One Situation. Two Number Sentences

If you had a chance to try some of Session 1 Next Step Tasks with students, analyze a couple work samples you consider interesting.

If you have not yet had an opportunity to try some of these tasks with students, you can still practice your analytical skills by looking at some of these work samples.

As you analyze the work samples, consider the following and record your observations in Section 2.1a of your digital handout.

1. Describe what is happening in this sample. Better yet, if you are using a collaborative document, take a photo of the student work you are discussing and upload it to share with the others.
2. Identify the problem type and the structure. Review types of addition and subtraction problem types and structures.
3. Analyze what this student able to do, what this student not yet understand and where might you go next with this student.

The big idea discussed in the video above is that "the same situation can be represented with different number sentences". In order for them to understand this idea they need to see the inverse relationship between addition and subtraction -- which is especially evident as they encounter structures other than the typical "Result Unknown" problems. (You can look back at those structures here).

Representing problems visually is key to having students see the inverse connection between the "semantic structure" of these problem and a corresponding "standard structure".

Let's deepen our understanding of the connections between situation, semantic number sentences, visual representations and standard number sentences.

Complete the "Exploring Inverse Relationships" chart in Section 2.1b of your digital handout. Fill in the chart to show the relationship between:

• a situation
• the semantic number sentence
• a visual representation to describe the situation
• the corresponding standard number sentence

• What are some of the advantages of being faithful to the actual context of the situation (e.g., making the diagram look like the objects in the situation) and the advantages of moving towards more abstract representations?
• What would cause you to be more or less abstract with your representation?

Use Section 2.1c of your digital handout to share the student work sample that grounded your role play and the subsequent conversation you imagined with the student in a digital handout.