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Differentiating instruction is really a way of thinking, not a preplanned list of strategies.Oftentimes, it is making decisions in the moment based on this mindset. To differentiate, teachers can change up how they group students. sometimes a mixed ability group might work best, While sometimes it might be appropriate to have same ability groups.So it is a matter of keep our eyes on the prize, what are the learning objectives? And what are the best roads for different students.

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While some students would be perfectly comfortable in a room full of their peers shaking cups full of counters and spilling them out, I am certain that others would feel overwhelmed by those sights and sound and could be provided with a quiet space to accomplish the task.

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The act of shaking the cup and spilling the counters could be converted into an interactive program in order to accommodate students whom are not comfortable with or not physically able to interact with manipulatives.

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Differentiating according to the learning environment shows an understanding of the needs of your students, and the conditions in which students learn best. Some students will want to sit quietly to figure out the coin activity on their own, while some will want to plan or talk it out with a partner, and others will want to be active - moving around and physically playing the coin activity out. Providing options of where they work in the class or how - quiet work at their desks, partner work on the carpet, talking or playing it out at the back table (allowing them to move to walk around to get there) will allow students access to the learning environment that helps them to succeed.

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When creating a product to demonstrate understanding, students should be given opportunities for scaffolded or tiered assignments according to student needs, and a choice of ways to demonstrate their learning on an on-going basis. Rather than just one opportunity to play and show results for the coin activity, students have multiple attempts to play and figure out how to show their product. We should be assessing their overall understanding of the coin activity, not just taking one snapshot of their understanding, at one time.

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As educators, we should think about how we present an activity and how we encourage multiple opportunities for students to have learning opportunities. Students should be given choices of how they play and explore the coin activity. Groupings can be changed at different times when they play the game, as well. For example, perhaps they will start to explore the game with a partner who they feel very comfortable with, and then later on they try it again with a partner that will challenge their learning - perhaps having one student acting as a teacher or guide for a struggling student.

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To differentiate content, we may choose to have some students start at a different entry point (ie/some students will need to learn and/or review what a nickel is, what heads and tails are), while some students will be able to jump right into the activity

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A comfortable and accessible learning space should b presented to the students, It can be their seats, or carpet, quiet corner or any other learning space that they might need and which is easy for a teacher to facilitate the whole lesson.

Stationary like paints, paper pencils or anything else that I required by the children should be accessible to the child.

Teacher should be available to guide a child if they are struck. In case where the learning level of two students is not similar the teacher can switch their groups.

The children should be allowed to move around in the physical space.

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Sumita Maini
In order to include all four types of learners visual, auditory,reading writing and kinesthetic the students should be given a choice in the way they want to present the solution to the class.
They could draw/ paint, use coins to show, solve the problem on the white board or just speak about the problem. Both the partners can take turns while presenting the problem.

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The class could be divided into pairs students depending on their choice or they ca work individually.

Students would be told to go back to their learning space.

Teacher could visit various groups to facilitate the learning. Guide the students who might need help. Give a challenging problem to the students who are fast to solve the problem in order to keep them engaged.

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Teacher can begin by bringing the whole class together on a Carpet and introducing the concept with the help of a visual aid/ a pack of coins, or a video which depict various ways to make four. The teacher can then introduce the problem that the students have to now find all the ways to make five. Que cards should be made in advance for more complex numbers for students who need challenge.

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To cater to different learning needs of students, differentiate the way they can consolidate their learning from the activity, be it:
- verbally explaining their findings to a partner, group or the teacher
- creating a visual chart of the results
- putting separate piles to show the results
Providing and differentiating the ways in which the students can show their learning will allow students with different learning styles to effectively consolidate their learning to the teacher to be assessed, but also to themselves to learn to the ideal best of their individual abilities.

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Observe students during the activity.  For those students who many be struggling, some ways to differentiate and cater to their needs may include:
- changing their workspace (somewhere quieter, more level)
- providing a partner/group settings to have another student to help aid in the struggling students, be it physically, socially, cognitively, emotionally.
- If in group settings, possibly changing group members where struggles may be apparent, due to challenge differences, group dynamic, speed of activity steps

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Multiples intelligence along with differentiated instruction will sure meet the needs of students and boost their engagements.

Teacher can start by doing the scaffolding method by demonstrating how to do a pile of 4.
Drawing and writing on the board to show them what is being explained. Asking the students at the same time ways to do piles of 4.

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Multiples intelligence along with differentiated instruction will sure meet the needs of students and boost their engagements.

When the teacher walks around, students will be asks to explain their finding in different ways a drawing, a little song or just by explaining their filled sheet of paper. They can work in pairs or invidually but they each have to explain.

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Place students in groups and observe them during the process to make sure they remain on task.
Assign a time for the work to be completed and also assign roles.
Have each group demonstrate and present their findings/results.
Allow time for peer feedback and questions.

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-Extra time to complete their work for students who have difficulties.
-Peer/Group support can be beneficial for both those who have difficulties and those who don't feel challenged .

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Have students show learning in various ways. Each student learns best by a different intelligence. For example the linguistic learner can present their product verbally, the logical learner can present their work mathematically on paper, while the kinaesthetic learner can use counters or coins to present their product to the teacher.

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Provide various workspaces for the student:
- quiet space in the hallway
- in the class working with a partner, small group or alone
- extra time with the teacher

Also for students having difficulty offer extended time for learning, plus peer or teacher assistance.

For students needing more of a challenge have them lead a group or provide instruction for struggling students. They can take a group in the hallway.

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Offer several math manipulatives students can choose from:
- actual nickels
- counters
- abacus
- marker and paper (students can draw and colour circles

To challenge other students bring the total number of groups of 5 to a higher count. Have them use mental math. For students on a different level they can have a lower minimum of groups of 5 to reach, using the manipulatives they're comfortable with. Also the option of working with a partner.

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Flexible grouping allows teachers to strategically group students based on the learning goals and needs of students.

You could pair students up with different skill levels for this activity so that one could lead by example, or create homogeneous groupings so that the students are working through the activity at the same speed.

Provide one on one prompting to a student, while other students are working independently.

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To eliminate confusion around heads or tails, or about the fact that the value of a nickel is 5, use those math tokens that are red on one side and yellow on the other side.

To make the task more complex, create the option of adding more nickels to the cup, and asking students to find all of the ways to make 10.

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Students could orally say the number sentences while the teacher scribes for them. Blank number sentences could already written out for the student ____ + ____ = 5 so that the student just fills it in.

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Students can complete this tasks in groups. The groups are composed of students with different abilities and levels.

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Students can also create a visual of their number sentence. They can complete the activity using whiteboards or chart paper that can later be shared with the class.

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Students can complete the task in different workstations where each station has a variation of the activity. For example, one station will have quarters or loonies and at each station there will a different amount of coins.

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At each workstation, students have a certain amount of time to determine how many different ways they can make 5. This could make it more challenging and more fun for the students.

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-Allow student to choose groups or partners whom they want to work with.
-Students can also choose to work independently.
--Teacher can put various manipulatives across the classroom at different stations.
-Students can switch to different stations, to explore different activities (worksheets, tan gram, ten frames, coins, colored counters, dice etc.)
- The physical classroom environment should be comfortable, where students can move around easily and access resources necessary for their learning process.

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Teachers can demonstrate the process by putting coins in a cup, shaking the cup and emptying out the coins onto a flat surface to count them.
-Now students can be divided into small groups, and be given the liberty to count, repeating what the teacher previously demonstrated, or student can use different manupulatives .
-Students can have multiple opportunities to learn how to count.
-Allow students to explore different ways to count to five or more.

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-Different expectations for students can be set by teachers according to the student's needs.
- Allow students to share their thinking in various formats.
- Visual learners can draw and show their learning.
- Students who are comfortable in writing numbers and sentences can display their learning progress.
-Teachers can record students' oral answers, which can be used for further assessment.

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- Use different math manipulatives according to the student's needs.
- Students can use 10 frames with coins, or coins of two different colours, representing heads and tails.
-Challenge students to try various combinations of making groups of fives, tens, fifteens, etc. using colored coins.
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- provide choices for students to work with a partner or independently, allow them to change their choice if they have realize upon reflection their first choice is not working for them.
- designate areas in the room for partners and independent workers, so that students seeking a quieter work area can find one.
- easy access to other learning tools for students who would prefer to change the tool from coins

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- to build on my comment for process, allow students to use a tool of their choice to explore and represent all the way to make 5
- then have the class participate in a gallery walk, students who wish to orally share their findings may choose to do so, others may wish to record their findings by labelling their representations with number sentences.

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- intro activity and allow students to explore
- once they have explored with the coins allow students to select a tool they are comfortable with (snap cubes, coloured tiles etc ) to continue the activity, exploring and representing the various ways they could make 5
- teacher is prepared with task adaptations to support students readiness

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- challenge extension: change number of coins used (e.g., 10, 15)
- challenge accommodation: counting to 5, or larger number of coins but focus remains on counting the set
- allow students to use coloured circles instead of coins and represent the various combinations on ten frames for further visual support whether goal remains as make 5 or 10 etc.

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Teacher may create various learning centres , such as activities with coins, dices, and playing cards for the same Math lesson, so that students’ needs, interest, and readiness are met.

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Rosa Tarulli
Different expectations of process and of outcomes might be set by the teacher for students with special needs to recieve better quality results per student.

The number expectation  of number sentences created could be reduced for students with attention difficulties.

Some students who may struggle with sound sensitivity  may be given the opportuntity to work in a quiet space alone to improve concentration.

If there are texture sensitivites a student may be able to use drawings to demonstrate grouping without the expectation of  touching manipulatives.

Students with motor difficulties could be provided an alternative method to demonstrate their learning rather than writting or drawing groupings and number sentences.  They could be provided with computer software to dictate or type their solutions to the problem.

Students who mastered the activity early, could be provided with a "challenge"  opportunity to think about how groups of various numbers can be show a relationship between addition and multiplication opperations, using number sentences.

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The teacher could arrange the room   for mobility or with a path marked with arrows.  Student pairs or small groups, could be asked to move around  at timed intervals.  They would address the problem at various stations with counters or coins of varying difficulty at each station, with a variance of the problem to solve each time.  The small groups would be vaired so students of vairous visual, auditory, or kinestetic capabilites would be grouped together to share ideas and colaborate their strenghts to solve the problem.

Alternatively, the rooom could be set up for a jig saw activity where an expert group would spend the most time at one station, solving the problem.  Later a secondary grouping of "experts" would be grouped together to describe their learning at the expert stations to members of a mixed group.  Students could be provided with a template document where they could record one example of each mixed group contribution.
In both senarios, the teacher facilitator would float around the groups providing assistance.  As well, he or she would consolidate the learning in a large group discussion where important learning could be accuately summarized verbally and visually.

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As a mind set activity, the teacher might play a video on the concept grouping whether as an introduction or review.
Students might then be asked to considers all the ways they can group different thing in daily life that they can think of by using a think pair share strategy. They would then come back to the large group to discuss these groupings and how they might be useful.
Rather than just shaking the cup for  students and asking them to make 5 the teacher could model one turn and demonstrate ways to record the outcome.  The Teacher would then turn the activity over to the students.

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Assist students with difficulties with prompts and give positive reinforcement. I would also put them in a small group with different strengths, then they can benefit from other kids.

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Rosa Tarulli - A different set of manipulatives could be used to address the problem to vary difficulty.  Individulas may be given coloured counters without values to group various ways to make five.  Alternatively, more types of coins could be included, such as dimes and pennies to included ways to make five out of mixed coin values.  

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Rosa Tarulli - A different set of manipulatives could be used to address the problem to vary difficulty.  Individulas may be given coloured counters without values to group various ways to make five.  Alternatively, more types of coins could be included, such as dimes and pennies to included ways to make five out of mixed coin values.  

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I would challenge the high students by giving challenging content such as 2 coins of nickels and 2 coins of dimes. Students need to find all the combinations possible.

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Some students are ready to use sentences to describe their work. I mean, they will present their ideas visually and vocally

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Having different "station" setups is one way to differentiate a lesson. In small groups students can physically circulate the room, completing a different step each way. At first they use counters and draw diagrams, then they write number sentences, then they complete practice using tech, or using dry erase boards. These are different ways for students to interact with numeracy. The teacher can even setup at one station as a check in to assess understanding.

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Varying the manipulative and tools used. Provide additional tangible items the students and display their findings, such as counting cubes, tiles, real coins or even use the smart board money tools so they can drag and drop the coins or write while they count.

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Most students could write out number sentences and also represent their arithmetic using diagrams. Some students would benefit from a demonstration in a small group. Student with fine motor skill difficulties sometimes cannot write their math expressions. It is important to check in on these students and have them verbally explain their thinking in small groups.

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The product should be displayed or given in the format the student is comfortable with. Drawing back to the videos we watched earlier about math learners, the teacher created an open discussion forum in her classroom, allowing students to freely share thoughts. This allowed students to contribute their findings in ways they are comfortable, therefore some may draw their findings, others may use mathematical tools and symbols, some may require manipulative to display their work while others can verbal provide an answer. The teacher can document their answers in anecdotal notes.

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Allowing various stations that incorporate a different way of counting. Giving the students free choice to walk around discuss with the different students and pick a station they are most comfortable with. One station can have tangible coins, another can have virtual coins. Another example is providing paper and writing supplies and allowing students to write down or draw their questions or findings.

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Instead of using nickels perhaps use counters.  Students may be confused by the number 5 on the nickel itself, and use them to count to 25. If there are blank counters used, it may make more sense to students unfamiliar with money.

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In order to explain the process of this game, it would be important to have differentiated explanations. For example, teachers may have a video of the game, have a song that is easy to remember that has the rules within it, have pictures showing step by step of what is required or in person demonstrations of the task.

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Using visual aids and physical resources within the classroom that students can use to help them count. The math rack that was discussed in the brownie dilemma is a good example of something that very visually depicts the different groupings of numbers.

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Creating a learning environment that is comfortable and accessible for all learners. For example, pillows on the floor for areas to sit, couches. As well as development a positive work environment from the very beginning, where students feel comfortable being wrong and making mistakes and asking questions.

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Setting up different stations that students can either freely walk around and join an activity. Set up a timer so they are aware of how much time they have and can then move onto something else to ensure they try different activities

Have a quiet table with worksheets (such as ten frames or playdough) and students can work independently or with a partner

Have a corner with math books or Ipads with math books or math apps that show additions facts for audio/visual students

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Using pictures to show groupings of 5 in circles and how they made 5

Using number sentences to show their thinking (ie. 4 +1 is the same as 1+4)

Using charts or ten frames to organize their thinking

Think-pair-share with a partner to discuss what they see and learn to share during whole class discussion

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Set up stations with different activities that groups can rotate through. Examples: Using cubes and drawing a small circle on paper, students roll the cubes onto the circle and see how many land in and out of the circle and to draw what they see on a chart labelled in and out. A bowling station where students knock down pins of a specific number and see how many are left. Chart paper mat with number sentences of 5 and using two different colored bingo dabbers to show the number sentence (ie. 3 red dots and 2 blue dots)

Small group discussion with teacher: using two colored chips and giving each kid a different amount and asking how many more they need to get to 5 and giving it to them in a different colour.

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Using a video to explain the content (concept) such as Jack Hartmaan I Can Say My Number Pair 5 (done through visual and song).

Using different sums depending on students ability

Providing a whole class example prior to exploration to explain number pairs and how to find different ways to make a number using 3 or 4 using their hands and showing how to draw groupings and number sentences beforehand

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The task was very specific for students to write a number expression to describe how many ways they found 5. A way to differentiate this activity would be to given them options/space to demonstrate their learning such:
- word sentences (ie 3 and 2 make 5, rather than 3 + 2= 5)
- orally communicate to the teacher and the teacher scribe
- take pictures with an ipad and either write their thoughts or voice over the pictures
- share their learning with a peer
- draw how many ways they've made 5
- and of course, if the student would benefit from finding ways to make a bigger or smaller number , depending on their needs, then that option should be be given to show their final product.

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Rather than coins, have students use other types of materials to make number with. For example: a 10 frame, coloured counters, dice etc. This will allow children to choose which material they feel most comfortable using and perhaps will be more socially relevant to their learning needs.

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Provide the option: students are encouraged to do the nickel activity, but provide at least one other "how many ways can we make five" activity (for example, provide 5 connecting cubes and ask students to connect them into as many possible PAIRS of shapes as they can, in order to answer the question), and also provide the option, for ambitious students, to figure out a way to answer the question themselves, and to then report back with their findings.

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Provide flexibility in regards to how students present their findings. Provide some options, and then also an open choice: as long as their message is communicated clearly. For example: You could... a) Create a chart showing all the math statements you've discovered that add up to 5, b) draw a picture showing the different combinations of heads and tails you've discovered which have all added up to 5, c) explain what your answer is in writing, and how you know it's true, d) other (your choice).

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You could differentiate for learning environment by setting up different 'counting stations' throughout the room. At most table groups, students are figuring out all the ways you could make 5. At a few table groups, students may be working with smaller or greater numbers. Students can choose which table group to work at, based on how well they handle working in smaller or larger groups; students can also choose table groups based on the level of difficulty they need (students will seek challenges they can handle, will avoid tasks that are too easy because it will bore them).

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Teacher can make comfortable students by permitting them  they can  join the group  by themselves but have the same number of students. Appreciate and  motivate
them by verbal and non verbal language and make them comfortable.

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Children make three types of piles- big, small and medium and a  group can make more than one pile. If a teacher find some students uncomfortable then those Students can be provided some other material for counting numbers like the number games or chess.

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Having making different groups of students like 4-5 give them 50 coins to each group .

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Students are supposed to make piles according to their own skill but coin shouldn't fall mean fallen one shouldn't be counted.A teacher can guide slow learner students to make smaller piles like with 10-15 coins pile. Even a teacher can sit with them for a short period to guide them how to balance the pile.

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For different students at different levels, they may be given the same activity with more complex numbers (eg. 10 coins). They could also be asked to predict combinations before testing to see if they are right.

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Have different stations set up all demonstrating the concept in a different way. Students will make their way around the room. One station they might use the coins, at another station they might have to sort 5 objects into different sized groups, one station might have them using manipulatives like counters, etc.

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-Students could be asked to present their findings in a way of their choice (drawing, writing words, writing numbers, explaining orally, etc.). Use of an exit card is a possibility for formative assessment.
-Students could be asked to create a new game based on the same principles, and give it to a friend to try.

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Give students choice in their environment. Set up quiet zones, areas for individual work, areas for partner work, and areas for larger group work.

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Have multiple learning tools provided. Include flexible pacing and use graphic organizers to jot down process.

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Students can share what they know with an elbow partner using "Think - Pair - Share" and then share with the whole class during carpet time

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Differentiate content by using various delivery formats - such as visual, auditory (music). Teacher can explain the task in a variety of delivery formats.

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Create flexible groupings such as rotating stations - have the same activity at each station but with different manipulatives. Students will rotate from one station to the other and try the coin activity with different objects such as lego, or dominoes, or playdough etc.

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Students work together to solve the problem in different ways 

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Students work together to solve the problem in different ways 

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Provide different manipulatives for the students to use in the activity using different ways to count such as (cubes) instead of coins 

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Provide different manipulatives for the students to use in the activity using different ways to count such as (cubes) instead of coins 

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Having students work together and present their ideas on how they solved the problem

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Having students work together and present their ideas on how they solved the problem

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Having students apply their thinking to scenarios outside the classroom, not necessarily nickels but maybe even using people, so students can move around and visualize the work kinaesthetically.

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In order for students to demonstrate their understanding of the coin activity I could provide numerous ways students can choose to express their findings - writing it down, drawing it, presenting it, not necessarily in the form of a math sentence. Also, while students complete the activity I could circulate and note down their thought processes.

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Creating flexible seating in the classroom - some students may choose to stand, sit in a chair, sit on the floor in order to complete the coin activity. As well as giving students a choice of whether they would like to work individually, in pairs, or in groups.

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Allow students to work individually or in pairs.

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For students who have difficulty expressing their thinking in writing, have them explain their work while you record.

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To extend the activity, add more coins and have students find all the ways to get 7, 8, etc.

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Provide numbered cue cards to help students visualize how 5 has been made. They match cards to create the sum in various ways.

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Make sure turns are taken slowly, with lots of time to watch and count (ideally to support those who struggle with vision, but helps all students to process their thinking)

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To build off what has already been posted here:
- use (coloured) cotton balls for those who hate the sound of coins, dice, etc. rattling around in a can.  Kinesthetic learners would also benefit.
- can be done on tables, on the floor, out in the hallway, on a rug.

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Provide a variety of tools and manipulatives (counters, dominoes, dice, bingo dabbers, etc.)

Celebrate different ways of demonstrating thinking and learning

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Use your counters to represent your addends in your number sentence

Use dots to represent the number sentence

Talk about your work while I annotate

Record you talking about your work

Record you doing your work

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Use more distinctly different counters (i.e., red ones and blue ones instead of heads and tails)

Scaffold for writing with numbers provided on cards

Make 5 and 10 frames available

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Use different sums

Provide an invitation to leaning that demonstrates a way to get started

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- Offering activities that adhere to varying levels/complexities. Choose activities that can be adapted and have the modifications made beforehand - more complex numbers

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- Presenting ideas through audio or visual means

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- Small groups of students re-teaching ideas to class

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Students can draw different the nickels in different combinations to represent 5.

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Instead of writing a Math sentence students can maybe demonstrate multiple ways to get the same answer:
1 + 1 + 1 + 1 + 1 = 5

1+4=5

3+2=5

etc.

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Students can use other math aids instead of coins, such as counters, dice, marbles etc.

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You can do the same activity at different tables with different coins and students can rotate partners

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Students can sit with different students at a table group and help each other solve it

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Write one suggestion on each post.  Add your name on each post.

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Write one suggestion on each post.  Add your name on each post.