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In this section, students encounter situations involving the questions “how many in each group?” and “how many groups?” They make sense of division in terms of finding the answers to these questions.
The focus here is on interpreting descriptions, diagrams, and expressions that represent division situations. Students see that the same diagram or expression can represent different questions. For example,...
In this section, students explicitly relate division to the unknown factor in a multiplication equation. For example, the quotient in is the unknown factor in . Students use this insight and their knowledge of multiplication facts to identify division facts.
To develop fluency, students reason about patterns in a multiplication table and notice that multiplication is commutative. For instance, if...
In this section, students use various strategies based on place value and properties of operations to multiply greater numbers.
Students first multiply one-digit numbers and multiples of 10 and observe the associative property of multiplication. They interpret to mean 3 groups of 2 tens, which is 6 tens. This means can be evaluated by finding or .
These insights enable...
In this section, students perform division in which the quotient or divisor is greater than 10. They apply what they know about place value, the two interpretations of division, and the relationship between multiplication and division to divide greater numbers.
The numbers in the division expressions encourage students to see the divisor as either the number of groups or the...