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• Writes and interprets numerical expressions using parentheses, brackets, braces and the order of operations

• Analyze patterns and relationships

• Understands the place value system

• Reads, writes, and compares decimals to thousandths

• Uses place value understanding to round decimals to any place

• Adds, subtracts, multiples, and divides decimals to hundredths, using concrete models or drawings and strategies based on place value, and properties of operations

• Fluently multiply multi-digit numbers

• Divides multi-digit numbers by two-digit numbers using strategies based on place value, the properties of operations and the relationship between multiplication and division

• Uses equivalent fractions as a strategy to add and subtract fractions 

• Solve word problems involving adding and subtracting fractions with like and unlike denominators 

• Solves problems involving multiplication of fractions and mixed numbers 

• Understands multiplication as scaling (enlarging or reducing; e.g., knows 5 x ¾ is less than 5 without performing the multiplication) 

• Solves problems using division involving fractions  (e.g. 5 ÷ ¼ = 20   ½  ÷ 4 = ?  )

• Converts like measurement units with a given measurement system and uses these conversions in solving multi-step, real world problems

• Represent and interpret data using line plots

• Geometric measurement: 

  • Recognizes volume as an attribute of three dimensional space 

  • Relates volume to multiplication and to addition

  • Uses concrete objects as well as formulas to measure volume

• Graphs points on a coordinate grid to solve real-world mathematical problems

• Identifies and classifies 2-dimensional figures by their attributes 

• Uses appropriate strategies and formulas to solve problems that involve area, surface area, and volume

Students are able to “stick with” problems and will try multiple methods to reach a solution.

Students understand that written numerals represent real world objects and quantities.

Students are able to explain their own mathematical ideas and strategies and they respond to the thinking of others.

Students represent problem situations in multiple ways including equations, mathematical words, labeled sketches, objects, making a chart, list, or graph.

Students select the appropriate tools and resources to solve a problem.

Students use detailed and accurate mathematical vocabulary to  communicate mathematical understandings.

Students notice attributes and structures in mathematics such as: sorts shapes by the number of sides or recognizes that 4 x 7 = 28  and 28 ÷ 7 = 4.

Students notice repetitive actions in computation and look for patterns that support computation: 12 x 5 is the same as 10 x 5 and 2 x 5 to arrive at 60.