ILLINOIS TEACH & TALK

Illinois Assessment of Readiness Mathematics Evidence Tables. Retrieved from: https://www.isbe.net/Documents/IAR-Grade-3-Math-Evidence-State.pdf

 

Students need time to explore these three properties of operations used in order to multiply fluently.

The teacher will encourage different ways to think about and solve multiplication problems. Once students use a strategy the teacher can point out the type of strategy used. For example, a student may choose to rearrange three factors; this is an example of the commutative property. This will promote student discovery and empower the student. Students can explore these strategies in a number talk and explain their thinking out loud. Students can also work with a partner or small group to think about multiplication of numbers in different ways. 

 

“Students do not need to know the formal names of the properties but to know the rules that can be

applied as strategies in order to multiply and divide.” ~Grade 3 flipbook

 

Progression Document CC OA K-5 pg. 23-25

Grade 3

 

Students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients.3.OA.1–7 These skills and understandings are crucial; students will rely on them for years to come as they learn to multiply and divide with multi-digit whole number and to add, subtract, multiply and divide with fractions and with decimals.

Note that mastering this material, and reaching fluency in single digit multiplications and related divisions with understanding,3.OA.7 may be quite time consuming because there are no general strategies for multiplying or dividing all single-digit numbers as there are for addition and subtraction. Instead, there are many patterns and strategies dependent upon specific numbers. So it is imperative that extra time and support be provided if needed.

 

Common types of multiplication and division situations

 

Common multiplication and division situations are shown in Table 3. There are three major types, shown as rows of Table 3. The Grade 3 standards focus on Equal Groups and on Arrays.• As with addition and subtraction, each multiplication or division situation involves three quantities, each of which can be the unknown. Because there are two factors and one product in each situation (product _ factor _ factor), each type has one subtype solved by multiplication (Unknown Product) and two unknown factor subtypes solved by division.

*Multiplicative Compare situations are more complex than Equal Groups and Arrays, and must be carefully distinguished from additive

Compare problems. Multiplicative comparison first enters the Standards at Grade 4

 

In Equal Groups, the roles of the factors differ. One factor is the number of objects in a group (like any quantity in addition and subtraction situations), and the other is a multiplier that indicates the number of groups. So, for example, 4 groups of 3 objects is arranged differently than 3 groups of 4 objects. Thus there are two kinds of division situations depending on which factor is the unknown (the number of objects in each group or the number of groups). In the Array situations, the roles of the factors do not differ. One factor tells the number of rows in the array, and the other factor tells the number of columns in the situation. But rows and columns depend on the orientation of the array. If an array is rotated 900, the rows become columns and the columns become rows. This is useful for seeing the commutative

property for multiplication 3.OA.5 in rectangular arrays and areas. This property can be seen to extend to Equal Group situations when Equal Group situations are related to arrays by arranging each group in a row and putting the groups under each other to form an array. Array situations can be seen as Equal Group situations if each row or column is considered as a group. Relating Equal Group situations to Arrays, and indicating rows or columns within arrays, can help students see that a corner object in an array (or a corner square in an area model) is not double counted: at a given time, it is counted as part of a row or as a part of a column but not both. As noted in Table 3, row and column language can be difficult.   The Array problems given in the table are of the simplest form in which a row is a group and Equal Groups language is used (“with 6 apples in each row”). Such problems are a good transition between the Equal Groups and array situations and can support the generalization of the commutative property discussed above. Problems in terms of “rows” and “columns,” e.g., “The apples in the grocery window are  in 3 rows and 6 columns,” are difficult because of the distinction between the number of things in a row and the number of rows. There are 3 rows but the number of columns (6) tells how many are in each row.  There are 6 columns but the number of rows (3) tells how many are in each column. Students do need to be able to use and understand these words, but this understanding can grow over time while students also learn and use the language in the other multiplication and division situations. 

 

Common Core Standards Writing Team. (2013, September 19). 

Progressions for the Common Core State Standards in Mathematics(draft).  K-5 Counting and Cardinality and Operations and Algebraic Thinking. Tucson, AZ: Institute for Mathematics and Educations, University of Arizona.

​

​

Also check out Student Achievement Partners Coherence Map