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Common Core Math Resources (Robert Kaplinsky)

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Common Core Math Resources (Robert Kaplinsky)

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I train mathematics educators who want their students to be better problem solvers.

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Connected to CCSS & Mathematical Practices

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Figure This! Math Challenges for Families - Challenge Index

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Home · Take a Challenge · Challenge Index · Math Index · Contact Us · About Technical Requirements · Printing the Challenges · Family Corner · Teacher Corner PowerPoint Presentation · Video Presentation · En Español · Purchase the CD

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Search by grade, topic, & standard

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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Grappling with New Concepts during a Common Core Math Workshop

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EL Education has revised​ the workshop model​ to align with the Common Core instructional shifts, embed ongoing assessment to increase responsiveness to student needs, and help students develop self-reliance and perseverance. The first component in this revised workshop​ (Workshop 2.0)​ asks students to "grapple" independently with a problem or task.

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Teaching Math to People Who Think They Hate It

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Teaching Math to People Who Think They Hate It

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Strogatz believes the key to this turnaround lies not in the material, or the inherent talent of the student, but in changing the way math is taught to liberal arts majors. The curriculum he teaches is called Discovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts (DAoM); it was developed at Westfield State University by Julian Fleron and three colleagues and funded by a grant by the National Science Foundation. The DAoM approach, which is publicly available through a free collection of books and workshops, is rooted in inquiry-based learning: It focuses on student-led investigations into problems, experiments, and prompts. The typical mathematics for liberal arts class on the other hand, is typically presented in lecture format, usually by non-tenure track instructors, and only serves to further disenfranchise students, Fleron claims.

Twelve years of compulsory education in mathematics leaves us with a populace that is proud to announce they cannot balance their checkbook, when they would never share that they were illiterate. What we are doing-and the way we are doing it-results in an enormous sector of the population that hates mathematics. The current system disenfranchises so many students.

Fleron's new vision for liberal arts math aims to intellectually stimulate students, to provide cognitive gains, and get students engaged with math rather than passively listening to a teacher talk about it at the front of a lecture hall. As stated on DAoM's website -"to nurture healthy and informed perceptions of mathematics, mathematical ways of thinking, and the ongoing impact of mathematics not only on STEM fields but also on the liberal arts and humanities."

In an email sent after his first week of class, Strogatz described what this vision looks like when implemented in the university classroom. Using an exercise from the DAoM book Games and Puzzles, Strogatz handed each of his students a pair of scissors, as well as a piece of paper with a scalene triangle drawn in the middle of it. (A scalene triangle is one in which all three sides are different lengths.) He then challenged them to cut out the triangle using only a singlestraight cut. When they looked baffled, Strogatz told them they could fold the paper any way they pleased before cutting it.

Strogatz himself admits that he had trouble the first time he played around with the exercise. At the end of class, Strogatz asked the students if they wanted a hint, but they shouted him down, refusing his help. As Strogatz wrote to me:

They were having a true mathematical moment. That is, they were deeply engaged with a puzzle that made sense to them, and they were enjoying the struggle. They were feeling what anyone who loves math feels, the pleasure of thinking, the pleasure of wrestling with a problem that fascinates. I told the students to think about the scalene triangle over the weekend and to try it in their dorm room. Over the weekend I started to get emails from some of them, expressing the excitement they felt when they solved it.

The usual arguments against inquiry-based learning, particularly when it comes to math education, is that practice and repeated drilling of basic concepts are necessary for a deep and durable education in math. I asked Strogatz about this tension, and he acknowledged that drilling is important, too. "I want my students to memorize and know basic facts, and I want them to understand what those facts mean, why they're important, where they come up in the real world. I want it all and I think students want it all too." He added:

If we only teach conceptual approaches to math without developing skill at actually solving math problems, students will feel weak. Their mathematical powers will be flimsy. And if they don't memorize anything, if they don't know the basic facts of addition and multiplication or, later, geometry or still later, calculus, it becomes impossible for them to be creative. It's like in music. You need to have technique before you can create a composition of your own. But if all we do is teach technique, no one will want to play music at all.

Strogatz and Fleron both envision a classroom in which math is taught as a both an intellectual discipline and a creative endeavor-where math is made, not just discussed. "As with any game, or playing music, or making a piece of art, it's doing the real thing that's inspiring. My students are actually making mathematics-in many cases, for the first time in their lives. And they're loving it. And why wouldn't they? It's a joyous, glorious experience. At every level. Little kids can make math. It may be the mathematical equivalent of finger painting, but it's still math."

Inspired, I challenged my son and husband to create their own scalene triangle origami. An hour later, they were still at it, debating possible folds, trying out multiple solutions, and making math together.

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Teaching Math to People Who Think They Hate It

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Strogatz believes the key to this turnaround lies not in the material, or the inherent talent of the student, but in changing the way math is taught to liberal arts majors.

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Why It’s Important to Talk Math With Kids

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Why It’s Important to Talk Math With Kids

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Flickr: Benjamin Rossen

Do you speak math with your kids?

Many of us feel completely comfortable talking about letters, words and sentences with our children-reading to them at night, helping them decode their own books, noting messages on street signs and billboards.

But speaking to them about numbers, fractions, and decimals? Not so much. And yet studies show that "number talk" at home is a key predictor of young children's achievement in math once they get to school. Now a new study provides evidence that gender is part of the equation: Parents speak to their daughters about numbers far less than their sons.

The report, published in the Journal of Language and Social Psychology, drew on a collection of recordings of mothers talking to their toddlers, aged 20 to 27 months. Alicia Chang, a researcher at
the University of Delaware, and two coauthors determined that mothers spoke to boys about number concepts twice as often as they spoke to girls. Children this age are rapidly building their vocabularies, Chang notes, and helping them become familiar with number words can
promote their interest in math later on.

That was made clear in another study, published in Developmental Psychology in 2010, which also used recordings of parents talking to their children to gauge how often number words were used (the kids in this study were between the ages of 14 and 30 months). Psychologist Susan Levine of the University of Chicago and her coauthors found huge variation among the families studied: Some children were hearing their parents speak only about two dozen number words a week, while others were hearing such words about 1,800 times weekly.

The frequency of number talk in the children's homes had a big impact on how well the youngsters understood basic mathematical concepts such as the cardinal number principle, which holds that the last number reached when counting a set of objects determines the size of the set ("One, two,
three-three apples in the bowl!"). A subsequent study by Levine found that the kind of number talk that most strongly predicted later knowledge of numbers involved counting or labeling sets of objects that are right there in front of parent and child-especially large sets, containing between four and ten objects.

Though it may not come naturally at first, parents can develop the habit of talking about numbers as often as they talk about letters and words. Some simple ways to work numbers into the conversation:

Note numbers on signs when you're walking or driving with children: speed limits and exit numbers, building addresses, sale prices in store windows.

Ask children to count how many toys they're playing with, how many books they've pulled out to read, or how many pieces of food are on their plate.

Use numbers when you refer to time, dates, and temperatures: how many hours and minutes until bedtime, how many weeks and days until a holiday, the high and low the weatherman predicts for that day.

With older children, math can become a part of talking about sports, science, history, video games, or whatever else they're interested in.

With practice, parents and children alike will find that math makes a very satisfying second language.

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Why It's Important to Talk Math With Kids

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Flickr: Benjamin Rossen Do you speak math with your kids? Many of us feel completely comfortable talking about letters, words and sentences with our children-reading to them at night, helping them decode their own books, noting messages on street signs and billboards. But speaking to them about numbers, fractions, and decimals?

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Conjecture Lesson Plan For 8th Grade Math

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Conjecture Lesson Plan For 8th Grade Math

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Math.Practice.MP2

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability todecontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability tocontextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

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Math.8.F.B.4

Common core State Standards

Math: Math

8: 8th Grade

F: Functions:

B: Use functions to model relationships between quantities.

4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. How do students represent functions in multiple ways?

2. How does noticing structure prepare students for making conjectures?

3. What can you learn from Ms. McPhillips about using the Common Core with students?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

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Students in Audra McPhillips' eighth grade class use the four representations of a function to solve a set of growing dots problems. Students begin by presenting their work from the previous day. Each student receives a handout with growing dots problems and looks for patterns. They represent the functions in a variety of ways.

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Teaching Students to Prove Their Mathematical Thinking through Questions, Charts, and Discourse

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Teaching Students to Prove Their Mathematical Thinking through Questions, Charts, and Discourse

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Teaching Students to Prove Their Mathematical Thinking through Questions, Charts, and Discourse

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Mona Iehl's third-graders at Polaris Charter Academy in Chicago develop their own understanding of how to solve math problems through cognitive guided instruction. They have time to grapple with problems and are guided to new understandings by Iehl's strategic use of questions. Following a period of grappling, students engage in discourse with each other and then work to prove their mathematical thinking to the group.

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Middle School Math Teaching Tip - Using Color

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Middle School Math Teaching Tip - Using Color

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Discussion and Supporting Materials

Thought starters

1. How does using color help students organize their thinking?

2. What kinds of problems are best suited for this strategy?

3. How does color help students' thinking become visible to others?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

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Using Color to Support Mathematical Thinking

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Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. How does using color help students organize their thinking?

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Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

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Using A Problem-Based Task With Fourth Graders To Create Deep Engagement In Math

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Using A Problem-Based Task With Fourth Graders To Create Deep Engagement In Math

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EL

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Using a Problem-Based Task with Fourth Graders to create Deep Engagement in Math | EL Education

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Fourth-grade teacher Jessica Proffitt, from Two Rivers Public Charter School in Washington, D.C., guides her students through a problem-based math task in which they individually and collaboratively grapple with a multiplication problem.