common core resources

There’s a tension, as a teacher, of a kid’s “right to rigor.” How do I know that this eight-year-old has sufficiently, mathematically, made their point, while also giving them some benefit of the doubt about what it’s going to look like if it’s a fragile or beginning thought.

Mia Buljan (2nd and 3rd Grade)

mentor interview

In this reflection, Mia Buljan observes how she seeks to understand her students’ development as young mathematicians, laughing that “a seven year old is a very imprecise tool to do math with!” She connects that developmental perspective to her teaching of the mathematical practices. She calls out how, for example, the mathematical practices 7 and 8, are “more mathy” because they are about identifying patterns and expressing regularity in reasoning. Her challenge is not to encourage students to identify patterns, but to recognize that not all of their patterns or rules may be mathematically sound; her job is to find problems or scenarios that require her students to test their thinking about their patterns and assumptions.

See how Mia's students demonstrate many mathematical practice standards in one lesson.

In this clip, Mia Buljan works with her students on a number talk, using a mental math approach to multiplying a two-digit number and a one-digit number. She invites her students to share their approaches to the problem, and probes them with questions to identify rationales for their reasoning.

As her 3rd-grade students work on a multiplication/division word problem, Buljan works with students Enmy and Esbin to dig deeper into their ways of making sense of the problem. She encourages Enmy to persevere and Esbin to let her do so, saying “Just let her try and figure it out. No coaching.”

See MP1 examples from all teachers

Mia Buljan circulates around her 3rd-grade classroom while her students work on a multiplication/division word problem. Buljan asks, “When you make two tens and four blocks, which number are you making?” The student responds, and Buljan continues to probe with questions to find out whether the student has identified the quantities and relationships in the problem situation.

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Mia Buljan’s 3rd-grade students defend their approaches to a multiplication number talk and respectfully engage each other when a student makes an error in his or her reasoning.

As her 3rd-grade students work on a word problem, Buljan circulates around her classroom. She says to two students, “He did it slightly differently. Can you guys get together and talk about what you think the problem means?”

After working individually on various problems, each of Buljan’s 3rd-grade students has selected a card on the board that represents the problem they worked. She then invites her students to “find the other people who have your problem and see if they agree with you.”

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Mia Buljan’s 3rd-grade students elect to use manipulatives to help them with a multiplication/division equal-grouping-scenario problem following a structure similar to “Sam's dad bought 24 hot dogs for Sam and his 3 friends. How many hot dogs can they each have?”

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Mia Buljan’s 3rd-grade students defend their approaches to solving various problems in a multiplication number talk. Two students respectfully engage each other when one of the students makes an error in her reasoning. She recognizes her error and corrects it in her problem-solving approach.

After her 3rd-grade students work individually on various problems, Buljan invites them to “find the other people who have your problem and see if they agree with you.” In their conversations, the students explain their thinking clearly to each other, striving to reach consensus about the best approach and solution to a problem.

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Mia Buljan’s 3rd-grade students engage in defending their thinking in a number talk. Students work with Buljan to connect the ideas of “switching over from adding, adding, adding, adding, adding, to thinking about multiplying.” Buljan connects and contrasts two students’ approaches to help identify different patterns to inform problem-solving.

After her 3rd-grade students work individually on various problems, Buljan invites her students to identify a card on the board that represents the problem they worked.

See MP6 examples from all teachers