Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: 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 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 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.

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Learning Domain: Number and Operations in Base Ten

Standard: Use place value understanding and properties of operations to perform multi-digit arithmetic

Indicator: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)

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This resource contains four videos displaying how we want students to exhibit Mathematical Practice 7: Look for and make use of structure. Emphasis on the student with the implications on how teachers need to design instruction that purposefully encourages student engagement. Might it be noted that some of these videos can be applicable for other Mathematical Practices as well. (e.g., Standard 8). The videos cover multiple mathematical content to convey that these Mathematical Practices are fluid and can be applied flexibly. With regards to the content each video addresses: the grade 4 (4.NBT.5); the grade 5/6 video (6.EE.2; the grade 9-12 (refers to the conceptual category of Geometry).

EK - HIDOE