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33 Representing Addition and Subtraction

Bonds of 10: Thinkboard

Mathematics

Develop the concept of addition and subtraction using Bond Blocks, diagrams, an equation, pictures and word story.

Develop fluency recalling a difficult to remember Bond of 10.

Language

  • bond
  • part-part-whole
  • addition
  • subtraction

Click this link to read Teacher Notes for more information about “Solving Word Problems”.

Differentiation

A little easier

Adapt a Worked Example

(i) Change the parts and whole

The teacher completes one thinkboard for a selected two-part bond of five. Students use this as a model, repeating the teacher’s thinkboard, but change the context of the parts and whole. For example, change the nouns from ‘fish’ (parts) in a ‘bowl’ (whole) to ‘cats’ in a ‘basket’.

(ii) Change the bond

The teacher completes one thinkboard for a selected two-part bond of five. Students use this as a model, repeating the teacher’s thinkboard, keeping the context the same, but change the numbers by using a different two-part bond of five. For example, change ‘2 and 3 fish’ to ‘1 and 4 fish’.

(iii) Change other students’ worked examples

Once students are confident adapting the teacher’s example, students can share their thinkboards with each other so as students can build a repertoire of word stories and representations of the operation. Students can then adapt their peers’ examples by changing the nouns for the parts and whole (eg fish for cats) or the numbers (a different bond of 5). Changing the nouns is easier than changing the numbers.

Concrete-Representational-Abstract: act it out

Assist students to understand the problem by instructing them them to act out of the equation before representing it with pictures and words. Students can act out the problem with:

  • Actual objects (for example, toy cars) that feature in their problem.
  • Objects such as blocks that represent the actual object. This is more difficult than using actual objects.

A little harder

Adapt a Worked Example

Change between active and static

The teacher completes one thinkboard for a selected two-part bond of five. Students use this as a model, repeating the teacher’s thinkboard, keeping the numbers (bond) and context (nouns) the same, but rewrite it with/out interaction occurring between the parts. For example,

  • static (Part are just there. They do not come or go.)
    “In my fish pond I have 2 spotty fish and 3 stripy fish. Altogether I have 5 fish” to  
  • active (Parts come or go. There is a change.)
    “In my fish pond I had 2 spotty fish (part). I bought 3 new stripy fish (part) and put them in the same pond. Now I have 5 fish (whole).

For more information refer to the “Solving Word Problems” Teacher Notes in regards to modelling a variety of problem types. Students typically find active problems easier than static ones.

Create a Question

Change the thinkboard story into a question. For each thinkboard story write three questions. Make the unknown (question) each part and the whole. For example, change “In my fish pond I have 2 spotty fish and 3 stripy fish. Altogether I have 5 fish”  to:

  • “In my fish pond I have 2 spotty fish and 3 stripy fish. How many fish do I have altogether?” (whole unknown)
  • “In my fish pond I have 2 spotty fish and some stripy fish. Altogether I have 5 fish. How many stripy fish do I have?” (part unknown)
  • “In my fish pond I have some spotty fish and 3 stripy fish. Altogether I have 5 fish. How many stripy fish do I have?” (part unknown)

Provide students a worked example. Use signalling to focus attention the the structure of the word question by highlighting in colour the parts and wholes in each question. Students can change the context (nouns for parts and wholes) or the numbers (bond).

Activity. Instruct students to:

  • Write one question on the front of a blank piece of paper
  • Record the answer on the back. Use the Bonds of 5: Representing Addition Thinkboard activity board as a template.
  • Swap and solve each other’s word questions.

Progression

In the next chapter of activities students focus on remaining bonds for the wholes 6, 7, 8, and 9 that have not yet been covered. The sequence of activities in this chapter is similar to past chapters: moving from identify bonds, to developing fluency, calculating, solving missing number equations and word problems. Go to

Activity 34

Bonds of 6, 7, 8, 9: Bonds, Building a Wall