CCSS.Math.Practice.MP7 Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Implementing in the classroom:
As stated in Practice 1, students should have a solid understanding of what the problem is asking and what they will be trying to solve. With that in mind, students also need the ability to look closely at a problem to identify any patterns or structure. For example, a teacher might help students organize their base ten blocks into the hundred, ten, one structure to help them count the total amount.
To increase the likelihood of student pattern recognition teachers can incorporate pattern work throughout the year and throughout the daily schedule. A morning math meeting framework is an excellent time to incorporate extra math pattern/structure exposure. Students can recognize, identify and apply pattern knowledge through calendar work, weather graphing and daily number.
To increase the likelihood of student pattern recognition teachers can incorporate pattern work throughout the year and throughout the daily schedule. A morning math meeting framework is an excellent time to incorporate extra math pattern/structure exposure. Students can recognize, identify and apply pattern knowledge through calendar work, weather graphing and daily number.
Classroom Connection
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Becca Sherman works with 4th grade students in a “number talk” to connect the basic components of the Singapore Bar Model with students’ original thinking, thus front-loading students with several applications of the Bar Model as a representation of equal parts. In the exploration problem the words “three times” becomes a division problem or a missing factor problem. The intermediary step of drawing a “math picture” or model of the problem, poses a challenge for many students who have limited exposure to models.
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