• ### Where are they now?

Can determine total number of elements in a collection of grouped items, but counts grouped items by 1s withoutany reference to group structure (i.e. uses make all/count-all strategy)

• ### Where to next?

Efficient counting using ‘easy’ composite units (2s, 5s and 10s). Elements of the groups still need to be modeled (e.g. counters within a circle). Use group structure and stress or rhythmic counting to determine total. Identifies x10 pattern.

• ### Purpose

Fluency with basic facts allows for ease of computation, especially mental computation, and therefore aids in the ability to reason numerically in every number-related area.  Although calculators and tedious counting are available for students who do not have command of the facts, reliance on these methods for simple number combinations is a serious handicap to mathematical growth (p167, Elementary and Middle School Mathematics)

• ### Building Addition and Subtraction skills:

The skill of multiplying and dividing draws on all of the skills studied in the whole number, addition and subtraction sections.  A failure to progress will generally indicate one or more of these skills needs to be revisited.

Student’s early multiplication and division knowledge is based fundamentally on the development of counting sequences and arithmetic strategies, along with skills of combining, partitioning and patterning (CMIT P30, LFN).  Early multiplication and division strategies focus on the structure and use of groups of things.  Rather than emphasizing individual items or number words, students develop increasingly sophisticated ideas of “composites”.  As they develop the concept of multiplication, students focus on groups of items and learn to treat the groups as countable units (CMIT, LFN, P. 6).

Important concepts in moving from step 4 to step 5:

Moving from key concept of Making equal groups

To the key concept of Recognising and using the structure of equal groups to determine totals

References to other resources:

Developing Efficient Numeracy Strategies Book 2 pp 92 – 107

### Activities and Assessments

Hundred Chart activity – Count and Circle

Focus: Students find patterns in the Hundred Chart (or Ninety Nine chart) by repeated adding of equal groups

Count and Circle instruction sheet

99 Chart

Rolling Groups

Focus: Students practice determining totals by using structure of equal groups

How: See Rolling Groups activity sheet

Rolling Groups instruction sheet

2, 5 and 10 dot card set

Chicken Scramble 2

Focus: Finding the total of a moderately large number of counters through grouping by 10s.

How: See Chicken Scramble 2

Chicken Scramble Sheet

Counter Grab

Focus: Using a visible, concrete group structure to calculate totals.

How: See Counter Grab sheet

Counter Grab Sheet