Rich tasks
What number am I?
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1. What number am I?
- An understanding of the properties of 0 and 1 are extremely helpful in solving the puzzle, so it may be best to assign the task at some point after the zero and one section on page 166 of the Student Resource Book.
- Ensure that students are also aware that:
- The number is randomly assigned to a shape, so there is no clue in the shape. Some students may try to establish a relationship between the digit and, for example, the number of sides the shape has.
- The same shape represents the same number wherever it occurs in the puzzle.
- Teachers could suggest that students find a way to keep track of the numbers 0-10 and the shapes they have identified as they explore to avoid repetition or accidental omission of a shape or digit.
- Remind students that only one number between 0 and 10 does not have a symbol, but they will not know for sure what that is until they have matched all the others.
Zero and one page 166
- Know that when any number is multiplied by one, the answer (product) will be the number itself.
- Know that when any number is multiplied by zero the answer (product) is always zero.
- Understand that when the same number is added and subtracted the number stays the same.
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Teacher notes
- Rather than just learn these rules, students should explore these rules for multiplying by zero and one.
- When learning about adding and subtracting the same number it is helpful to use materials with small numbers so that students understand that when a number is added and then subtracted there is no change to the quantity.
- For teachers who want to revise for themselves the use of algebraic symbols and the trajectory of algebra in the curriculum this video may be helpful. https://www.youtube.com/watch?v=NybHckSEQBI
Equals, greater than and less than page 168
- Understand that the equals sign shows that both sides of an equation balance because they have the same value.
- Indicate whether one side of an equation is equal to, greater than, less than or equal to the other using either =, > or <.
- Interpret a relationship diagram and make statements about the relationships shown.
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Teacher notes
- This section explicitly covers the meaning of the ‘equals’ symbol (=) which is used to indicate that quantities on both sides of the equals sign have the same value or ‘balance’. The most common misconception about this symbol is that it indicates that an answer should follow. This misunderstanding may become evident when the usual order of an equation is reversed or both sides of an equation contain an operation, for example, 2 + 3 = 4 + 1
An excellent reading by Charles Darr on the meaning of “equals” and common student misconceptions about can be found at this link: https://www.nzcer.org.nz/system/files/set2003_2_04.pdf - Students may also be interested to know that there is a symbol for not equal (≠).
- Less than (<) and greater than (>) symbols are used to compare the quantities on either side of an equation that does not have the same value on each side. Remembering which way the symbol should face is often student’s greatest hurdle for using these correctly.
One of the most popular ideas for remembering the direction of the symbol is the “Hungry crocodile/shark jaws” where the wide part of the mouth faces the bigger number.
It is also a good idea to encourage students to read equations that contain these symbols out loud, for example, “6 + 1 is greater than 3 + 1”, rather than describing them. For example, “ 7 goes by the open mouth end” or “4 is at the pointy end”. - Writing two parts of an equation on either side of the board and having students indicate with their arms whether they think the equation is equal (parallel arms in front of body), > or < (shape made with both arms to the appropriate side) is a fun warm up that engages all students in active decision making.
- Arrows in relationship diagrams allow comparison between items in two sets. Remind students to check the words describing what each arrow means, for example, “is less than”.
It is important for students to practise reading across, or writing a sentence about the diagram using the meaning of the arrows to make a statement, to describe the relationship shown, for example, “2 is less than 4”
Solving equations page 172
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Teacher notes
- Students are thinking algebraically when they use one example of a strategy to solve other similar problems, determine whether an equation is true or false on the basis of properties they are familiar with for example, the commutative property of addition or multiplication, inverse property of addition and subtraction, properties of 0 and 1, and use these properties to identify unknowns in simple equations.
- In the NZ curriculum, the number strand involves calculating using appropriate and efficient strategies and estimating to make sure that results make sense. Algebra is associated with the number strand and at this level encourages students to identify and represent patterns and relationships. The range of number strategies which students are able to use affects the way students predict and develop general rules about the patterns and relationships they notice.
- If students seem unfamiliar with some or most of the strategies in this section, you could find where to revise these by referring to the “What students should already know” for this chapter.
Using a calculator page 174
- Use a calculator to add, subtract, multiply and divide large numbers.
- Check to see whether an answer from a calculator makes sense.
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Teacher notes
- Calculators are a mathematical tool often used in algebra to explore or extend number patterns beyond the range that a student can work out mentally. Calculators are not a substitute for learning basic facts or using a range of known strategies to solve problems, but it is important that students are able to use this familiar piece of technology.
- Students should be encouraged to check that their answers make sense whether they use a calculator or not.
- If possible, have the same model of calculator for each student, and choose a basic rather than scientific model at this level. This makes explanations and instructions easier for the teacher to give, and for students to understand and support each other.
