In this unit students use the traditional tale of the gingerbread man as a context for ordering and comparing lengths. A “sessions” approach is used, with five related but not sequential activities.
- Compare the length of two objects directly.
- Order three or more objects by length.
- Select objects that are the same length as a given object.
Early length experiences must develop an awareness of what length is, and a vocabulary that can be used to discuss length. Young students usually begin by describing the size of objects as big and small. They gradually learn to discriminate in what way an object is big or small and use more specific terms. The use of words such as long, short, wide, close, near, far, deep, shallow, high, low and close, focus attention on the attribute of length.
This unit focuses on students comparing lengths. Although comparing is at the early stages of the measurement learning framework adults will often measure things without using measurement units.
In mathematics it is often useful to have an estimate of the size of an answer to ensure the accuracy of calculations that have been used. The comparisons of lengths in this unit lay the foundation for estimates in area and volume, and for estimates generally.
In comparing three lengths, students implicitly realise the transitive nature of length. Hence if gingerbread man A is taller than gingerbread man B and gingerbread man B is taller than gingerbread man C, then gingerbread man A is automatically taller than gingerbread man C. There is no need to check the heights of A and C. The difference in height follows from the first two comparisons. This ordering ability is a valuable property of numbers and has many uses throughout mathematics. When it is not present, it causes some difficulties.
- Session One: copies of the gingerbread family (Copymaster One), large sheets of black paper.
- Session Two: copies of the gingerbread man template and the recording sheet (Copymaster Two and Copymaster Three) for each student.
- Session Three: large sheet of paper with river drawn or painted on, cardboard, small blocks to support bridges.
- Session Four: strips of paper of varying lengths.
- Session Five: one gingerbread man per student (Copymaster Two), variety of coloured paper for clothes (e.g. wrapping paper), wool for hair.
Begin this series of lessons by reading or recounting the story of the gingerbread man. It is a well known story which students enjoy. Continue to re-tell the story, or parts of the story, throughout the week to help maintain the focus for the activity sessions.
As students work promote the use of language that makes comparisons between lengths, for example the same length, shorter than, longer than. Emphasise the importance of making sure both objects are lined up at one end when comparisons are being made.
Session One: Gingerbread Families
In this Session students order a family of gingerbread men from shortest to tallest, using a variety of measuring words.
Provide each student with a copy of the gingerbread family sheet (Copymaster One).
- Discuss the family. Encourage students to visually estimate lengths before cutting out the gingerbread men.
Who is the tallest?
Who is the shortest?
If we were to put the gingerbread men in a line from tallest to shortest who would be first?
Who would be second? Third?
- Have the students cut out the gingerbread family and order them from tallest to shortest. Emphasise the importance of making sure their feet are all in line when comparing heights.
- Colour in the gingerbread family as desired and glue onto a black backing sheet.
Session Two: Something Taller, Something Shorter
In this Session students find classroom objects that are taller than a gingerbread man, shorter than a gingerbread man or the same size as a gingerbread man.
Session Three: Building Bridges
In this Session students build a model bridge to go over a river drawn on a large sheet of paper.
- Provide each student with a gingerbread man template (Copymaster Two) and ask them to cut him out.
- Discuss the height of the man.
Who can think of something in our classroom that is longer than the gingerbread man?
Who can think of something that is shorter than the gingerbread man?
- Provide each student with a recording sheet (Copymaster Three) and ask them to find and draw onto the sheet five things that are longer than the gingerbread man, five things that are shorter than the gingerbread man and five things that are the same length as the gingerbread man.
- Compare the objects that are found.
Did anybody find the same objects?
Did anyone found something unique?
- Students can check the charts of others by re-measuring objects around the room to see whether they are longer, shorter or the same size as the gingerbread man.
- Show students the drawing / painting of a river and ask them about the story. How did the gingerbread man cross the river in the story?
What could we build to help him cross this river?
- Provide the students with blocks, card and sellotape to make bridges. Leave the “river” at the table where they are working so they can directly compare the width of the river with the lengths of the bridges they are making.
- Once the bridges are complete have the students place them over the river to see if they are long enough.
Could the gingerbread man go over this bridge? Is it long enough?
- They can also compare the lengths of their bridges with the bridges of others. Who has the longest bridge?
Who has the shortest?
Whose bridge is longer / shorter than Paul’s?
Session Four: Gingerbread Men Chains
In this Session students make and decorate chains of gingerbread men then compare the lengths of their chains.
- Show the students how to make a chain of gingerbread men by folding a strip of paper, tracing around a template and cutting out the shape. Emphasise the importance of not cutting the “hands” off on the folds so the gingerbread chain remains joined.
- Students select a strip of paper, then make and decorate a chain of gingerbread men.
- Have students compare the lengths of the chains they have made
Who has the longest / shortest chain?
Which chains are longer / shorter than Andrew’s?
- Ask students to join all the chains they have made together and estimate how far the chain will stretch.
Session Five: Get Dressed Man!
In this Session students cut out clothes to fit a template of a gingerbread man.
- Provide students with a template of a gingerbread man (Copymaster Two) and a variety of coloured paper to use to make clothes.
- Discuss with students what the gingerbread man would like to wear.
How big will his clothes need to be?
How can we make sure the clothes we make will fit him?
- Ask the students to make some clothes for the gingerbread man, and demonstrate how they could trace around the man to make sure the clothes are big enough.
- Once the clothes are completed students can compare the sizes of the clothes they have made before they paste them onto the men.
Who has made the longest pair of trousers?
Whose trousers are shorter than Emily’s?
- If desired students can complete their gingerbread man by drawing a face on him and gluing on wool for hair.