# Teaching the relationship between addition and subtraction

### How Is Addition Like Subtraction? | Wonderopolis Free worksheets, online interactive activities and other resources to support children learning the relationship between addition and subtraction. Lesson: Inverse Relationship Between Addition and Subtraction Developing the Concept. Once children are proficient in finding related facts, they are ready to. Principles and. Standards for School Mathematics (National Council of Teachers of standing and procedural understanding of addition and subtraction. Building on connections and relationships among these and other mathematical.

Remember, we talked about related facts. Well, today we are going to talk about a fact family. All the facts in a fact family are related. Pick up 4 red cubes and 2 blue cubes.

### MathSteps: Grade 1: Inverse Relationship Between Addition and Subtraction: What Is It?

I will put the red cubes together and the blue cubes together. Now I will place the blue cubes on the end of the red cubes to make a train. What fact can you make from this train? Watch as I turn the train end to end. What fact do you see now? What is the same about the two facts? Can we show a subtraction fact using this train? Elicit from children that you can break one of the colors of cubes off the train. Break the blue cubes off the train. What subtraction fact have I made? This time break off the red cubes. What subtraction fact have I made this time? What do you notice about the four facts that we just made? Children should say that there are two addition and two subtraction facts and that all four facts have the same 3 numbers. How are the numbers related? The same numbers are used in all four facts. Repeat with other fact families that have four facts.

Then use 3 red and 3 blue cubes to make a train.

### Number families and relationships | nzmaths

Change 7 to 6. Continue to make available to the students, digit cards, cards with addition, subtraction and equals symbols, tens frames and counters, paper and pencils. Have students pair share their recordings. Discuss what is the same or different about them this depends on which number they change. They should draw a box around sets of four equations that they have written that are the same as a partner has recorded.

Activity 3 Conclude this session by summarising on the class chart, the features of a family of related facts: Write and read sets of related addition and subtraction equations. Explain, in their own words, the inverse relationship between addition and subtraction. It is not necessary for students to know the name for this. Activity 1 Begin by reading together the concluding notes from Session 1.

Distribute sets of Family Shuffle cards Attachment 1 to students. To recognise related addition and subtraction equations Explain how to play. Each student has one set of 16 shuffled cards.

These are dealt out, face up, in a four-by-four array. Two cards any are removed from the array and set aside, creating two empty spaces in the array. The two cards that were set aside are replaced to complete the array.

Students could write their own sets to create alternative puzzles. Ask students what they notice about what is happening with the numbers. Read to the class or have written on the class chart this scenario. Discuss what is happening in these equations. Record several of these in words and in equations on the class chart.

Read to the class or have written on the class chart this scenario or a similar one relevant for the class. Once again, discuss what is happening in these equations. Explain that we say this relationship between addition and subtraction, is known as an inverse relationship. Record this in answer the question posed in Step 2 above. Have students suggest a meaning for inverse, then confirm this with a dictionary. Make paper, pencils and felt pens available to the students.

Session 3 Recognise that addition is commutative but that subtraction is not. Recognise how knowing about number families is helpful for solving problems. Solve number problems that involve application of the additive inverse. Activity 1 Begin by sharing the student work from Session 2, Activity 2, Step 6. In particular highlight the commutative property of addition.

Also highlight the related subtraction facts.

## How Is Addition Like Subtraction?

Distribute the addition and subtraction grids Attachment 2 to each student. Use the larger class copies to model how to complete each grid. Highlight the importance of the students writing their observations about each grid once they are completed.

These observations should include number patterns and the fact that the subtraction grid cannot be fully completed. Once completed, have students share what they notice and record their observations. On the class addition grid look for the same sums for both addends. Discuss the pattern and also notice the pattern of doubles Write this statement on the class chart and read it with the students: We can carry out addition of two numbers in any order and this does not affect the result.

Introduce the word commutative. Record a student statement that states, in their words, that addition is commutative, subtraction is not. Activity 2 Have students complete the number problems on Attachment 3.