Students will demonstrate the concepts and skills that they have developed through these contexts and learning experiences.

The purpose of this assessment is for students to demonstrate their understanding of the following big ideas.

• Multiplication can involve determining the total quantity given the number of equal groups and the size of each group;
• The order of the numbers in a multiplication sentence does not matter (commutative property);
• The strategy of doubling and halving is possible due to the associative property of multiplication;
• The distributive property of multiplication supports the strategy of partial products (where one or both factors can be decomposed over addition or over subtraction).

The independent assessment will allow students to demonstrate concepts and skills related to the following learning goals:

• I will use an array to model multiplication.
• I will describe real-world examples of multiplication.
• I will explain the commutative property of multiplication.
• I will share strategies for multiplying one-digit and two-digit numbers.

Students might write and/or model their answers independently. Students can also be interviewed by their teacher.
An alternative assessment opportunity should be offered if this tool will not successfully capture what the student knows, understands or can do.

In today’s math talk, students will apply the knowledge and skills they have developed in this unit. Each multiplication sentence in this string stands alone and lends itself to one of the properties, and at least one strategy that we have explored.

While each of the following multiplication sentences were crafted to elicit various multiplication properties (commutative, associative and distributive properties), the choice is ultimately up to each student to leverage which properties and strategies feel most helpful to them.

Students are encouraged to begin independently selecting effective strategies and models based on the factors within the multiplication sentence.

48 x 6
16 x 22
23 x 54
7 x 45

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Students will be prompted with:

Without counting, determine the number of windows on
the street facing side of this apartment building.

You’ll notice that only the dimensions are showing and a clock tower is blocking a good portion of the apartment building and therefore, making it impossible for students to count by 1s.

Although different students may use different multiplication properties, the visual number talk video will model how a student might factor the 6 columns into 3 groups of 2 columns and re-associate the 2 with the 48.

By using the associative property of multiplication, students are essentially halving the 6 columns and doubling the number of windows in each column which results in an equivalent number of windows.

From here, students now have 3 groups of 96 windows which may be easy for some students to calculate, but more difficult for others. 

One approach might be to then leverage a compensation strategy to re-write 96 as 100 – 4:

3 x 96 = 3(100 – 4)

In doing so, we are now forcing the use of the distributive property of multiplication to craft partial products 3 x 100 and subtracting the 3 x 4 to compensate.

Ensure that you allow different students to share different strategies and name the properties of multiplication that you are leveraging as you go to raise student awareness, fluency and flexibility with noticing and naming these properties.

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Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Students will have an opportunity to independently complete the following assessment where they will communicate their understanding of the behaviors of multiplication.

If the student’s understanding is unclear based on the product submitted, you might consider following up with a conversation. Understanding the student’s cognitive process will help you understand where the student is along their learning trajectory. This information will be critical in determining the appropriate next steps.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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