This unit develops students’ understanding of, and proficiency in, using five-based grouping.
Gelman and Gallistel (1978) provided five principles that young students need to generalise when learning to count. These principles are:
The first three principles are about how to count. The final two principles are about what can be counted:
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The contexts for activities can be adapted to suit the interests and experiences of your students. For example:
Use a variety of equipment to explore five based grouping: a slavonic abacus, five-based tens frames, unifix (or similar) linking cubes, and students’ hands. Using a variety of representations is a powerful way to develop grouping knowledge. These tasks illustrate grouping with numbers from 5 – 10 but can be used with smaller and larger quantities.
An important connection is between the parts that make ten. If a student knows that in 7 + ? = 10 the missing number is three, then they may transfer that fact to the answer to the problem 3 + ? = 10. For example:
Show me seven fingers.
How many more fingers make ten? How many fingers are you holding down?
Write 7 + 3 =10 and say, “Seven plus three equals ten.”
Show me three fingers.
How many more fingers make ten? How many fingers are you holding down?
Variations
Students work in pairs. One student makes a number up to ten with their fingers. The other says the number and writes the numeral for it big in the air.
Find different ways to make a number to ten, for example, seven can be 5 + 2, 3 + 4, 1 + 6 and 0 + 7. Finding ways to make numbers between 10 and 20 is possible in pairs or threes.
The Slavonic abacus is five based. The purpose of the colouring is to enable instant recognition of a quantity without counting. Try not to use counting to confirm a quantity as that is counter-productive to the intention of either knowing the quantity or working it out from known facts.
For example:
Make a number between 5 and 10 on the top row. Shift the quantity in one move, not one counter at a time.
Show me that many fingers. Note that this gives all students time to work out an answer and it also provides a way for you to see what each student is thinking.
How many beads are there?
How did you know there were eight?
Encourage grouping-based strategies, such as “I can see five and three” and “There are two missing from ten, so I held two fingers down.”
Variations
Ask the students to convince a partner how many beads have moved.
Ask the students to write the number for the beads on the palm of their hand in invisible ink then show you.
Move to “ten and” groupings such as ten and four to develop teen number knowledge. Students work in pairs to show that many fingers or write the number on the palm of their hand.
Hold up a single tens frame, such as nine, for no longer than one or two seconds. The aim is for students to image the five-based patterns rather than count the dots one by one.
How many dots did you see?
Show me that number on your fingers.
Write that number big in the air for me.
Discuss the structure that students saw. “I saw five and four.” “I saw one missing from ten.” I saw three threes.”
Variations
Play 'tens frame flash' in pairs or threes. Players take turns to be the ‘flasher’ and show the tens frames, with the other students stating the number of dots on each tens frame as quickly as possible.
Instead of writing the number, talk to a partner about what you saw.
Write what is found with symbols like, 8 + 2 = 10, 10 – 2 = 8.
Progress to two tens frames being shown. Start with numbers less than five, e.g. four and three. Move to ten and another tens frame for teen numbers, e.g. ten and six. Try ‘close to ten’ frames, like nine and eight, with another tens frame, e.g. nine and five.
Variations
Students play in pairs with one being the hider and the other the estimator.
Start with a number other than ten, e.g. eight stacks made of five and three.
Students match stacks to finger patterns to help them find the number of missing cubes.
Students write equations for the stacks problems, e.g. 7 + ? = 10.
Progress to taking some cubes from each end. Progress to using two stacks of ten to start, depending on the number knowledge of the students.
Dear family and whānau,
In maths we have been working on some number facts. Facts with five are really important because, once we know them, we can use them to help work out other facts. You can practise facts with five with your child at home. Hold up one hand showing five fingers and one hand showing just some fingers. Ask "how many fingers altogether?". Let them test you as well!
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/learning-count-five-based-grouping at 8:30pm on the 26th February 2024