Dynamic Paper

Be sure to check out the Dynamic Paper app from NCTM's Illuminations site.  This app allows teachers to customize and print out graph paper, grids, number lines, tessellations, spinners, pattern blocks and more.  Users control the number of sections in the spinner and colors.  Likewise, users set the size of the sides of pattern blocks or the range of the number line. 


Dynamic Paper is a great resource for teachers designing activities to support math learning.  It's also an invaluable tool for teachers needing to differentiate classroom learning activities to meet the varied needs of learners in their classrooms.


Check out Dynamic Paper.

Coin Antennas

Students draw antennas on coin pictures to represent the value.   Each antenna is worth 5 cents.   This means a dime has two antennas, a nickel has one antenna, a penny has no antennas, etc.   


This strategy capitalizes on students' strength in counting by fives.   They simply point to each antenna as they count by 5s, then count on by ones to include any pennies.   This method is also efficient because students do not need to sort and reaarange coins; they simply draw antennas on coins in the order given.   
This method is especially effective for K-2 regular and special ed. students who will eventually outgrow the need for antennas.   


NOTE: some teachers call the antennas "hairs" and talk about the penny as "bald" because it has no hair.   Whatever works for you and your students is the best strategy. 

Last Snowman Standing Game

The snowmen face off in this game of addition facts. But beware! A toss of the die may mean the sun melts a snowman. Students practice addition facts as they try to be the last snowman standing because in this game the first person to remove all of his/her snowmen loses the game!

Download the  Last Snowman Standing Game for directions and game mats for three different versions of the game:

• Sum of Two Dice Version to practice addition facts
• Difference of Two Dice Version to practice subtraction facts
• One Die Toss for a simplified version to analyze the probability of a die toss

Data Collection: The directions for each version also include directions for data collection and analysis of the outcomes of the games. Be sure to incorporate these activities, if at all possible, as games offer a highly motivational study in probability. Students love to "play games" to collect data. They're also eager to analyze games so that they learn how the game works and what strategies they can use to improve their odds of winning.

Differentiation: This game offers many opportunities to differentiate the activity. First of all, teachers are able to select from three different versions. Secondly, each teacher should differentiate the game analysis to meet the instructional level of his/her students. Most students can handle the questions with teacher guidance. Older students and talented primary students may be challenged to analyze the game and answer the questions in small groups.


Read about the Last Snowman Standing game on Mathwire.

Active Participation Strategy: Let Go and Let Students...

Let go and let students...:   This phrase reminds teachers to put students in charge of their learning and in charge of explaining themselves. This practice incorporates multiple effective strategies to support student learning:

• Give students the chalk or marker and ask them to come to the board or overhead to explain their thinking.   Resist asking students to tell you what they did while you write what they did.   Asking students to write as they explain allows them to organize their thinking and provides insight to teachers about what strategies and organizational methods students use effectively and independently.   This strategy also provides practice for the expected independent test performance.
• Ask another student to repeat a student's explanation or insight.   Resist the urge to repeat or paraphrase each student's response.   Ask classmates to do this instead, fostering active participation/listening skills in all students.
• Ask students to read directions or problems aloud rather than reading them yourself.   Once again, this practice encourages students to develop effective reading skills for math activities and tests.   If reading levels are an issue in your classroom, you might begin with buddy reading, pairing students to effectively mitigate this issue.
• Ask students to define math vocabulary terms in their own words.   Post the best definitions around the room.
• Post samples of effective problem-solving solutions that meet tough requirements of the problem-solving rubric you use to grade student responses.   Make overheads of student samples and review them regularly so that all students see examples of effective ways to organize solutions and explain thinking.
• Expect students to be capable of some independent work.   Voice this expectation to students as in "I want to see how each of you does on Math Boxes #3 and #4 today, so please begin with those boxes.   I believe that everyone can do these by themselves and I will be around to check.   After you finish these two math boxes, you may do the others in any order you choose."
• Quickly spin off students who are capable of independent work.   Provide enrichment activities that go beyond current grade-level expectations and require higher-order thinking skills for solutions.   Encourage these students to play harder versions of math games (i.e. more cards, larger numbers, etc.)
• Differentiate and scaffold instruction to effectively meet the varied needs of learners in your classroom.   Provide enrichment activities for talented students while you work with small groups who need additional instruction or scaffolded support/encouragement during independent practice.   Use flexible grouping based on informal assessment of student responses during instruction.

More Active Participation Strategies

Download Mathwire's Active Participation Strategies for Math Classes:  a one-page text-only summary of the strategies discussed above.

Download Mathwire's Active Participation Strategies for Math Classes:  the full text of this section with pictures.

Scrambled Eggs Game

Successfully skip counting by 5s is an important mathematical foundation for the 5 times table, for counting nickels, for rounding numbers, etc. Counting by 5s and counting by 10s are often the first rote skip counting a student learns. While some students will naturally learn the count through classroom activities, other students will need deliberate intervention to master this sequence. 

 Scrambled Eggs Game

Distribute large cards with multiples of 5 to students. Ask students to quietly assemble themselves in correct order, holding the card in front of them. Time the class in this activity, if this motivates your class to master the sequence. 

NOTE: Cheap, white paper plates work well for this activity. Write large numbers with a black sharpie pen.  Paper plates stack easily for storage and also hold up well through repeated use. 

Partner Game: Each partner shuffles a set of count by five cards and turns them face down.  On the word "GO!" each partner turns over the first card and places it roughly before him/her.  Each student turns over one card at a time, ordering the cards before him/her until all cards are in correct order.  First student to correctly order the sequence of cards wins the game.  

• Download Count by 5 Cards for individual student use. Copy on card stock, cut apart, and place in baggies for partner game use.

Hundred Board Puzzles

Students learn the patterns in the hundred board by assembling puzzles. Teachers are able to assess student use of patterns in rows and columns by observing the student at work.

Differentiation:  This task is easily differentiated to accommodate the varied levels in a first grade class by changing the number of pieces and the shape of the pieces. Puzzle bags should be sequentially lettered so that students progress through harder versions of the task. Finally, students are asked to create their own puzzles for classmates to solve.

Extension:  Use a 101-200 number grid so that students extend patterns and become more familiar with 3-digit numbers.


Materials: 

• See Hundred Board Activities on Mathwire to download a hundred board template that may be used to create the hundred board puzzles.
• Copy the template onto card stock to make the puzzles heavier and easier to assemble.

Last Snowman Standing Game

The snowmen face off in this game of addition facts. But beware! A toss of the die may mean the sun melts a snowman. Students practice addition facts as they try to be the last snowman standing because in this game the first person to remove all of his/her snowmen loses the game!

The snowmen pictured above were created with two wooden beads glued together, then painted white, The face was added with sharpie pens. Just be sure to buy the beads that have a flat bottom so that the snowmen will stand. Or, use any manipulative as snowmen.

Download the Last Snowman Standing Game which includes directions and game mats for three different versions of the game:

• Sum of Two Dice Version to practice addition facts
• Difference of Two Dice Version to practice subtraction facts
• One Die Toss for a simplified version to analyze the probability of a die toss

Data Collection: The directions for each version also include directions for data collection and analysis of the outcomes of the games. Be sure to incorporate these activities, if at all possible, as games offer a highly motivational study in probability. Students love to "play games" to collect data. They're also eager to analyze games so that they learn how the game works and what strategies they can use to improve their odds of winning.

Differentiation: This game offers many opportunities to differentiate the activity. First of all, teachers are able to select from three different versions. Secondly, each teacher should differentiate the game analysis to meet the instructional level of his/her students. Most students can handle the questions with teacher guidance. Older students and talented primary students may be challenged to analyze the game and answer the questions in small groups.  

Active Participation: Using White Boards

Active Participation: Using White Boards

A few years back, NCTM sold buttons that said “Math is not a spectator sport.” This is so true as we know that students have to be ACTIVELY involved in math lessons in order to construct meaning for themselves. White boards are my favorite tool for easily adding participation to classroom lessons and activities. Each student must write on his/her white board, allowing the teacher to see what each student is thinking. This makes it easy to evaluate learning throughout the lesson and modify, reteach or enrich, as needed, to meet these identified needs. Teachers who sprinkle these quick, written checks throughout lessons find it easy to form small groups for additional instruction or guided practice. They also identify more capable students who do not need the extra practice and would benefit from some enrichment activity.

Cheap White Board Alternative
Each student should have a whiteboard, dry erase marker and eraser that is kept in his/her desk for easy retrieval. If you do not have whiteboards, or need more to have one for each student, consider using the cheap alternative. Place a sheet of white card stock in a shiny sheet protector and use this as a white board. You could use regular paper, but the card stock is heavier and holds up better. It will also remain upright when students hold up their white boards for checking. Erasers can also be small pieces of black felt so each student can have his/her own.

Use White Boards to Assess and Differentiate Instruction
Students love working with white boards. There’s something about the dry erase marker and the ability to wipe the slate clean and start over that appeals to even the most reluctant students. Unlike paper and pencil, wrong answers and mistakes are easily wiped away in the process of learning. Focusing on only one problem at a time also helps students who need chunking to reduce visual clutter or students who are overwhelmed by a whole blank worksheet or workbook page. So, get out the white boards, markers and erasers this year and start planning to use them throughout each math lesson. They are an extremely valuable tool as you quickly evaluate student understanding of the lesson’s objective. They are also provide a way to assess previous learning before beginning a new unit to be certain that students have the requisite concepts and skills.

Some Suggestions for Using White boards to Increase Active Student Participation:

• 
  Do Now or Warm-up Activity

: Give students the date (24) or any number, and have the students write as many different names for that number as they can in 1-2 minutes. Have students share their results in small groups, then ask groups to share their best responses.

Check for Understanding: ask students to write their response on the white board. Circulate around the room as students are writing. After several moments, ask students to hold up their responses. Call on specific students to share their thinking.
o Write another fraction that is equal to ½.
o Which is larger 7.2 or 7.20? Why?
o What do you call the number that appears the most often in a data set?
o When you measure around the yard for a new fence, are you finding the perimeter or area of the yard?
Transition Times: give students a task to do as you check homework, distribute papers, etc. Tell students they will have to explain their thinking when you check whiteboards.
o Write the fact family for these numbers: 4, 5, 9
o Write as many different names as possible for the number 12.
o Write down 5 fractions that are between ¼ and 5/8.
o Show 4 different ways to make 45 ¢.

Guided Practice: have students do several examples on the white board for checking. Identify the students who have mastered the day’s objective and release them to independent work. Gather students who need more practice at a small table and guide them through additional examples, as needed, until they are ready for independent work.

Jeopardy-type review at the end of a unit: every student gets to answer so you quickly identify any sticky points before testing

And so on and so on and so on…

More Active Participation Strategies:

Check out additional active participation strategies on Mathwire: http://www.mathwire.com/strategies/is.html#active

What’s your favorite way to use white boards in your math lessons? Post a comment with your favorite strategy.