Mathematics Instructional Focus for Grade 5 Marking Period 1
What is the instructional focus for this marking period?
In Grade 5 week 1, students apply foundational understandings of properties of operations and the base-ten system to
multiply multi-digit whole numbers using the standard algorithm. Building upon understandings developed in Grades 3 and
4, students use place value and properties of operations to explain computation with the standard algorithm. Students
estimate products and reason about when the standard algorithm is the most efficient strategy for determining a product.
It is expected that Grade 5 students who are fluent with their understanding of multiplication are flexible in their choice of
strategies and can justify the efficiency of their choice. The standard algorithm becomes part of a repertoire of strategies
and does not supplant other useful strategies, such as compensation. The expectation that Grade 5 students fluently
compute products of whole numbers is revisited in marking periods 2 and 4 to allow time for all students to develop
fluency.
In weeks 2–3, students develop understandings about measuring volume and relate volume to multiplication and division.
Students recognize volume as an attribute of solid figures. Students learn how this measurement of space (i.e., cubic
units) relates to measurements of area (i.e., square units) and length (i.e., linear units). Students measure volumes of
rectangular prisms with whole number side lengths by filling them with layers of unit cubes; this helps them understand
and apply formulas for the volume of a rectangular prism. Students recognize volume as additive and solve problems
involving volumes of solid figures composed of non-overlapping rectangular prisms.
In weeks 3–4, Grade 5 students identify, write, evaluate, and interpret numerical expressions. Students use parentheses
to formulate expressions, including expressions that represent applications of the associative and distributive properties.
This work is foundational for middle school in the content of Expressions and Equations, in which students work with
variables and use the conventions for order of operations to interpret and evaluate expressions.
In Grade 5, students extend understandings about place value to make generalizations about the relationships between
digits in adjacent places. Building upon work with tenths and hundredths in Grade 4 Number and Operations–Fractions,
students extend place value understandings to decimals through the thousandths place. In weeks 5–6, students read,
write, compare, and round decimals. When they use whole-number exponents to denote powers of ten, students make
connections to work with multiples in Grades 3 and 4. Students use place value to explain patterns in the number of zeros
in products of whole numbers and a power of 10 as well as the location of the decimal point in products of decimals and
powers of 10.
In weeks 7–8, students extend strategies and methods of recording computation with whole numbers in earlier grades to
operations with decimals in Grade 5. Students apply their understandings of properties of operations and place value to
add and subtract decimals to hundredths using concrete models, drawings, and written methods. They estimate sums and
differences, explain their reasoning, and relate strategies to written methods.
Beginning in week 9 and continuing into marking period 2, work with 1-digit divisors in Grade 4 is extended to finding
whole-number quotients of whole numbers with up to 4-digit dividends and 2-digit divisors. Students develop
understanding of division based on place value, properties of operations, and the relationship between multiplication and
division. In marking period 1, instruction focuses on dividing 2- or 3-digit numbers by 2-digit multiples of ten. Students
apply understandings about place value and fluency with multiplication and division facts to estimate and calculate
quotients and represent their thinking with visual models and equations.
Why will students learn this?
Enduring Understandings and Essential Questions
Number patterns and relationships can be represented in multiple ways.
 How do symbols help you interpret and evaluate numerical expressions?
The structure of the base-ten system is uniform, and base-ten units can be understood in terms of other base-ten units.
 What generalizations can be made about place value patterns?
 What strategies can be used to read, write, and compare decimals?
 How does understanding place value help in rounding decimals?
Flexible methods of computation involve understanding place value concepts and properties of operations.
 What are efficient strategies for multiplying and dividing multi-digit whole numbers?
 How can you model and represent operations with decimals?
Area and volume formulas as derived from linear measures.
 Why is volume measured in cubic units?
 What is the relationship among linear, area, and volume measurements of a solid figure?
 What strategies can be used to determine volume?
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