Mathematics
useful linksMath is Fun - dictionary or math terms with examples
e-ako - Sign in using the student login. e-ako is a resource created to support students' development of a sound knowledge and understanding of important maths ideas from levels 1-5 of the New Zealand Curriculum. Khan Academy Sign up. An email has been sent (choose the most recent one. Class Share code if necessary AXDBJX2V Prodigy: Your class code is: FD9C9C Have your students visit prodigygame.com/play select new student, and enter your class code. Prodigy (FD9C9C) Sumdog (Check for the latest Contest or Challenge) TimesTables (Learn your timestables) Multiplication.com (math games) Number Practice Sheets Math Games (Help learn the basic facts) Maths Help Videos New Zealand Maths Curriculum (click the strand and level) Math Dictionary - Check out mathematic terms and meanings. Geoboards Creating Geometric Stars Tangram Puzzles or Tangram Game FloorPlanner Group 1
Group 2 |
What We are Learning: Number
Achievement Objectives: Level 3 L3.1 Number and Algebra
Level 2 |
Number Strategies
Compatible numbers:
Tina catches 6 fish, Miriam catches 7 fish and Liam catches 4 fish. How many do they catch altogether? Discuss and record 6 + 7 + 4. The students model this with three piles of counters. Ask how these numbers can be added by combining the 6 and 4 piles. Encourage them to add the 6 and 4 first to give 10 which makes the answer 17 obvious.
Compensation:
Equal Additions:
For a problem like 445 – 398, the fact that 398 is very close to a tidy number, namely, 400,suggests that a useful way of solving it is by equal additions, in this case, of 2. The problem then becomes 447 – 400, whose answer is obviously 47.
Problems like 73-19=?
Previously this problem was reversed to solve 19 + ? = 73 by adding. Another useful and powerful method here is to subtract 20 from 73 to give 53 and add one to give 54. A problem students often have with this second method is whether to add or subtract the one. The number line makes it obvious why one is added. Eventually, the students need to choose between these two methods for themselves.
Rounding:
There are at least two useful methods for solving such a problem. For example, in the case of 78 + 99: either 78 + 100 = 178, but this is one too many, so the answer is 177, or transfer one from the 78 to the 99. So 78 + 99 is the same as 77 + 100 = 177.
Doubles:
Problem: “Work out 153 + 147.”
Record 153 + 147 on the board or modelling book. Show $153 and $147 with play money. Discuss the fact that transferring $3 gives $150 and $150, so the answer is obviously $300.
Problem: “To work out 79 + 79, Harry works out $80 + $80 with play money first and then says 79 + 79 must be 158.”
Reversibility:
Problem: “At her party, Glynnis provides 67 sweets. At the end of the party, she has 34 left. How many sweets did her guests eat?” The students model 67 as six tens and seven ones and experiment to see why 34 will be left. The connection the students need to make is that the problem can be solved by working out 67 – 34 or by solving 34 + ? = 67
Compatible numbers:
Tina catches 6 fish, Miriam catches 7 fish and Liam catches 4 fish. How many do they catch altogether? Discuss and record 6 + 7 + 4. The students model this with three piles of counters. Ask how these numbers can be added by combining the 6 and 4 piles. Encourage them to add the 6 and 4 first to give 10 which makes the answer 17 obvious.
Compensation:
Equal Additions:
For a problem like 445 – 398, the fact that 398 is very close to a tidy number, namely, 400,suggests that a useful way of solving it is by equal additions, in this case, of 2. The problem then becomes 447 – 400, whose answer is obviously 47.
Problems like 73-19=?
Previously this problem was reversed to solve 19 + ? = 73 by adding. Another useful and powerful method here is to subtract 20 from 73 to give 53 and add one to give 54. A problem students often have with this second method is whether to add or subtract the one. The number line makes it obvious why one is added. Eventually, the students need to choose between these two methods for themselves.
Rounding:
There are at least two useful methods for solving such a problem. For example, in the case of 78 + 99: either 78 + 100 = 178, but this is one too many, so the answer is 177, or transfer one from the 78 to the 99. So 78 + 99 is the same as 77 + 100 = 177.
Doubles:
Problem: “Work out 153 + 147.”
Record 153 + 147 on the board or modelling book. Show $153 and $147 with play money. Discuss the fact that transferring $3 gives $150 and $150, so the answer is obviously $300.
Problem: “To work out 79 + 79, Harry works out $80 + $80 with play money first and then says 79 + 79 must be 158.”
Reversibility:
Problem: “At her party, Glynnis provides 67 sweets. At the end of the party, she has 34 left. How many sweets did her guests eat?” The students model 67 as six tens and seven ones and experiment to see why 34 will be left. The connection the students need to make is that the problem can be solved by working out 67 – 34 or by solving 34 + ? = 67
Standard Written Form (addition)
Problem: “Find 235 + 487 by a standard written method.
Use a compact form.”
Discuss how five and seven produce two ones and one 10 and 12 tens produce two tens and one hundred.
Problem: “Find 235 + 487 by a standard written method.
Use a compact form.”
Discuss how five and seven produce two ones and one 10 and 12 tens produce two tens and one hundred.
Decomposition (subtraction)
Now establish a standard written form for subtraction using a similar method to A Standard Written Form for Addition.
A good way to do this is to explain why 546 – 278 requires 546 to be renamed 4 hundreds + 13 tens and 16 ones and link this to the setting out on the right.
Now establish a standard written form for subtraction using a similar method to A Standard Written Form for Addition.
A good way to do this is to explain why 546 – 278 requires 546 to be renamed 4 hundreds + 13 tens and 16 ones and link this to the setting out on the right.