Lesson 2: Making the Best Playdough

Setup

The tables and partners are set up as they were for Lesson 1, with table coverings and all necessary materials including the recipe for green playdough and for yellow playdough. 

Narrative

[not given yet] 

Launch (narrative could include comments on timing)

Students will have time in pairs to follow two more recipes. This time, in addition to practicing counting with one-to-one correspondence and counting on, they will also be thinking about and practicing attending to precision while measuring with tablespoons. 

Task Statement

Having practices and learned about careful measuring yesterday we are ready to make two more batches of playdough. We’ll use the same procedures with partners taking turns being the scooper and the other being the reader/counter. Today we’ll also practice using our finger to level off the Tablespoons when we need to.  

When we’re done making our yellow and green playdough, we’re going to try to figure what might make a recipe better or worse.  All of our recipe used the same four ingredients, and they all started with 16 Tablespoons flour. But they use different amounts of oil, water and salt. So while you’re making your playdough batches today, attend to precision and think about whether the number of spoonfuls of an ingredient makes a difference and if so, how?  Once you’ve completed a batch, knead it thoroughly. Then make the next batch. 

Orchestrating and Monitoring (narrative could include comments on timing)

While students work, the teacher should circulate and take anecdotal records and digital photos of students at work.  It is anticipated that students should be able to work fairly independently.  

If you notice pairs who are not working well together, redirect them toward the goal of the lesson, reminding them about the need for careful counting and attending to precision.  

Discussion (could be synthesis; narrative could include comments on timing) 

After all pairs have completed both new batches, students should discuss the following: 

• How the making process worked in these batches compared to the previous day’s attempt
• Whether students think one recipe is better or not, and if so, in what ways
• Whether they think the recipes have more wet or more dry spoonfuls
• Ideas for how they could compare the two recipes

Anticipated Solutions

Students will create their two new batches of playdough more successfully and with far less variation from pair to pair than in the previous day.  That is to say, students are more carefully attending to aspects of precision and are using mathematical tools in better ways. 

Anticipated Misconceptions and Challenges

No mathematical misconceptions expected.  Some students may still struggle with one-to-one correspondence.  This only improves with time and practice, and so the lesson is serving its purpose, even if students’ batches aren’t ideal.  

Images for Classroom Use 

Green Playdough Recipe

• 16T Flour
• 6T Water
• 1T Oil
• 4T Salt
• 6 Drops of green food coloring

Yellow Playdough Recipe

• 16T Flour
• 5T Water
• 2T Oil
• 6T Salt
• 6 Drops of yellow food coloring

Setup

Because tables are still messy from playdough making and students will return to that for Activity 3, this is best done away from the tables with clipboards. Each pair needs a set of linking cubes (2 colors, total about 40) and a Data Calculation sheet for one of the recipes. (If there are three pairs per table, use a second copy of either the yellow or green recipe.) 

Narrative 

Students will use linker cubes to represent the number of Tablespoons they used. Each team at the table will compute for a different color playdough recipe.  They will: 

• building a tower to represent each ingredient (e.g., 16 cubes tall = 16 T flour). 
• Students will use towers to help them determine the total number of wet and dry Tablespoons
• Students will confirm their calculations by practicing counting on from the highest number.  
• Students will then compute the total number of tablespoons of ingredients used in their recipe by counting the total number of cubes and by taking the larger number (dry) and counting on from there and adding the number or wet tablespoonsful.  

Table groups will then compare their results, using language such as more than, less than, and the same as to talk about their quantities. The activity concludes with a whole class discussion about comparing quantities, what they think the wet and dry ingredients do.  They are also likely to contemplate the role of warm water and oil in the texture of the playdough.

Launch (narrative could include comments on timing)

Students analyze the recipes of the green and yellow playdough, determining and comparing the quantity of wet and dry ingredients.  They may also determine the quantity and compare total spoonfuls for a recipe. As a whole group, they will discuss their counting strategies and the quantities they found.  This conversation provides an opportunity to practice describing quantities as more than and less than other quantities. During this conversation they should also discuss what makes playdough “good”?  They should practice trying to describe the textures they like and discuss the impact of each of the four ingredients. What does water, or flour, or salt or oil contribute to the texture? What would happen if we added more water?  Or more salt?    

Task Statement

Your table group needs to analyze our recipes to find out how many spoonfuls of our wet ingredients, how many spoonfuls of our dry ingredients we used in our recipes.  Then you’ll use that to figure out how many spoonfuls in all were in each recipe used all together. We want to think about these quantities so we can figure out what makes “good playdough” and think about if we think that one recipe was better than another.  If we can figure that out, we can use our ideas about ingredients to try to make our Blue playdough better. We want to be able to easily compare our quantities. These Data Calculation sheets will help us organize the numbers to help us think about them. Your job is to do some big number thinking to find some totals we can compare.  Each pair from the table will analyze one recipe and then you’ll talk together about your result. After that we’ll talk as a whole group about what we’ve discovered.

Orchestrating and Monitoring (narrative could include comments on timing) 

While students work, monitor them for on task work.  It should take about 5 minutes for groups to complete their sheet. Eavesdrop for students who are using phrases including more than, less than, and are counting on from a number rather than going back to the beginning and counting all. If students are “counting on” see if they are strategically counting on from the bigger number or just the first one they encounter.  

When pairs seem to be done, encourage them to check their results with another pair that worked on their same recipe and resolve any discrepancies.  Once students have checked their results, they should work with their tablemates (or another pair who did the other recipe) to compare results before the group discussion. 

It is tempting to ask questions of groups to see what they’re thinking.  However, doing so could slow down their progress or impede their thinking. It is not a time for evaluation.  Rather, focus on trying to observe out the following: How are students figuring out the total. Are they “counting on” or “counting all.” Are they accurate in counting numbers beyond 10?  Did they need to use the same color to represent a single ingredient, or not. Are they able to use one-to-one correspondence when counting with a partner? 

Discussion (could be synthesis; narrative could include comments on timing) 

Students should bring their data sheets and all three bags of playdough with them to the discussion.  As students begin to discuss their results, record findings on the whiteboard for reference during the conversation. (See anticipated solutions). The discussion should take about 5 minutes. 

Discussion flow: 

• Focus the discussion initially on helping student practice making more than, less than, and equals observations.  
• Based on what their analysis, discuss characteristic of the playdough and what makes some batches better than others.  Help them hypothesize what the different ingredients add to the texture and why a recipe worked better or worse than another. Focus on works like smooth, powdery, sticky,… and see if these can be connected with specific ingredients.  
• Have students select their worst batch (probably blue) and discuss with their partner whether they want to make it wetter or dryer, and then which ingredient they want to add.  Then they should predict how many spoonfuls with make it better.  

Anticipated Misconceptions and Challenges

It is anticipated that some students will struggle to count on, rather than counting all. This conception develops over time.  If students have not fully developed this skill, this provides an opportunity for them to practice. It is worth some time to allow students to count and recount to ensure they have counted properly.  

Images for Classroom Use

Green Dry

• 16 Tablespoons Flour
• 2 Tablespoons Salt
• Total Dry: ____ tablespoons

Green Wet

• 4 Tablespoons Water
• 2 Tablespoons Oil
• Total Wet: ____ tablespoons

Green total

• Wet + Dry = _______ tablespoons

Yellow Dry

• 16 Tablespoons Flour
• 4 Tablespoons Salt
• Total Dry: _____ tablespoons

Yellow Wet

• 6 Tablespoons Water
• 1 Tablespoon Oil
• Total Wet: _____ tablespoons

Yellow Total

• Wet + Dry = ________ tablespoons

Student Online Materials (will be links for teacher to post) 

Setup

Students return to their table with their worst batch. The ingredients are already set up and ready for use. 

Narrative

The purpose of this activity is to use the knowledge gained throughout the cycle to improve one batch of playdough strategically.  

Launch (narrative could include comments on timing)

Students will decide one ingredient they will add to improve their worst playdough.  They will estimate how many Tablespoons the improvement will require. They will predict and then count out and iteratively knead their playdough to make it as good as possible.  Note, some playdough batches will never become great, and it is also possible to add too many spoonfuls and pass the point of good playdough.  

Task Statement

With your partner decide on one ingredient only that you will add to help your worst batch of playdough.  Then make an estimate for how many Tablespoons you’ll add of that ingredient based on your experiences so far. Record your ingredient and your estimate on your Estimate and Record sheet.  Then using just that one ingredient, carefully measure and count spoonfuls, tallying as you go. It is helpful to knead the dough after every 2 or 3 spoonfuls to see if you need more. Then when you’re done, record your final number of spoonfuls.  Note, if it is starting to get too wet or too dry, stop adding spoonfuls.  

Orchestrating and Monitoring (narrative could include comments on timing) 

While students work, observe their conversations.  Listen for hypotheses about ingredients as well as language for comparing quantities and measurements (e.g., more, less, same as, equal…) Observe tallying/counting one-to-one correspondence.  Take digital photos. 

Discussion (could be synthesis; narrative could include comments on timing) 

(no separate discussion for this activity) 

Anticipated Solutions

Most but not all pairs will improve their worst playdough.  In a few cases, students will add too many Tablespoons of their chosen ingredient, going past the stage they are hoping for. 

Anticipated Misconceptions and Challenges

For groups that aren’t successful in making the batch better, be prepared with questions just as, “why do you think it didn’t work as well as you predicted it would?”  “If you were going to do it again, what would you do differently?”  

Images for Classroom Use (maybe links?)

Student Online Materials (will be links for teacher to post) 

Lesson synthesis (conceptual, maker ideas, math content, generative--set stage for next lesson) including learning cycle wrap up. Time estimate: 5-10 minutes

Conclude the lesson with a whole class discussion in which the students talk about what they learned.  Prompts may include: 

• What did you learn about measuring?
• What did you learn about attending to precision?
• How did your estimates compare with your actual number of spoonfuls in your revised playdough?  How did your results come out? What would you do differently? 
• How did you handle counting larger numbers?  What strategies did you get to practice? 
• How did you and your partner work together? 
• What did you learn about playdough and how to make it? 

This is also a time when the teacher can share his/her observations about what students were doing and how they were improving.  Highlights might include projecting digital photos of students while they worked, showing better measuring techniques, counting strategies observed, use of comparison language, recording numbers, etc.  

Highlight for students how the lesson cycle helped them learn a few new things and get better at (practice) many things they had done before.  

Highlight their growth in important mathematical practices.  

Ask students how making playdough connects with other things they like to make, and reflect upon the process of revising something that you’ve made that didn’t turn out well.  

Wrap up the cycle by letting students know that you will share the recipes with them and their family (e.g., in the class newsletter or website) and that they can make more at home and teach their families how to make playdough using 4 simple ingredients.