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.
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.)
Brainstorm ways to solve the first part of the problem. Strategies of drawing a picture, using equipment or acting it out could be raised.
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?
Have the students plan ways to record their solution. Possibilities include drawing a picture, a diagram, some writing or a flip-fold page.
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?
To conclude the session, have several students share their findings, including the method of recording, with the class. Ensure several different methods of recording are presented and discuss the different ways students used to think about the hiding frogs.
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.
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 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.
_____ 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.