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<\/a><\/p>\nGets students tackling problems that have more than one solution<\/h4>\n
So often we give students problems where there truly is one solution.\u00a0 They get very accustomed to “filling in the box” and seeking the right answer rather than digging in and finding the complexity of the math.\u00a0 Finding quality open-ended math tasks can help them see that math is far more intricate than merely finding a quick answer!<\/p>\n
Helps students learn to make sense of a complex problem<\/h4>\n
Indeed, one of the Standards for Mathematical Practice involves students tackling a problem to determine what it’s asking.\u00a0 If we consistently give students simple word problems that accompany our units, we take away all that thinking.\u00a0 For example, when I teach a unit on multiplication if I only present word problems that involve multiplication–I’ve taken the thinking away.\u00a0 Using more complex tasks forces students to think about what type of math they need to do and to dig in to get started.<\/p>\n
Allows students to choose from multiple strategies or entry points<\/h4>\n
Similarly, these open-ended math tasks are perfect for giving students an entire arsenal of strategies–many of which can work in any given situation.\u00a0 When there are multiple steps and lots of information, there are different places for students to dig in and get started.\u00a0 Similarly, students can move back and forth between different parts of the task as they work and made progress toward understanding.\u00a0 When given a task like designing a new library display, students can collect all the different pieces of information in the task and CHOOSE what makes sense to get them started.\u00a0 They may start with a sketch or an estimate or any number of other strategies, but there is a LOT to grab onto as they begin.<\/p>\n
Encourages math talk and discourse<\/h4>\n
This is pretty self-explanatory!\u00a0 When you assign a rich math task, there is a lot to talk about.\u00a0 When we ask students to tackle them, it only makes sense to give them “talk time”.\u00a0 This is truly one of the best parts about using quality problems.\u00a0 The opportunity to share thinking and help get classmates “unstuck” is invaluable.<\/p>\n
We’ve all seen the memes making fun of word problems.<\/p>\n “If Lois buys 16 watermelons…”<\/p>\n “There are 693 kittens…”<\/p>\n (You get my\u00a0drift.)<\/p>\n Quality open-ended tasks are MEANT to be real-world math.\u00a0 Students are asked to solve real-world problems.\u00a0 They may be working with a budget.\u00a0 They may need to make decisions about “how many” or “which ones”.\u00a0 Students may need to design something.\u00a0 THIS is math.\u00a0 When you find math problems that mimic students’ real lives, it’s priceless.\u00a0 Our students eat lunch in the cafeteria.\u00a0 They go on field trips.\u00a0 They have sleepovers.\u00a0 This is engaging math.<\/p>\n Like I mentioned before, teaching math in isolation takes away the thinking and deep understanding.\u00a0 By using rich math tasks, students are forced to examine ALL the math they know as they look for ways to accomplish their goal.\u00a0 They may need to add and subtract.\u00a0 They may need to make a chart.\u00a0 Sometimes they may see that drawing an array can help them solve a multiplication problem. In a great task, they may need to do all of these things for one problem!\u00a0 So often, we fail to give students enough credit for being able to do this kind of work, and we do them a disservice when we don’t give them those opportunities.<\/p>\n <\/p>\n As we rush to work through the endless list of standards for our grade levels, we cannot forget to include the math practice standards in our plans.\u00a0 When you read through these 8 standards, you can see the role open-ended math challenges play.\u00a0 In fact, every single one of those standards can be met when we provide students with this type of math work.<\/p>\n As I mentioned before, providing students with these rich tasks encourages accountable talk.\u00a0 They are perfect for partner and small group work.\u00a0 In fact, using these to explicitly teach students HOW to work together, how to coach each other, and how to encourage each other is invaluable.\u00a0 Building relationships and adopting a growth mindset is a critical piece of learning productive struggle.\u00a0 Learning to struggle and overcome challenges TOGETHER is a key part of our math coaching.<\/p>\n Unlike more simplistic math problems, open-ended tasks can naturally differentiate.\u00a0 Some students may want access to calculators.\u00a0 Some may draw pictures.\u00a0 There may be a time when groups of students choose to use manipulatives to model their math thinking.\u00a0 As teachers coach, they can give math “hints” as needed to students based on their needs.\u00a0 I have used countless math tasks where I have assigned the same task to ALL students but have provided differing levels of support as they tackle them.\u00a0 Remember, students can still work on problem solving skills and strategies if they haven’t yet mastered algorithms.<\/p>\n A perfect example is a back-to-school shopping challenge where students have a budget and a set list of things to purchase.\u00a0 There are multiple things to consider–from the number of items required to the different prices at different stores.\u00a0 Should we save this rich task for students ONLY when they have mastered the additional algorithm with decimals?\u00a0 Of course not.\u00a0 We can have students work in teams, give calculators or other tools–or anything that will make the task more accessible.\u00a0 This is an example of providing QUALITY education to all students and is a powerful way to build math confidence and self-esteem.<\/p>\n This is big.\u00a0 Rather than teachers being the lecturer or “provider of knowledge”, these tasks naturally lend themselves to teachers serving as coaches.\u00a0 So what?<\/p>\n I think this point is being made throughout this post, but I’ll reiterate it here.\u00a0 When there is more than one solution, there are countless solution paths.\u00a0 When there are multiple solution paths, students see the value in thinking differently and there is not one “right” way to do business.\u00a0 What a powerful message!<\/p>\n To make it even more powerful, make sure you build in time to SHARE strategies.\u00a0 Whether you have students showcase their work under a document camera, share their ideas in small groups, project their work, or hang it up–celebrate the amazing solutions students come up with!\u00a0 Even more valuable?\u00a0 Make sure students know that the final answer is less important than the process to get there.<\/p>\n Do we want students to realize that we value their thinking?\u00a0 You bet.\u00a0 Learning to think independently and creatively is another one of those life lessons that will extend far beyond your math class.\u00a0 It’s how REAL problems get solved.<\/p>\n As I stated before, of course, we want students to do math accurately and get correct solutions.\u00a0 The truth is, when students tackle these complex tasks, there are lots of places where errors can occur.\u00a0 If we stress getting a correct answer over the complex processes, all value is lost.\u00a0 The value in these tasks is the process of understanding the problem, choosing strategies, modifying strategies when needed, selecting models or tools to use, estimating, reviewing answers, organizing work, and so much more.<\/p>\n When students know that WE value their hard work as much as correct answers, it’s so freeing for them!\u00a0 They see that we value their thinking and strategies and even their mistakes.\u00a0 This takes away any compulsion to get the answer from others or to shut down due to frustration.<\/p>\n As you can see, the power of these tasks is obvious.\u00a0 Unfortunately, very few math programs provide enough of them to really help students develop these skills.\u00a0 Because of that, one role I have taken on as a curriculum designer is to try to fill this gap by creating tasks like this for different age levels.<\/p>\n Convinced?\u00a0 Give some a try!<\/strong><\/p>\n CLICK HERE<\/strong><\/a> to grab a free guide that summarizes this blog post AND tells exactly what skills some of my open-ended tasks cover.<\/p>\n CLICK HERE<\/strong><\/a> to see a bundle of tasks for grades 2\/3 (or for beginning problem solvers in grade 4)<\/p>\n Looking for tasks for experienced grade 3 problem solvers and grades 4\/5?\u00a0 CLICK HERE!<\/strong><\/a><\/p>\n![\"Increasing](\"https:\/\/theteacherstudio.com\/wp-content\/uploads\/2021\/08\/6-667x1000.png\")
<\/a><\/p>\nAllows students to see real-world applications of math<\/h4>\n
![\"Using](\"https:\/\/theteacherstudio.com\/wp-content\/uploads\/2021\/08\/3-1-667x1000.png\")
<\/a><\/h4>\nHelps students see the interconnectedness of math concepts<\/h4>\n
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Immerses students in the Standards for Mathematical Practice along with the math content<\/h4>\n
Provides an excellent forum for partner and small group work<\/h4>\n
Naturally differentiate as students take \u201cjust right\u201d approaches to solving them<\/h4>\n
Allows teachers to serve as coaches as they watch and interact with students as they solve them
![\"Helping](\"https:\/\/theteacherstudio.com\/wp-content\/uploads\/2021\/08\/8-667x1000.png\")
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Encourages creative thinking and strategies<\/h4>\n
Encourages students (and teachers) to focus on the PROCESS over the solution<\/h4>\n