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Skill- Place Value with numbers greater than 100
Intervention File It
Source or adapted from - Intervention Tool Kit for Math by Lauren Reynolds
Materials:
Mini file folder boxes (or a small box, like a recipe card box)
Index cards
Instructions for administration:
1. Start with 10 mini file folders. Write on the tab of each folder a 3 or 4 digit number you wish your students to focus on. Place the folders in a small box like a recipe card box.
2. Next, prepare the index cards the reflect the numbers you wrote on the tab, but this time write the expanded notation or another representation of the number instead of the standard form (written form, base ten blocks picture, number disks picture, etc.)
3. Give the student the box of mini file folders and the stack of cards and ask them to file each index card in the appropriate folder in the box.
Suggested Progress Monitoring Tool:
Write ____________________ with numerals in standard form. (Teacher should choose any four-digit number in written form, such as three thousand, two hundred ninety-six)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
How is the digit 7 in 657 similar to or different from the 7 in 756? (Note: Teacher should change the numbers and place values each time this question is asked to see if the student demonstrates thorough understanding, any three-digit number would be appropriate)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Place Value with number greater than 100, Comparing Numbers
Intervention High Roller
Source or adapted from - Intervention Tool Kit for Math by Lauren Reynolds
Materials:
Number Dice
Instructions for administration:
1. Divide participating students into small groups and give each group three or more Number Dice.
2. In turn, each student in the group rolls the dice and creates the greatest number he can with the numbers rolled. All students in the group say the number out loud.
3. The process continues as students take turns rolling the dice and attempting to take over the title, High Roller, with the group always saying the number out loud before the next person begins.
Suggested Progress Monitoring Tool:
Can you compare _____ and _____ using the symbols >, <, or = ? (Teacher should choose any three-digit number, possibly even those that use the same digits, but in different positions, such as 716 and 671)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Place Value
Intervention How Many Tens and How Many Hundreds?
Source or adapted from - NZ Maths HYPERLINK "http://www.nzmaths.co.nz/resource/how-many-tens-and-hundreds" http://www.nzmaths.co.nz/resource/how-many-tens-and-hundreds
Materials:
play money
Instructions for administration:
Preliminary Knowledge
The students need to know 10 hundreds make 1 thousand and vice versa, and 10 thousands make 1 ten thousand and vice versa.
Using Materials
Problem: The Bank of Mathematics has run out of $1000 dollar bills. Alison wants to withdraw $2315 in $1, $10 and $100 dollar. How many $100 notes does she get?
Repeat for: $2601, $3190, $1555, $1209, $2001, $1222, $2081.
Using Imaging
Problem: Tickets to a concert cost $100 each. How many tickets could you buy if youhave $3215?
Write $3215 on the board. Shield 3 one thousands, 2 one hundreds, 1 ten and 5 ones.
Ask the students what you can see. Discuss how many hundred dollar bills you couldget by exchanging the thousands. Discuss which bills are irrelevant (the ten and theones).
Shielding and Imaging only: Examples. Find the number of hundreds in:
$1608, $2897, $2782, $3519, $3091, $4000.
Using the Number Properties
Examples. Find the number of hundreds in: 3459, 8012, 9090, 6088, 3280, 5823,
7721, 2083.
Challenging examples: Find the number of hundreds in: 13 409, 28 002, 78 370, 12 088, 45 290, 82 356, 21 344.
Find the number of tens in: 3709, 8002, 8579, 5208, 4829, 82 333, 12 897,
30 897, 89 000, 50 890
Suggested Progress Monitoring Tool:
Progress toward Math Standards Task, Math Progress Monitoring Rubric
Progress Monitoring Task:
What number would you write to show _____ tens and _____ ones? (use numbers like 13 tens and 5 ones, or 17 tens and 5 ones where the value of the tens digit will exceed 100)
Can you show me that number with base-ten blocks? Can you show me the number with number disks?
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Number Sense & Reasoning
Intervention Add a Unit to Your Number
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials: none
Instructions for administration:
1. Write a number on the board (start with numbers between 0-10, then move larger, 10-50, 50-100, and so on.)
2. Now, suggest some units to go with it, and ask the student what they can think of that fits. For example, suppose the number is 9. What do you think of what I say 9 dollars? 9 hours? 9 kids? 9 meters? 9 oclock? 9 hand spans? 9 gallons?
3. Spend some time in discussion of each. Let the student suggest units as well. Be prepared to explore some of the ideas either immediately or as projects or tasks to share with parents at home.
Suggested Progress Monitoring Tool:
This intervention should be done in combination with another intervention that includes a formal progress monitoring tool. This intervention should increase a students overall sense of number, rather than measure a specific skill.
Skill- Number Sense & Reasoning
Intervention Is it reasonable?
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials: none
Instructions for administration:
1. Select a number and unit-for example, 15 feet.
2. Ask these questions: Could the teacher be 15 feet tall? Could your living room be 15 feet wide? Can a man jump 15 feet high? Could three children stretch their arms 15 feet?
3. Pick any number, large or small, and a unit with which the student is familiar with. Then make up a series of these questions and discuss the students thoughts.
Suggested Progress Monitoring Tool:
This intervention should be done in combination with another intervention that includes a formal progress monitoring tool. This intervention should increase a students overall sense of number, rather than measure a specific skill.
Skill- Number Sense & Reasoning
Intervention Build it in Parts
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials: base-ten blocks or little ten frame cards
Instructions for administration:
1. Provide students with one type of material, such as base-ten blocks or little ten-frame cards.
2. The task is to see how many different combinations for a particular number, such as 83, students can make using two parts. (If you wish, you can allow for more than two parts.)
3. For each combination, students are challenged to see and read their representation in two parts. Each different combination can be displayed on a small mat, such as a quarter-sheet of construction paper.
4. For each representation, have students write an addition equation that matches the way they identified the parts within the decomposition.
5. Writing combinations encourages reflective thought focused on the part-whole relationship and decomposition of numbers. It also helps make apparent the clear connection between part whole concepts and addition concepts.
Suggested Progress Monitoring Tool:
This intervention should be done in combination with another intervention that includes a formal progress monitoring tool. This intervention should increase a students overall sense of number, rather than measure a specific skill.
Skill- Number Sense, Reasoning, & Rounding
Intervention Who am I?
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials: number line
Instructions for administration:
1. Sketch a number line labeled with 0 and 200 at opposite ends. Mark a point white a question mark that corresponds to your secret number. (Estimate the position the best you can.) Students try to guess your secret number. For each guess, place and label a mark on the line.
2. Continue marking each guess until your secret number is discovered. As a variation, the endpoints can be different-for example, try 0 and 1000, 200 and 300, or 500 and 800.
3. For students with disabilities or very poor number sense, it is important to mark the guesses that have occurred and where they are located. Labeling those number at their actual locations will support students reasoning in the process of identifying a secret number.
Suggested Progress Monitoring Tool:
Make an X halfway between 0 and 100 on this number line. Write the number that is halfway between 0 and 100 below the X. Where would 23 go on this number line? What about 65? (Teacher can and should vary the endpoints, i.e. between 100 and 200, 0 and 1,000, etc. to meet the students individual needs)
Teacher Observation Notes:
0 100
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Rounding
Intervention Round Off
Source or adapted from - Intervention Tool Kit for Math by Lauren Reynolds
Materials: blank Bingo cards, game markers (pennies or counters), markers
Instructions for administration:
1. Decide to which place value or which multiple of 50 you want students to round off numbers. For the purpose of these directions, lets say you want them to round to the nearest 50.
2. Supply each participating student with a BINGO game card, game markers such as pennies or counters, and a marker. Ask each student to write the numbers 200, 250, 300, 350, 400, 450 and so on in the boxes of the game card, repeating numbers if she chooses.
3. Call out a number; lets say you choose 352. Each student needs to determine which multiple of 50 is closest to the number 352. She then marks that number (in this case, 350) on her game card.
4. After students have marked their cards, be sure to state the correct answer and, if necessary, draw a number line segment to show why its correct. Continue calling numbers until someone fills in an entire row vertically, horizontally, or diagonally, and calls out: Round Off!
Suggested Progress Monitoring Tool:
What is ____ rounded to the nearest multiple of 10? (Teacher should choose any two-digit number, such as 67 or 12)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
What is _____ rounded to the nearest 100? Can you show me how you know using a number line? (Teacher should choose any three-digit number, such 314 or 560)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Number Sense & Reasoning
Intervention Close, Far, and In-Between
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials: white board or chart paper
Instructions for administration:
Ex.
1. Put any three numbers on the board. If appropriate, use larger numbers. With these three numbers as referents, ask questions such as the following?
- Which two are closest? Why?
- Which is closest to 300? 250?
- Name a number between 457 and 364. Name a multiple of 25 between 219 and 364.
- Name a number that is more than all of these.
- About how far apart are 219 and 500? 219 and 5000?
- If these are big numbers, what are some small numbers? Numbers about the same? Numbers that make these seem small?
2. Discuss any unreasonable answers with the student to clarify.
Suggested Progress Monitoring Tool:
Make an X halfway between 0 and 100 on this number line. Write the number that is halfway between 0 and 100 below the X. Where would 23 go on this number line? What about 65? (Teacher can and should vary the endpoints, i.e. between 100 and 200, 0 and 1,000, etc. to meet the students individual needs)
Teacher Observation Notes:
0 100
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Place Value (to 1,000)
Intervention Too Many to Count?
Source or adapted from - Teaching Student-Centered Mathematics, John A. Van de Walle
Materials:
more than 1,000 small items
*This intervention is recommended for a small group, not individually.
Instructions for administration:
1. Show students a large plastic bag or cardboard box with more than 1000 items. For example, you might use a set of straws or Styrofoam packing peanuts. First, have the students make and record their estimates of how many straws are in the bag. Discuss with students how they made their estimates.
2. Give portions of the straws to tables or pairs of students to count. Suggest early on that they may want to use rubber bands to create bundles of 10 or 100. If they bundle by 10, then ask, How can we use these groups of 10 to tell how many straws we have? Can we make new groups from the groups of 10? What is 10 groups of ten called?
3. Once they see a bundle of 100, let them change their estimates if they wish.
4. When all bundles or groups are made, count the thousands, hundreds, tens, and ones separately. Record on the board as 1 thousand + 4 hundreds + 7 tens + 8 ones.
5. In this activity, it is important to use a groupable model so that students can see how the 10 groups of 100 are the same as the 1000 individual items. This connection is often lost in the rather simple display of a 1000 cube in the pre-grouped base-ten models.
Suggested Progress Monitoring Tool:
Write ____________________ with numerals in standard form. (Teacher should choose any four-digit number in written form, such as three thousand, two hundred ninety-six)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
How is the digit 7 in 657 similar to or different from the 7 in 756? (Note: Teacher should change the numbers and place values each time this question is asked to see if the student demonstrates thorough understanding, any three-digit number would be appropriate)
Teacher Observation Notes:
Rubric Score (circle one): 1 2 3
Not yet: Student shows evidence of misunderstanding, in either an incorrect concept or ineffective procedure.
Got It: Student essentially understands the target concept.
1 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required.
2 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding and/or the learning may not be transferring outside of the intervention time back to Tier 1 time. Further teaching is required.
3 Proficient:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics. It is clear that the student is transferring this concept to Tier 1 and in the regular classroom setting. There is evidence to support this.
Skill- Number Sense with Large Numbers
Intervention How Long?/How Far?
Source or adapted from - Teaching Student-Centered Mathematics 3-5, John A. Van de Walle
Materials:
none
Instructions for administration:
1. In this activity, talk about real or imagines distances with students by posing investigations for them to consider such as, How long is a million baby steps?
2. Other ideas that explore the length of a million objects or people include estimating a line of toothpicks, dollar bills, or candy bars end to end; student holding hands in a line; blocks or bricks stacked up; students lying down head to toe.
3. Standard measures-feet, centimeters, meters- can also be used, with students noting that larger numbers emerge when the smallest units are used.
Suggested Progress Monitoring Tool:
This intervention should be done in combination with another intervention that includes a formal progress monitoring tool. This intervention should increase a students overall sense of number, rather than measure a specific skill.
Skill- Place Value with Numbers > 1,000
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 HYPERLINK "http://www.ablongman.com/vandewalleseries/Vol_2_BLM_PDFs/BLM5-6.pdf" http://www.ablongman.com/vandewalleseries/Vol_2_BLM_PDFs/BLM5-6.pdf.
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:
This intervention is meant to help students conceptualize larger numbers. This is not easily measured with traditional progress monitoring but instead, could be measured by asking general questions regarding number sense to get a feel for the students understanding. For this reason, progress monitoring graphs, etc. have been intentionally left off.
Suggested questions:
Ex. What patterns did you notice in the thousands chart? What is 10 more than _____? What is 100 less than _______? How many tens are in a 1,000? How many hundreds?
457
364
219
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