Grade 5/6 Compacted Mathematics Instructional Focus for Marking Period 1
What is the instructional focus for this marking period?
The content of Grade 5/6 Compacted Mathematics instruction in marking period 1 is from the CCSS/C2.0 Grade 5 course.
Any Grade 5 content not addressed in Grade 5/6 Compacted Mathematics Marking Period 1 was included in the Grade
4/5 Compacted Mathematics course. The four marking periods of the CCSS/C2.0 Grade 6 mathematics course are
compacted into Marking Periods 2–4 of Grade 5/6 Compacted Mathematics.
Instruction in marking period 1 weeks 1–5 of Grade 5/6 Compacted Mathematics focuses on multiplication with fractions.
The learning progression is designed to develop critical understandings about multiplying fractions rather than simply
addressing the algorithm for the computation. While computing these products may seem simple, it is critical to first build
a strong foundation of the meaning of multiplication with fractions. In preparation for work with ratios and proportional
reasoning, students apply understandings about multiplication to compare the size of a product to the size of one factor
based on the size of the other factor, without calculating. The special case of multiplying by 1 is related to fraction
equivalence. Developing understanding of multiplication as resizing is an opportunity for students to reason abstractly and
make generalizations. In week 1, students multiply a fraction by a whole number; unit fractions are used to reason about
partitive contexts representing whole number products. In week 2, the learning is extended to multiplying a fraction by a
fraction without subdividing (e.g.,
). Students continue to work with multiplication of fractions in weeks 3–5 by using
area models to represent multipication of a fraction by a fraction with subdividing, including factors >1. In week 5, students
reasoning about partitive contexts with products that are not whole numbers. Students also apply their understanding of
the area of a rectangle with fractional side lengths to solve problems.
In week 6, students apply and extend previous understandings of division to divide unit fractions by whole numbers and
whole numbers by unit fractions. Students use visual fraction models and the relationship between multiplication and
division to make sense of division word problems as well as create their own word problems. In week 7, students apply
understandings about fractions to represent and interpret a data set of measurements in fractions of a unit (
) using a
line plot.
In week 9, students build upon the concept of division as equal sharing as well as understandings about division of whole
numbers in order to interpret a fraction as the division of the numerator by the denominator. Applying and extending these
understandings to divide fractions by fractions is a CCSS/C2.0 Grade 6 expectation.
In marking period 3 of Grade 4/5 Compacted Mathematics, students applied foundational understandings of properties of
operations and the base-ten system to multiply multi-digit whole numbers using the standard algorithm. To allow
additional time for all students to develop fluency and to check that students have retained depth of understanding, this
expectation is revisited in marking period 1 week 2 of Grade 5/6 Compacted Mathematics. 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.
In weeks 8–9, understandings about place value and operations with whole numbers and fractions are extended to
operations with decimals to hundredths. The learning progression is designed to develop critical understandings about
operations with decimals rather than simply addressing algorithms or computational procedures. In week 8, students
multiply decimals to hundredths. Students use place value strategies and area models to multiply a whole number by 0.1
or 0.01, a whole number by a decimal other than a unit decimal, and a decimal by a decimal. Problems with decimal
factors involve multiplication of tenths and tenths or tenths and hundredths. In weeks 8–9, students develop their
understanding of division with decimals. Strategies for dividing by a unit fraction are extended to dividing a decimal by 0.1
and 0.01. Students use place value strategies and properties of operations to reason about dividing a decimal by a
decimal; numbers are purposefully chosen so quotients of decimals divided by decimals (to hundredths) are whole
numbers. Students also extend understandings of division as equal groups to divide a decimal by a whole number.
Students’ work with reasoning about operations with decimals provides a strong foundation for the CCSS/C2.0 Grade 6
expectations for fluency with addition, subtraction, multiplication, and division with decimals.
In week 9, students also extend their understanding about converting measurement units to include converting from
smaller to larger measurement units within a given measurement system (e.g., 5 cm to 0.05 m, 9 feet to 3 yards).
Students use these conversions to solve multi-step problems.
Sample learning tasks in compacted mathematics are not aligned with the Thinking and Academic Success Skills or
Model Integrated Day for the rest of the contents in Grade 5.
Montgomery County Public Schools, Maryland
Curriculum 2.0 - Grade 5/6 Compacted Mathematics 2014
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Grade 5/6 Compacted Mathematics Instructional Focus for Marking Period 1
Why will students learn this?
Enduring Understandings and Essential Questions
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?
A variety of strategies can be used to perform operations and solve problems with fractions.
 What strategies can be used to model and represent operations with fractions?
 How can previous understandings about operations with whole numbers help you make generalizations about
operations with fractions?
 How can equivalent fractions help you represent, interpret, and solve problems?
 How can product s and quotients of fractions be interpreted?
Measurement units within a system are built upon each other.
 How are units of measure within one system related?
 How can you use conversions within a given measurement system to solve problems?
Montgomery County Public Schools, Maryland
Curriculum 2.0 - Grade 5/6 Compacted Mathematics 2014
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