Geometric measurement:  understand concepts of angle and measure angles. 
4.MD.5 	Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a.	An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle.  An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. 
b.	An angle that turns through n one-degree angles is said to have an angle measure of  n degrees. 
4.MD.6 	Measure angles in whole-number degrees using a protractor.  Sketch angles of specified 
measure. 
4.MD.7 	Recognize angle measure as additive.  When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.  Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 
4.G.1 	Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.  Identify these in two-dimensional figures. 
4.G.2 	Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.  Recognize right triangles as a category, and identify right triangles. 
4.G.3 	Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.  Identify line-symmetric figures and draw lines of symmetry. 

Generate and analyze patterns.
4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of 
the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and 
the starting number 1, generate terms in the resulting sequence and observe that the terms 
appear to alternate between odd and even numbers. Explain informally why the numbers will 
continue to alternate in this way.
Extend understanding of fraction equivalence and ordering.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction 
models, with attention to how the number and size of the parts differ even though the two 
fractions themselves are the same size. Use this principle to recognize and generate 
equivalent fractions.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by 
creating common denominators or numerators, or by comparing to a benchmark fraction 
such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the 
same whole. Record the results of comparisons with symbols >, =, or <, and justify the 
conclusions, e.g., by using a visual fraction model.
Build fractions from unit fractions by applying and extending previous understandings of 
operations on whole numbers.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring 
to the same whole. 
b. Decompose a fraction into a sum of fractions with the same denominator in more than 
one way, recording each decomposition by an equation. Justify decompositions, e.g., by 
using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 
1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed 
number with an equivalent fraction, and/or by using properties of operations and the 
relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same 
whole and having like denominators, e.g., by using visual fraction models and equations 
to represent the problem. 

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole 
number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model 
to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 
5/4 = 5 × (1/4).