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BANSHO

Planning Sheet (grade 4/5)

Numeration – Subtraction

Curriculum Expectations

|Grade 4 |Grade 5 |

| | |

|Overall Expectation: |Specific Expectations: |

| | |

|Solve problems involving the addition, subtraction… of single and|Solve problems involving the addition, subtraction, … of whole |

|multi-digit whole numbers, and involving the addition and |numbers, using a variety of mental strategies; |

|subtraction of decimal numbers to tenths and money amounts, using|Add and subtract decimal numbers to hundredths, including money |

|a variety of strategies; |amounts, using concrete materials, estimation, and algorithms; |

| | |

|Specific Expectations: | |

| | |

|Add and subtract two-digit numbers using a variety of mental | |

|strategies; | |

|Solve problems involving the addition and subtraction of | |

|four-digit numbers, using student-generated algorithms and | |

|standard algorithms; | |

|Add and subtract money amounts… | |

Mental Math Subtraction Strategies (in order of efficiency):

• Adding-on strategy

• Partial Subtraction strategy

• Compensation strategy

• Constant Difference strategy

• Traditional algorithm

Numeration: Subtraction

1. Subtraction

Adding-on strategy

Prior Knowledge/Activation:

How can you look at 10 + 18 = 28 as a subtraction?

Discussion: thinking about subtraction does not always mean “taking away” from a number, but rather the difference or distance between two numbers.

Today’s Problem:

Mr Wendler had 634 cups of lemon juice. Unfortunately Ryan drank 318 of them. How many cups of lemon juice does Mr. Wendler have left?

Consolidation:

Subtraction can be thought of as the distance between two number, the space in between them (we call the difference). You can start at the smaller number and count your way up to the bigger number.

HW: 10 random subtractions (2 digits)

Looking for: Adding-on strategy

318

+100

418

+100

518

+100

618

+ 2

620

+ 14

634

______

total = 316

Also looking for: FRIENDLY NUMBERS (possibly a number line)

Also possible, start at 318 add 2 (320) add 80 (400) add 200 (600) add 34 (634)

Answer is 2+80+200+34 = 316

2. Same as yesterday, but with a different problem. In the consolidation look for students to make connections between the different ways the Adding-on strategy can be presented (a.: counting up by friendly numbers, b.: counting to a friendly number and then counting up, c.: using a number line (this has been the most popular in my class)).

Possible question: A car dealership had 763 cars on their lot. They had a week-end sale. On Saturday they sold 150 cars. On Sunday they sold 224 cars. How many cars were left on the lot Monday morning?

3. Subtraction

Partial Subtraction strategy

Prior Knowledge/Activation:

How many ways can you subtract 12 from 30? After students have produced some work on sheets (put on blackboard), focus discussion on place values (i.e.: 30 take away 12, 12 is the same as 10 and 2, so you can answer by thinking of the question as 30 take away 10 is 20, take away 2 is 18).

Today’s Problem:

There are 856 pennies in a jar. Mr. Wendler begins rolling them up in coin rolls. He gets tired after rolling 325 pennies. How many pennies does he have left to roll?

(note: 325 is chosen because it is made up of friendly numbers, and will therefore be easier to look at in terms of place value)

Consolidation:

Open up a discussion making connections between the Adding-on strategy and the Partial Subtraction strategy. One uses friendly numbers; the other one uses place values, place values being a more efficient route to solving the problem.

.

Using Partial Subtraction Strategy

856 – 325 856 – 300 = 556

556 – 20 = 536

536 – 5 = 531

300 20 5

HW – 5 random subtraction questions (3 and 4 digit)

4. Subtraction

Compensation strategy

Prior Knowledge/Activation:

(26 – 9 =) How would thinking of this problem as (26 – 10 =) help me solve it? Use a number line do demonstrate.

Today’s Problem:

There are 565 worms in a compost bin. Mr. Wendler took out 285 of them to go fishing. How many worms will be left?

Consolidation:

Subtraction is the distance between two numbers, so if you change one number in order to make the question easy to do using mental math, then that difference needs to be adjusted in your answer.

Compensation Strategy (565 – 285)

565 – 285 = (285 + 15 = 300)

565 – 300 = 265 (shortened the distance between the numbers)

265 + 15 = 280 (therefore have to lengthen the distance to original size)

HW – 5 random addition questions (3 and 4 digit)

5. Subtraction

Constant Difference strategy

Prior Knowledge/Activation:

Review yesterday’s strategy, focusing on keeping the distance between two numbers the same in order to solve a problem.

Today’s Problem:

290 golf balls were in the basket of balls. Mr. Wendler went out to practice his golf drives. He used 140 golf balls. How many were left?

Consolidation:

Continue making connections between keeping the distance between 2 numbers the same being subtraction. If you keep the distance the same you can make the math easier to do mentally. So whatever you do to the first number to make it more friendly, you also have to do to the second number.

Constant Difference Strategy:

290 – 140 =

(290 + 10) 300 – (140 + 10) 150 = 150

HW – 5 random addition questions (3 and 4 digit)

6. Subtraction

Traditional algorithm

Prior Knowledge/Activation:

Using base ten blocks, show (23 – 5), in order to demonstrate how you have to borrow from the tens to solve the problem.

Today’s Problem:

56 stones were in a pile. 18 of them were used to build a retaining wall. How many were left?

Consolidation:

Open up a discussion connecting any of the mental math strategies with the traditional one. Does the traditional strategy end up showing the distance between 2 numbers? How is borrowing similar to the compensation strategy, or the constant difference strategy?

Traditional Strategy:

4 16

56 5 6

-18 -1 8

3 8

HW – Worksheets using traditional strategy for practice.

7. Try one (or two or three) with decimals (money problems) and see if they can transfer the strategies to money (or single decimals).

8. Test

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