In this unit students investigate the different number pairs that numbers can be broken into, using the context of frogs in ponds. They list all possible combinations for a given number, working with numbers up to 9.
This unit is all about how numbers are made up of other, smaller numbers, an essential concept underlying addition and subtraction. The unit helps develop two ideas:
Students need to investigate these relationships many times. Once students believe that 2 and 3 is always 5 they see a real reason to remember it.
Students working on this unit will be using the strategy of count all, or counting from one, to solve simple addition and subtraction problems. Students at this stage have a counting unit of one and given a joining or separating problem they represent all objects in both sets, then count all the objects to find an answer. Objects may be represented by materials, or later, in their mind as an image.
From this stage of counting all, students will move to counting on, a stage where they realise that a number can represent a completed count that can be built on.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. As this is an early level 1 unit the numbers may need to be extended beyond 10 for some students. Have equipment available for students to use.
The frogs and pond context for this unit can be adapted to suit the interests and experiences of your students. For example: cars in/out of a parking building, eels hiding/swimming in a river, kererū flying/perched in a tree. You can use the names of New Zealand’s native frogs: Archey’s frog, Hochstetter’s frog and Hamilton’s frog. The name of a local lake or river could be used for this unit. Te reo Māori numbers could be used throughout this unit.
Introduce the problem by sharing a picture of a native frog:
5 frogs live in a pond.
If 2 of the frogs are sitting on the rock, how many are hiding in the pond?
How many different ways are there for the frogs to be, in and out of the water? (There are 6 ways for the frogs to be in and out of the water: none on rock and 5 in pond, 1 on rock and 4 in pond, 2 on rock and three in pond… etc.) Numbers spoken in Te reo Māori can be used also.
Encourage the students to tell you how they know the number of frogs hiding in the pond. Allow the students to describe their ideas and encourage explanations.
How did you know how many frogs were hiding?
Tell us about your thinking.
Could there be any other number of frogs hiding if 2 are on the rock?
How do you know?
Read the second part of the problem and let the students try to solve this, in pairs or on their own. (The frogs need to be treated as identical or there are multiple solutions for each number pairing.) Let the students experiment with the pairings of the digits. The following questions may help support their problem solving:
How do you know how many frogs are on the rock?
Does there always have to be a frog on the rock? Or hiding in the pond?
How are you keeping track of the ways that you find?
Over the next two to three days, revisit the problem with the frogs in the pond, varying the number of frogs living in the pond and sitting on the rock. Explain that because the pond is such a nice place to live, more frogs keep moving in. When reading numbers, use both English and te reo Māori.
Three appropriate number combinations to use would be:
6 frogs live in the pond, begin with 3 on the rock.
8 frogs live in the pond, begin with 2 on the rock
9 frogs live in the pond, begin with 4 on the rock.
These problems are provided on the problem copymaster.
Each day follow a similar lesson structure to the introductory session, with students becoming more independent in their search for solutions as the week progresses. Conclude each session by having students share their solutions and compare their different ways of working.
As a conclusion to the weeks work, have the class work together to make a wall chart illustrating the different combinations of frogs in and out of the water, when 7 frogs are living in the pond (8 possible combinations):
Dear family and whānau,
At school this week we are completing a maths unit on native frogs in ponds. This unit is all about how numbers are made up of other, smaller numbers, an essential concept underlying addition and subtraction. The unit helps develop two ideas:
Children need to investigate these relationships many times. Once children believe that 2 and 3 is always 5 they see a real reason to remember it.
At home this week please help your child to solve the inside and outside the house problem below. Encourage them to record the numbers and draw pictures to show people inside and outside. Toys could be used to show these number relationships. Discuss these in your home language also if you wish to.
_____ people live in my house.
If there are 2 people inside my house then _____ people are outside.
If there are _____ inside my house then _____ people are outside.
If there are _____ inside my house then _____ people are outside.
If there are _____ inside my house then _____ people are outside.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/frogs-ponds at 8:30pm on the 26th February 2024