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  • Jon Orr

    May 1, 2019 at 11:59 am

    Choose a lesson from our curated list or choose another task and use the Anticipating template to anticipate what your students will do to solve the problem.

    As a bonus you can use the Making Math Moments That matter planner to anticipate.

    Share your thoughts, questions, and comments here.

  • John Gaspari

    February 20, 2021 at 8:37 pm
  • John Gaspari

    February 20, 2021 at 8:41 pm
    • Kyle Pearce

      February 21, 2021 at 6:36 am

      I love the progression here!

      I’m wondering about a concrete manipulative solution. Might students consider using snapping cubes or similar for this problem especially if they’re new to volume?

      • John Gaspari

        March 21, 2021 at 9:22 pm

        Thanks for the suggestion. I’ll try to have snap cubes available when I do this lesson.

  • Jody Soehner

    February 28, 2021 at 3:31 pm

    I really like the solar panel task and chose to look at that one. I introduce ratio tables, double number lines and arrays as tools to use in various contexts so feel most of those will be go to tools. I have not had students use arrays for large numbers so am curious if any will use that strategy. We have already done some algebra with 2 2 steps so that is a possibility. Unit rate has not been addressed this year so this is an excellent time for a student to explore and find that strategy.

    • Kyle Pearce

      March 1, 2021 at 6:38 am

      fantastic! Let us know how it goes. Did things go as planned? What didn’t? What worked well? What would you change next time?

  • Scott McNutt

    March 2, 2021 at 8:34 pm

    I do want to thank you for the many resources that you are sharing through this workshop. Your lesson planner is exactly what I am looking for to help guide me with planning the problem-based lesson.

    Looking at the corner to corner for my lesson of choice, I will be uncovering the Pythagorean Theorem towards the end of March with my 7th-grade group. Knowing my 7th graders, they are very visual and will try to draw out the problem. So my anticipation has a lot of drawing.

    Strategy 1: Best guess by knowing that the string should be longer than the measures of 9.1, 9.3, and 3.2. I will probably guess with their understanding of triangles somewhere between 10 to 20 meters. At this time, I would challenge them to draw a scale drawing of the triangle using the dimensions they are guessing.

    Strategy 2: I can see a scale drawing of the birds-eye view of the 9.1 x 9.3 m room to use the scale to measure the diagonal of the room. And use that height with the 3.2 m to create another scale drawing to find the length of the string from one corner to the other.

    Strategy 3: At this point, we have gone through triangle inequalities for right, obtuse, and acute triangles. Students may notice the pattern with the right triangle and begin working on the Pythagorean theorem (But would not be explicitly taught to them yet)

    This is a challenging one because I know I want to withhold information, but I do not see an efficient way to approach this corner to corner without using the Pythagorean theorem. I will use a fantastic problem in my classroom, but I think there would have to be some previous experience with a square plus b square is equal to c square.

    • Kyle Pearce

      March 3, 2021 at 6:43 am

      Pythagorean is a tough one as we don’t have the time to allow students a week to explore and completely emerge the idea. However, though estimating, students might be able to come close to approximating. Then, maybe have a few Pythagorean triple triangles and some tiles asking them to explore… then, ask purposeful questions as they explore to see what they come up with.

      Finally, you may need to “reveal” what he discovered.


    March 12, 2021 at 4:58 pm

    For a problem like when will the cars meet (the racing cars desmos activity that we will explore with cars going same speeds as well) I foresee students a lot of students guessing and checking. I will ask them how to record their thinking in a way to avoid making the same guess twice. I will ask them when they know they are right.

    I forsee some making a table (a three column or two seperate ones). I will ask them when they know they are right. I will ask them if they notice anything about the pattern in the table. I will ask them if they can be efficient after they finish or give them a problem where the answer is big and see if we can find a way to skip ahead in the prediction.

    • Jon Orr

      March 13, 2021 at 7:07 am

      Great anticipation here @david.diehl depending on your level some students will also determine the rates at which the cars are travelling and use that to aid them.

      You’ll want to plan which strategies you’d like to showcase first, second, and last. I usually try to have the last strategy the one I’d like them to use moving forward. If that strategy doesn’t come from them then that’s ok! You get to show it to them.

  • Laura Las Heras Ruiz

    April 20, 2021 at 4:23 am
    • Kyle Pearce

      April 20, 2021 at 6:18 am

      Very cool. I wonder if you’d be able to hold back those questions first a do a notice and wonder initially?

  • Jeremiah Barrett

    June 8, 2021 at 1:10 pm

    I chose to use Corner to Corner and anticipate student solutions. My template also includes an inaccurate solution that I anticipate students using. Some students will use the relationship between area of a triangle and rectangle to incorrectly predict the length of the diagonal.

  • Kathleen Bourne

    June 15, 2021 at 4:19 pm
  • Gerilyn Stolberg

    June 26, 2021 at 11:00 am

    I selected the Cover the Square task. I believe that my students would need to physically use the smaller squares to cover the large square. When given the triangle task I think some students would need to physically cut the square into triangles whereas others might already know that 2 triangles make a square and then just double the number for square (two fours is 8), some might add 2+2+2+2+2+2+2+2 to find the triangles and finally some might use 4 x 2 = 8.

    For the last task where they are given smaller squares- again I will have some student who will cover the entire square and count the squares, some students will cover one square and and then add that number 4 times, a final group later in the year might just find the area of the first square and then multiple that by 4.

  • Anthony Waslaske

    July 1, 2021 at 4:27 pm


    I solved it with a double number line, graphically, and through a table and equation.

  • Penny Johansson

    July 2, 2021 at 1:52 pm

    Grade 3: the Knotty Rope

    Anticipated Solutions:

    1. counting by 4s until the reach 44 (skip counting on a number line or counters)

    2. counting backwards from 44 by 4s on a number line or counters

    3. 4 goes into 40 10 times, then one one more knot to make 11 knots

    4. 44/4 =11

  • azuka ojini

    July 3, 2021 at 10:06 pm

    From the curated list, the Solar Panel task serves my purpose well. I noticed the steps taken to guide the lesson through making prediction, and the gradual release of information. However, clearly the multiple representations for solving this problem will help me to deliver the lesson.

    I suppose I could use the double number line as a guide to support the prior knowledge for generating a table of values and graphing the solution.

    • Jon Orr

      July 6, 2021 at 6:57 am

      We would also encourage the double number line as it is versatile and if you “tip it up” it turns into a ratio table.

  • Andrea Cadman

    July 6, 2021 at 11:04 am

    I came up with basically the same thing as Antony (above). It is likely that the majority of my students will work the problem the first way shown using the number lines, only I doubt the kids will show their work as organized/formally as it is shown. One of the things I am anticipating doing quite a bit is asking a lot of questions to guide the students in taking their work and using better organization methods such as tables, number lines, graphs, etc. So often, I find the students are heading in the right direction with their solutions, but their work is such a mess that they lose track of what is going on and end up not being able to complete the task. When this happens repeatedly, the students think they are not good at math when really they are just not good at organizing their thoughts and getting their ideas down in a way that makes sense.

  • Terri Bond

    July 10, 2021 at 5:21 pm

    For my fourth grade lesson, I am choosing the How Many Donuts Are in the Box? task. The standard is Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares up to 15 x 15. I can’t think of a better way to make them want to learn this standard than by looking at a huge box of doughnuts (donuts?)! I am anticipating that students will not only use different methods for solving, but they will use different numbers to multiply based on whether they “count” the covered donuts around the sides. I usually see a very wide variety of understanding within one class, so I’m trying to address all the solutions that I truly believe I would see.


    Some students will only consider the donuts that they see and leave off the ones that are covered, so for those students, I’m going to go with 23 x 13 because that’s about what I see in the clear plastic window.

    A solution that some students will use is to draw their own representation of the donut box, and then count them one by one. This would be students who have very little understanding of using multiplication. Some kids in this category might also circle groups of 10 or 20 in their drawing and then count the total.

    Some students might ask for manipulatives to work it out so that they can first build an array that looks like what they see, and then count them.

    Another possible solution would be repeated addition 23+23+23+23+23 = 115 (5 groups of 23) 23+23+23+23+23=115 (5 more groups of 23) 23+23+23= 69 (3 groups of 23) Finally add the partial products 115 + 115 + 69 for a product of 299. Some kids will make a column addition stack of 13 – 23’s or 23 – 13’s if they haven’t learned that they can group them together. These students would most likely make the most mistakes.

    Some students, who would use the same strategy as above, but consider the covered donuts would estimate 35 x 25. Repeated addition as above for a product of 875.

    Students may also use the area model / distributive property method that we call “box method” for partial products of 30 x 20 = 600, 30 x 5 = 150, 20 x 5 = 100, 5 x 5 = 25. Add the partial products in the boxes 600+150+100+25 = 875.

    Some students may use the standard algorithm to find a product of 875, or they may misuse it and get 625. (3×2 in the tens would give them a 6 in the tens place, and 5×5 in the ones place is 25, so they write that down in the “ones place.” This is the usual go-to method that kids use before the formal teaching of box method or standard algorithm.

    Some students will correctly use the standard algorithm to find 875.

    Other students will use the partial product method stacked up 600+100+150+25=875

    • This reply was modified 3 months, 1 week ago by  Terri Bond.
  • Lori Plate

    July 11, 2021 at 5:19 pm

    For this lesson, I chose the “Solar Panels” task on proportional reasoning. Since I teach 8th grade, I have anticipated that some of my more advanced students will use the cross-multiplication method for solving proportions.

    In 8th grade, we also use tables a lot to represent our data. Many of my students struggle with math and haven’t grasped tables yet, I have included an incorrect method that I think some of my students will come up with. I thought this would be a good way to have students figure out why it didn’t work.

  • Lisamarie Barnes

    July 13, 2021 at 4:47 pm

    First graders should have exposure to the terms more than, less than, and/or equal to. Therefore this activity will help me to evaluate their understanding and readiness to associate these terms into symbols.

  • Jon Orr

    July 14, 2021 at 6:59 am

    It’s great to see you all use such great representations. @lisamarie.barnes @lori.plate @terri.bond you’ll find the sheet will allow you to be super flexible in the classroom to see which students are using which representation.

  • Jennifer Maher

    July 14, 2021 at 4:52 pm

    From Classroom-Ready Rich Math Tasks, K-1

    Task# 56 – Bake Sale

    The Task has students partitioning shapes into halves and fourths. The culminating task asks students to create an argument about whether or not both square cakes have the same amount of white frosting. The goal is to realize that equal shares do not need to have the same shape, but the same area.

    The first image is the final task. The second image are my anticipated student representations of halves and fourths. The final image is my anticipated solutions to the final task.

  • Linda Andres

    July 25, 2021 at 1:46 pm

    From experience, I know that my students will come with many different levels of understanding patterning. I am not sure I understand this task well but appreciated the opportunity to think through possibilities and direction. I feel like I posted this but can’t find it on here so will try again.

    • This reply was modified 2 months, 3 weeks ago by  Linda Andres.
  • Betsy Lesley

    July 25, 2021 at 5:44 pm

    I explored the Solar Panels task, because I need to spend more time on proportions with my 7th graders. Based on their work last year, I know some students will build a table, some will jump right to a proportion and others will find the unit rate, then multiply. (Not realizing they are doing the same steps as those who went right to a proportion—hoping they will see the connections this year! )

  • Holly Dybvig

    July 25, 2021 at 8:21 pm

    Multiplying and dividing decimal numbers.

    I anticipate that students will:

    1. misplace the product or quotient when using multi-digit numbers.

    2. Forgetting to add or subtract.

    3. When multiplying they may drop the decimal down; when dividing they may forget to float the decimal up.

    Taking out the algorithm and allowing them to use rounding or decompose the numbers to make friendlier numbers will help them find their mistakes once they move on to the algorithm.

  • Marjorie Allred

    July 26, 2021 at 1:15 pm

    I chose the one where you find the area of Saskatchewan. There are several ways to find the area of a trapezoid. I think that the picture in the lesson would lead students to divide it into a rectangle and two triangles. You could cut it into two triangles as shown in the video with the lesson. You could take the two triangles on either side of the rectangle and push them together to make one triangle and add that triangle to the area of the rectangle. You could take two trapezoids and flip one over to make a parallelogram, find the area of that parallelogram and divide by two. You could draw a line parallel to one of the sides to make a parallelogram and a triangle. You could cut the trapezoid in half and form a parallelogram that is half as high as the trapezoid and has a length equal to the sum of the two bases.

  • Betsy Murphy

    August 2, 2021 at 8:54 pm

    I really like the black box defrost learning activity/lesson. I could definitely use this to kick off my proportion unit. I like the you anticipate student thinking, my students would probably go to unit rate to figure this out, as well as equivalent fractions/ratios or a proportion. I would also like to anticipate some incorrect solutions so I can support student learning/questions. Such as, using a number line but only counting with the given amounts, so not being able to get to the half pound… I’m struggling to think of more incorrect solutions but I will work on these, I really like this task. I will also definitely use the popcorn pandemonium, great proportional reasoning tasks..

  • Mary Jackson

    August 5, 2021 at 11:23 am

    I chose the Sliding Shelves Activity.

    Before: I anticipate that students will have trouble initially identifying with the idea of floating shelves and plan to show them actual pictures of floating shelves as a part of the initial reveal.

    Maple Floating Shelf with Hidden Bracket

    Having students Notice and Wonder and leading them to the appropriate questions to consider will be a challenge. I also will have students estimate and make predictions.

    During: I anticipated that most students will use protractors with the problems so I will hand out clear ones to each group if they request them. Remembering that there are 180 degrees in a straight angle and in linear pairs could also be a common error.

    I will also be ready to use the prompts and extensions mentioned in the lesson guide.

    • Kyle Pearce

      August 6, 2021 at 8:05 am

      Great work Mary!!
      It seems like you’ve spent the time necessary to understand how to deliver the lesson and withhold information. How’s your confidence feeling?

  • Velia Kearns

    August 6, 2021 at 6:53 pm

    Chosen Lesson: R2D2 Post-Its

    I watched other pages listed in the Lesson or Resources you provided of others that work on 3-Act Lessons, and whom incorporated the work you show in this course, and I am seeing better how to incorporate this material:

    https://docs.google.com/spreadsheets/u/0/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/pub?output=html” from Dan Myer (from:”https://blog.mrmeyer.com/2007/the-comprehensive-math-assessment-resource/“)

    • This reply was modified 2 months, 1 week ago by  Velia Kearns.
  • Tracy Arriola

    August 8, 2021 at 5:39 pm

    Knotty Rope

  • Mary Herbst

    August 9, 2021 at 8:18 am

    I chose the lesson on finding the area of a trapezoid. First I anticipate that some students will decompose the trapezoid into 2 triangles and a rectangle, and find the area of the 3 polygons. Next I saw that some students might notice that the two triangles would be congruent and so they’d find the area of the rectangle and then the area of the two triangles combined before adding the polygon areas. Next I saw that some students might already know the standard algorithm and use that instead. Finally I saw that some students might be able to draw a line to divide the trapezoid into a parallelogram and a large triangle, thus finding the areas of the two polygons and adding them together.

  • Valérie Perreault-Murphy

    August 12, 2021 at 1:16 pm

    I wish I could think of more ways my students would solve this! I have not taught this grade level in 6 years, I’m forgetting where they start. This does make me try to think outside the box, though, as I recall incredibly random yet valid ways of solving math questions.

    The module also makes me wish teachers had more time to meet with teachers from various levels. How helpful it could be to work with a teacher in an above grade to see their struggles and see how lower levels can adjust to help pave the way. I look at some of the work from grade 3 teachers on here and it helps me identify some aspects of my teaching I can fine tune.

  • Vanessa Weske

    August 12, 2021 at 5:34 pm

    For the solar panel task students might:

    1. Use the standard algorithm to divide the total number of panels by 5 and then multiply to get the total offset.

    2. Use a double number line to show offset per every 5 additional panels.

    3. Use a double area model to show the proportional relationship

    4. Setup a proportion of number of panels to offset.

    5. Calculate the unit rate of offset per 1 solar panel.

  • Denny Nelson

    August 18, 2021 at 2:30 pm

    I’m guessing that some would use ratios. Others would look for numbers like the grams or calories and then divide. The picture seems to show 1 in 7 chips are hot. Some might use a table or a double number line.

  • Peggy Allen

    August 28, 2021 at 2:19 pm

    Activity: Soup-du-jour

    I don’t find it easy to think of all the representations students may have.

  • Serina Signorello

    September 7, 2021 at 1:54 pm
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