Stage 3 - number and algebra - number sentences

Complete number sentences involving missing numbers or missing operations; use inverse operations to solve number sentences

Strategy

Students can:

  • complete number sentences involving missing numbers or missing operations
  • use inverse operations to solve number sentences

Activities to support the strategy

At this Stage, students will typically use trial-and-error methods to find solutions to number sentences. They need to be encouraged to work backwards and to describe the processes using inverse operations. Students need to be able to justify their solutions and communicate their strategies using mathematical language.

Activity 1– inverse operations

1. Pose this problem for students to solve:

  • I am thinking of a number.
  • When I take 9 away from the number my answer is 19.
  • What number am I thinking of?

Students discuss and write a number sentence that could solve the problem. Compare responses. Determine that the number sentence could be either addition or subtraction, e.g.

? - 9 = 19  and ? = 19 + 9

Discuss what is meant by inverse operations.

2. Demonstrate how to complete a number of calculations working backwards. Talk aloud the strategy using ½ mathematical language and point out the inverse operations being used.

find (blank) so that 125 divide by 5 = and then find blank so that blank x 5 = 125

3.Students complete number sentences where the operation sign is missing, e.g.

8 blank 4 = 6 blank 6

Activity 2 - missing numbers

Students complete number sentences by finding a missing number, e.g.

9 x blank = 10 x 4.5

  • Students write similar problems for their partner to complete.
  • Ask students to verbalise strategies they know which would help them solve the calculations.
  • In groups, have students explain the processes they used to solve the number sentences.

Activity 3 – what kind of calculation do you get?

  • Access the Red dragonfly mathematics challenge web version of the book
  • Open the challenge titled -what kind of calculation do you get? (2)
  • Have students work in pairs to solve the equations.
  • Students then share their strategies with the class.

Activity 4 – number sentences

Complete the following activities from Talking about patterns and algebra (PDF 2879.83KB)

  • Completing Number Sentences pp.131–134
  • Incomplete number sentences
  • Find the hidden numbers
  • Lesson Breakers p. 135
  • Incomplete number sentence
  • Problem sentences

Activity 5 – equations and expressions

Students use the Noodle learning object to explore algebra. This interactive resource explores and interprets word problems by evaluating expressions and solving equations in different contexts. Included are print activities, solutions, learning strategies, and a board game.

References

Australian curriculum reference: ACMNA133

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence.

NSW syllabus reference: MA3-8NA

Analyses and creates geometric and number patterns, constructs and completes number sentences

NSW numeracy continuum reference

Aspect 3: Patterns and number Structure – Number Properties.

Teacher resources

Nrich website

Curriculum Support

Numeracy app

What is My Number? Pick a number - any number! What is My Number will do a few calculations and… voila! Your number will magically appear!

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