Download Standard 7 for Mathematical Practices Look for and make use of

Standard 7 for Mathematical Practices
Look for and make use of structure
Mathematically proficient students:

look closely to discern a pattern or structure.

Young students 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 the
distributive property.

In the expression x2 + 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.

step back for an overview and can shift perspective.

see complicated things, such as some algebraic expressions, as single objects or composed of several objects.
original formatting
Standard 7 for Mathematical Practices
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.
PRACTICE STANDARDS WITH 6–8 COMMENTARY
9
7. 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 x 2 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 3px yq2 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.•
Draft, 4 May 2014, comment at commoncoretools.wordpress.com.
• In middle school, students might use the structure of the number line to demonstrate that the distance between two rational
numbers is the absolute value of their difference, ascertain the
relationship between slopes and solution sets of systems of linear equations, and see that the equation 3x
2y represents a
proportional relationship with a unit rate of 3 2 1.5.
{ • They might recognize how the Pythagorean theorem is used to
find distances between points in the coordinate plane and identify
right triangles that can be used to find the length of a diagonal in
a rectangular prism.
• Proficient middle school students can also step back for an
overview and shift perspective, as in finding a representation of
consecutive numbers that shows all sums of three consecutive
whole numbers are divisible by three. They can see complicated
things as single objects, such as seeing two successive reflections across parallel lines as a translation along a line perpendicular to the parallel lines.