## 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).

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.

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

Stay tuned for next week’s post!

## 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 –

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.

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.

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:

## 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

## – 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.