

4. Repeat steps #1-3 as students expand their rote counting ability up to 100.

Part B: Kick Off- Counting forward from a number other than one

1. Explain to students that it is possible to start counting from any number and that you are going to teach them how to do so. Review or establish a student friendly definition for the word forward.

2. Repeat steps 1-4 from Part A above, while teaching counting forward from numbers other than one.

Part C: Blast Off- Countdown

1. Explain to students that now they know how to count forward, they are ready to learn how to count backward. Explain that counting backward is the same as a countdown. Connect this to countdowns for rockets blasting off. Establish a student friendly definition for backward. This is an opportunity to connect this act of forward and backward to the notion of opposite concepts.

2. Repeat steps 1-4 from above in Part A while teaching counting backward from numbers. Students who are fluent rote counters from one to ten can start with counting backward from ten. Start from five for the initial backward counting activity.

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 1. I’ll tell you when to stop.” (Stop at 50)

“Start counting at 34. I’ll tell you when to stop.” (Stop at 70)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Rote Counting within 100 |

|Intervention – Counting Up and Back |

|Source or adapted from - |

|Teaching Student-Centered Mathematics PreK-2nd Version, John A.Van de Walle |

Materials:

- number cards labeled with standard form and word form

Instructions for Administration:

Note: This is best done in a small group setting, not individually.

1. Counting up to and back from a target number in a rhythmic fashion is an important counting exercise. For example, line up five children and five chairs in. As the whole group counts from 1 to 5, the children sit down one at a time. When the target number, 5, is reached, it is repeated: the child who sat on 5 now stands, and the count goes back to 1. AS the count goes back, the children stand up one at a time, and so on, “1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2…” Children find exercises such as this both fun and challenging. Any rhythmic movement (clapping, turning around, doing jumping jacks) can be used as the count goes up and back.

2. You can modify this activity by varying the range of numbers. For example, use 15 to 20 if the student is working on the teen numbers and use something like 55 to 65 if the student is ready to move to larger numbers. To modify this activity for ELL students, give each child one card from a set of cards with the target numerals (i.e. 1 to 5, 15 to 20, 55 to 65) and the corresponding number word. These cards will provide a visual to help children connect the written numeral and number word to the number being said.

3. Another option involves having children stand in a circle and count around the circle to a target number. One child starts the count at number 1; the next child says the next number in the sequence, and so on, until a child says the target number. That child sits down and the next child starts the count again at 1. The activity continues until one child is left standing. You can vary the activity by using shorter or longer sequences, by starting the count at a number other than 1, or by having the children count backward from a target number. Challenge children by asking them to predict who will sit down next or will say a particular number.

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 1. I’ll tell you when to stop.” (Stop at 50)

“Start counting at 34. I’ll tell you when to stop.” (Stop at 70)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Skip-Counting within 120 |

|Intervention – Skip-Counting on the Number Line |

|Source or adapted from - NZ Maths |

Materials:

- Large Number Lines

- Sticky notes

Instructions for administration:

Put sticky notes on the number line to show the multiples of two, five, and 10 being learned by skip counting.

Say the sequence as you point to the sticky notes. Ask the students to predict what other numbers would be noted if the skip-counting continued.

Pose problems like, “When skip-counting by twos (or fives or tens), will the number 27 have a sticky note put on it? How do you know?”

Gradually remove the sticky notes until the skip-counting sequence is known. Mask parts of the number line with a strip of card. Point to the position of each multiple and ask the students say it. Repeat the activity by skip-counting backwards. Include skip-counting from new starting points, for example, skip-counting by fives starting at three gives 3, 8, 13, 18 ...

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Count by 2’s. I’ll tell you when to stop.” (Stop at 30)

“Count by 5’s. I’ll tell you when to stop.” (Stop at 110)

“Start at 90 and count by 5’s. I’ll tell you when to stop.” (Stop at 125)

“Start at 39 and count by 10’s. I’ll tell you when to stop.” (Stop at 119)

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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- Counting with Numbers Greater than 100 |

|Intervention – The Thousands Chart |

|Source or adapted from - Teaching Student-Centered Mathematics 3-5, John A. Van de Walle |

Materials:

- BLM 6 (Blank Hundreds Chart) found at .

Instructions for administration:

*This intervention is recommended to be done in small group of students with similar needs, rather than individually.

1. Provide students with several sheets of the blank hundreds charts (BLM 6 from above).

2. Assign partners or groups of three students the task of creating a 1-1000 chart. The chart is to be made by taping 10 charts together in a long strip. Students should decide how they are going to divide up the task with different students completing different parts of the chart.

3. The thousands chart should be discussed as a group to examine how numbers change as you county from one hundred to the next, what the patterns are, and so on. In fact, hundreds chart activities done in the primary grades can all be extended to a thousands chart.

Suggested Progress Monitoring Tool:

Progress toward Math Standards Task, Math Progress Monitoring Rubric

Progress Monitoring Task:

“Start counting at 198. I’ll tell you when to stop.” (Stop at 213)

“Write _________ (choose four numbers within the range of 0-1,000, include both two and three digit numbers, for example, “Write 137.”).” If incorrect, please write the student’s response next to the given number.

“Read these numbers… (choose four numbers within the range of 0-1,000, include both two and three digit numbers, for example, “19 and 278.”) If incorrect, please write the student’s response next to the given number.

Progress Monitoring Date: ________________

|Student Response: |

| |

| |

| |

|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. |

Appendix A Sample Recording Sheet

Student Assessment Recording Sheet

Use this with formative assessment tasks, classroom activities, and observations. | | | | | | | |Name |Date |Date |Date |Date |Date |Date | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

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