Differentiated Formative Assessments

Differentiated Formative Assessments

Do some of your students finish early while others struggle to start the problem? If you’re a teacher then the answer is probably, YES!

We have teamed up with some of our teacher partners to help support teachers with the age old task of differentiation. We co-designed formative assessments to support learners of any pace. Look for the tag #differentiated to find these assessments. They incorporate language supports, bonus problems and hints. Best of all, there are custom legends to identify if a student is emerging, demonstrating or exceeding in their fluency of a standard.

Sometimes students struggle to answer math problems because of the language demands, not the math content. We don’t want these students to miss out. We also want to make sure they can participate in doing the classroom math. This is where language supports and sentence starters come in. If a task asks students to explain their thinking, a sentence starter will help get them going on the mathematically juicy part of the sentence without having to worry about all of the writing demands.

tap an image prompt

– Tap an Image Prompt –

For the above task, students need to identify where on the line represents the greatest velocity and then explain their thinking. Some students will have trouble getting started with the writing so we included some sentence starters in the scratchpad.
sentence starters

– Sentence Starters –

Now, students can focus on the mathematics without getting bogged down in the writing. If you have learners who don’t need the sentence starters, encourage them start their sentences in other ways.

In addition to the challenge of writing, assessments can contain new vocabulary that trip students up. For example, a student may forget what velocity means. With the language support below, they get a gentle reminder that lets them focus on relating the graph to the motion of an object. This makes the assessment about the math instead of their vocabulary.

– Velocity Language Supports –

As the teacher, you can remove any of these supports that don’t fit your class. Simply go to scratchpad settings and tap the text box , then press the orange x. Remember to click “save” when you are done.

While some need extra support, other students will be ready to demonstrate mastery of the standard.  Thus, #differentiated polls have bonus problems in select tasks. Bonus problems in the scratchpad relate to similar content to the original task. For example, the tap an image task from above has the following bonus problem.

Example of a Bonus Prompt
– An Example Bonus Problem –

The bonus problem above goes beyond the comparative nature of the task. It asks students to find the slope of the line when it has the greatest velocity.

Bonus problems also work to assess if students understand the greater context of the problem. Reviewing answers and student responses can ignite productive discussion for everyone. For example, a different bonus problem asks students to write a story, including units, that corresponds to the graph.

– Write a Story Bonus Problem –

The discussion about the responses to this bonus problem will be informative to everyone.  On the next task, all students are asked to pick between potential stories for a similar graph.

distance from home problem
– Distance From Home Problem –

Hearing their peers share how stories connect to the previous graph makes the pathway for success more clear to all students. Search #differentiated in the explore content tab or follow one of the links below to get started with differentiated tasks. Or create your own! 

Visit our page on Formative Assessment for more on how to use these strategies in your classroom.

Share on twitter
Share on facebook
Share on linkedin

New Feature: Active Learning Through Student Volunteers

New Feature: Active Learning Through Student Volunteers

Woot Math has a new feature to help you promote active learning during formative assessment activities in your classroom. You might be thinking, “Wait...doesn’t Woot Math already do that?”. That’s right. Students have always been able to show their work during formative assessments. Now, they can also volunteer to present their work or have the teacher use their work as an exemplar.

Ask for Volunteers

Student work is always saved when running a formative assessment. After students complete the task, in teacher-led mode teachers can review examples of anonymous student work in real-time with the class. Now, the teacher can also ask for volunteers by clicking on the volunteers tab. Once they do, students can now volunteer to share their work with the class.

Students can volunteer

– Students Can Volunteer to Show Their Work –

Select High Quality Student Work

Once students have volunteered, the teacher sees tiles from each of the student volunteers. The teacher can then determine which student volunteer they want to project by simply clicking on the tile.

Teacher sees a list work from student volunteers

– Teacher Sees Work From Student Volunteers –

For this problem, Joelle and Aaron have volunteered their solutions. The green check box indicates that they both have the correct answer. The teacher can turn off revealing the correct answer by deselecting “reveal answer”. Sometimes it is helpful to project student work without the answer revealed – students can then use critical thinking and analytical skills when they have to justify their responses before being told if they are correct.

Promote Active Learning: Have Students Present Their Work

To promote active learning, the teacher can select one of the volunteers to explain their solution. In this case, it appears that Joelle has shown more extensive work than Aaron. Work for this blog post comes from the activity called Pythagoras’ Park. Students apply their understanding of the Pythagorean Theorem to story problems about walking through a park. Check it out here.
Students engage in active learning through presenting their work and solutions

– Projected Volunteer Student's Worked Solution –

We see that Joelle has used the Pythagorean Theorem to solve the question. She also remembered to find the positive and negative solutions to 25=c². This attention to detail makes it a great opportunity for active learning. Joelle can present her thinking to the class while other students can learn from her example. Of course, the teacher can also use this feature to present students’ work on their behalf.

This is a great feature to try out if you are looking to get your students more engaged in active learning. You can also use this feature to encourage students to take risks. Reassure them that it is good to share their thinking, even if they aren’t 100% correct yet.

We recommend you check out the Pythagoras’ Park activity as a review of they Pythagorean Theorem. It would also work well as a quick refresher for students who have already learned it! Previewing the activity now using the link below. Or, login to wootmath.com and search for “Pythagoras” in the Shared Gallery.

Preview Pythagoreas’ Park

Visit our page on Formative Assessment for more on how to use this free tool in your classroom.

Share on twitter
Share on facebook
Share on linkedin

Scratchpad Tutorial: Assess Student Work

This week we talk about a fun new activity that walks you through the features of the scratchpad. This activity orients students to some of the great features of Woot Math for Formative Assessment. Showing your work is important in math and so is formative assessment. With Woot Math you collect and assess student work it digitally saving you time and getting them doing great work! 

It covers content up through fractions, computing radicals, knowing what pi is and computing exponents, all of which is normally covered by 8th grade, sometimes sooner. So if your students haven’t encountered them yet you can make a quick alteration to the activity and it should work for earlier middle-school students.

The first task asks students if the table feature can auto populate results (it can) and then to show their work. This little known feature of the scratchpad can be very helpful for students in using tables to support their work. If the first column has a variable (any letter) and the second column is an expression with that variable, it will automatically compute the values for you. Below is an example of some great work from a student on this task that you can access from the bookmarks tab:

– Task 1: Example of Great Work –

The next task asks students to write an equation on the scratchpad and then select how challenging they found it. The equation intentionally has all of the different components of the expression editor so they get practice with exponents, radicals, rational expressions and pi (typing pi and then space-bar gives you 𝝅).

– Task 2: Writing an Equation on the Scratchpad –

The results to this task will give you student responses to the multiple choice question but the custom legend is coded to see if they got the question right or not. Anyone coded purple wrote the correct equation on their scratchpad. The custom legend allows you to assess student work on the scratchpad as well as their responses. This gives you even more choices for how to design rich assessments.

Task 3 has the students tap on the mistake in the projected problem and then solve it correctly in the scratchpad. This gives the students the choice of using the drawing tool, the text tool or the expression editor.

– Task 3: Tap the Mistake –

We recommend you suggest the text or expression editor if students are using a mouse or touchpad. For tablets, the drawing tool can be an efficient way to show your work.

The fourth and final task has students use the calculator on the scratchpad to compute the value of an expression. If students are having trouble with the calculator, encourage them to try the arrow keys on the calculator (or keyboard) to get the fractions to show up in different places. Parentheses also help if you are unsure about order of operations.

– Task 4: Scratchpad Calculator –

A fun tip: students can type s to write a square root, ^ to make an exponent, / to make a fraction and pi to make 𝝅. These notes are also in the scratchpad of this task as a support for students. Also, for a fun extension problem, you can ask them what other shortcuts they can find.

Analyzing student work lets you learn how students think about solving math problems. Having them show their work with these tools will help you learn how they are thinking and help you better conduct formative assessment.

Get started by previewing the activity right now, or login to wootmath.com and search for Scratchpad Tutorial in the Shared Gallery.

Preview the Activity

Visit our page on Formative Assessment for more information on implementing these strategies in your classroom.

Stay tuned for next week’s post!

Math Misconceptions and Productive Discourse

Assessing Math Misconceptions

The first problem is a tap-on-the-mistake type. Students need to analyze the projected procedure and find the mistake (if there is one). Recognizing math misconceptions is a great exercise. 

Task 1 - Tap on the Mistake

– Task 1: Tap on the Mistake –

With tasks like this, everyone has the opportunity to do productive mathematics. If a student don’t know how to solve an inequality or where to start, they can evaluate the projected work. Everyone gets to apply their prior understandings of mathematics to this problem.
 
The fact is, your students might not catch this mistake. It is a subtle and often forgotten rule that dividing or multiplying an inequality by a negative requires flipping the inequality. If your students ask why this rule is true, you can tell them to think of it as multiplying each side by -1 and then dividing each side by 4. Inequalities are like unbalanced scales. One side is heavier than the other. When you multiply each side by -1, you are changing all negatives to positives and all positives to negatives, this means the scale will reverse. If one side weighed 10lbs and the other weighted 2 lbs the side with 10lbs is lower. Multiplying each side by -1 means the low side now weighs -10lbs (think of it as 10lbs worth of upward force from balloons). The other side is now -2lbs. 10lbs up will pull more than 2lbs so the side with 10lbs up is now higher. The scale has flipped so the inequality needs to flip.

Discussions about Math Misconceptions

Some of your students will likely choose the correct answer, and some will likely “choose no mistake was made. Now is when the sneaky and magical power of Woot Math shines! Deselect the reveal answer button to reveal student responses as a heatmap without revealing who was correct.

– Uncheck Reveal Answer–

Some of your students might no think there is an answer, some (hopefully) got it right, and some may have chosen another place in the work. Those who got it wrong may have been guessing or may be going off of a juicy misconception… aka: a productive learning moment. For more on the value of learning from mistakes, check out Woot Math’s CEO, Krista Marks, Ed Surge article on Aha moments.

After you click show results, your heatmap might look a little something like this:

Task 1: Heatmap of Student Responses

– Task 1: Heatmap of Student Responses –

Small Group Discussions

This is a great opportunity for students to discuss the problem, either as a whole class or in small groups. You can ask the students to come to a consensus as a group. This is where another one of our favorite features comes in handy. With the “assign groups” button, Woot Math automatically groups of 2-6 students. You can choose to generate these groups based on if they put the same answer (homogeneous), a different answer (heterogeneous) or at random
Automatic Student Grouping

– Student Grouping –

With heterogeneous grouping by answer, each group should have someone who got it right (as long as you have enough students getting it right). Now, each of the groups is set up for success. Woot!

Get started by previewing the activity right now with the link below. Or, login to wootmath.com and search for Warm Up: Modeling with Linear Systems in the Shared Gallery.

Visit our page on formative assessment for more on how to use these strategies in your classroom.