Number and algebra – addition and subtraction 1

• uses a range of strategies and informal recording methods for addition and subtraction involving one-and-two digit numbers MA1-5NA

Content

• represent and solve simple addition and subtraction problems using a range of strategies, including counting on, partitioning and rearranging parts (ACMNA015)

Linked syllabus content

Whole numbers 1

• recognise, model, read, write and order numbers

National Numeracy Learning Progression mapping to the NSW mathematics syllabus

When working towards the outcome MA1-5NA the sub-elements (and levels) of Quantifying numbers (QuN7-QuN8), Additive strategies (AdS2-AdS6) and Number patterns and algebraic thinking (NPA4) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

Materials

• dice – dots
• numerals, 1-6, 1-9 depending on student ability
• paper, pencil, whiteboard, pen, device for recording
• diagrams
• copyright

Teacher instructions

The purpose of this task is to gauge students’ understanding of using and recording a range of mental strategies to solve addition and subtraction problems involving one- and two-digit numbers

Students are given 1 or 2 dice with dots or numerals and a target number within the range 1-10, 10-20, 20-30 or similar (depending on ability). This number can be chosen by a student eg 16, 24, 50.

Students work with a partner or in a small group to take turns to roll the dice. Students working with 1 die roll this and record the number then add subsequent rolls. They add the numerals or dots, record the answer on a whiteboard, paper or on a recording device. The first student who reaches the target number without going over gets a counter. Students may elect to discard a die if working with two, when they are close to the target number.

Prompts could include:

How did you solve that? Which strategy did you use?

Where did you start counting from? I saw you counting in your head, with your fingers

Can you check your answer (if the teacher is unsure of which strategy the student used)?

This activity can be adapted for subtraction by starting at the target number and subtracting 1 or 2 dice (after adding them together), to get to zero. Students may elect to discard a die when they are close to zero.

Student instructions

Ask a student to pick a target number

Take turns to roll your dice and record the number.

Share with the group how you solved the problem.

Keep adding/ subtracting your dice amounts rolled until you exactly reach the target number. You may discard 1 dice when you are getting close to the target number.

Give your peer who reaches the target number a counter.

Repeat this activity again focussing on subtracting to reach zero.

Possible areas for further exploration

Students can choose to add or subtract their numbers if they are going to go over the target number during the addition activity.

Where to next?

Focus on developing strategies:

• cannot count the dots on their die – provide concrete materials for the task eg. A ten frame and counters to assist with perceptual counting forwards and backwards by ones
• count the dice dots from one – replace the die/ one of the dice with a numeral die to assist with using other strategies
• using doubles and near doubles
• use combinations to 10
• bridging to 10,
• using place value to partition numbers,