Purpose

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.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
• 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.
Description of Mathematics

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 develop implicit knowledge of 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.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

• beginning the unit by comparing the heights of a pair of students and asking the remaining students deciding who is the tallest. Choose pairs of clearly different heights
• working with individual students to confirm, that when comparing lengths, they know to line up the starting points of the objects being compared
• providing multiple opportunities throughout the school day to directly compare the length of objects (e.g. pencils, width of books, skipping ropes, sticks, poi).
• encouraging tuakana-teina by purposefully pairing and grouping students together.

While this unit is firmly focused on the story of the gingerbread man and a river crossing, it should be adapted to include other fictional characters that your students are familiar with, or are interested in. Māori myths and legends (pūrākau), Pasifika myths and legends, or those that reflect the cultural make-up of your students could offer a culturally relevant context for this learning. Students could also compare the heights of cut-outs of animals or native birds. The gingerbread cut-outs could also be adapted to reflect students’ whānau. This could be followed with discussions around who is the tallest and shortest in their whānau. Within this, you would have to be sensitive to the family/community relationships experienced by your students.

Te reo Māori vocabulary terms such as tāroaroa (tall - person), poto (short), tāroaroa (height of a person), teitei (height, tall), roa (long,length) could be introduced in this unit and used throughout other mathematical learning. Numbers in te reo Māori can be used alongside English throughout the unit.

Required Resource Materials
• Scissors, glue, crayons or similar, sellotape, glue, pencils
• Session One: copies of the gingerbread family (Copymaster 1), large sheets of black paper.
• Session Two: copies of the gingerbread man template and the recording sheet (Copymaster 2 and Copymaster 3) 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 2), variety of coloured paper for clothes (e.g. wrapping paper), wool for hair.
Activity

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 retell the story, or parts of the story, throughout the week to help maintain the focus for the activity sessions. Consider using different stories, that may better reflect the cultural diversity of your class (e.g. The legend of Matariki and the six sisters, the story of the stone that blocked the road round the Cape at Matauea, Safotu). The gingerbread templates could be adapted to reflect any characters.

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. Model this by showing the difference in measurements when items are, and are not, lined up correctly.

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 1).

• 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. Items from nature, or from other contexts for learning could also be used here (e.g. branches, trees, rulers, kete).

#### Session Three: Building Bridges

In this Session students build a model bridge to go over a local river drawn on a large sheet of paper.

1. Provide each student with a gingerbread man template (Copymaster 2) and ask them to cut him out.
2. 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?
3. Provide each student with a recording sheet (Copymaster 3) 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.
4. Compare the objects that are found.
Did anybody find the same objects?
Did anyone find something unique?
5. 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.
6. Show students a 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?
7. 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.
8. 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?
9. 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 (or other chosen characters, e.g. Matariki) then compare the lengths of their chains. This could be related to how many people in each student's whānau.

1. 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.
2. Students select a strip of paper, then make and decorate a chain of gingerbread men.
3. 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?
4. Ask students to join all the chains they have made together and estimate how far the chain will stretch.
5. As a class, decide which chains are the longest and shortest. Write sentences to describe these (e.g. Tama’s chain is the longest. Mia’s chain is the shortest). Support students write sentences to display beside their character chains, that describe the length of their chain in comparison to the length of another student’s chain (e.g. my chain is longer than Mia’s, and shorter than Tim’s). Display these sentences beside the chains.

#### Session Five: Get Dressed Man!

In this Session students cut out clothes to fit a template of a gingerbread man.

1. Provide students with a template of a gingerbread man (Copymaster 2) and a variety of coloured paper to use to make clothes.
2. 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?
If you have reframed the context of this lesson (e.g. around How Māui slowed the sun) you could make further links by investigating what early Māori and Pasifika people wore)
3. 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.
4. 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?
5. If desired students can complete their gingerbread man by drawing a face on him and glueing on wool for hair.
Attachments