4 Additional Problems K 3

Teaching through Problem Solving, K–3 Additional Problems / 103

Additional Problems Using Literature

Band-Aids: A poem by Shel Silverstein in the book Where the Sidewalk Ends.5

Annotation: In this poem, a child is covered with an unusual amount of Band-Aids even though he doesn’t have any cuts or scrapes.

Weighing Band-Aids

Curriculum Correlation

Grade 1

Shape and Space (Measurement), Specific Outcome 1:

Ø Demonstrate an understanding of measurement as a process of comparing by:

· identifying attributes that can be compared

· ordering objects

· making statements of comparison

· filling, covering or matching.

[C, CN, PS, R, V]

Grade 2

Shape and Space (Measurement), Specific Outcome 2:

Ø Relate the size of a unit of measure to the number of units (limited to nonstandard units) used to measure length and mass (weight).

[C, CN, ME, R, V]

Shape and Space (Measurement), Specific Outcome 3:

Ø Compare and order objects by length, height, distance around and mass (weight), using nonstandard units, and make statements of comparison.

[C, CN, ME, R, V]

Grade 3

Shape and Space (Measurement), Specific Outcome 4:

Ø Demonstrate an understanding of measuring mass (g, kg) by:

· selecting and justifying referents for the units g and kg

· modelling and describing the relationship between the
units g and kg

· estimating mass, using referents

· measuring and recording mass.

[C, CN, ME, PS, R, V]

5. Shel Silverstein, Where the Sidewalk Ends (New York, NY: HarperCollins, 1974), p.140.

Materials

· box of Band-Aids

· balance scale

· measuring objects; e.g., marbles, paper clips, cubes, pennies

Activity

Bring in a box of Band-Aids. Using a balance scale, students will explore measuring the weight of the box of Band-Aids, using nonstandard units; e.g., marbles, paper clips, cubes, pennies.

Ask students to estimate, and then check to see, how much the box of Band-Aids weighs. Record the estimates and actual weights in a table; e.g.,

How much does a box of Band-Aids weigh?
Measuring Unit / Estimate / Actual

Have students determine the amount of Band-Aids that were used in the poem and take that amount out of the box. How many are left inside the box? Make a new estimate for how much the Band-Aids from the poem will weigh. Students may consider their estimates and discoveries from step 1 above to assist with their estimates.

Grade 3 adaptation

Students should weigh the Band-Aids using gram weights to balance the scale, rather than nonstandard measuring units.

Boxes of Band-Aids

Curriculum Correlation

Kindergarten

Patterns and Relations (Patterns), Specific Outcome 2:

Ø Sort a set of objects based on a single attribute, and explain the sorting rule.

[C, CN, PS, R, V]

Grade 1

Patterns and Relations (Patterns), Specific Outcome 3:

Ø Sort objects, using one attribute, and explain the sorting rule.

[C, CN, R, V]

Grade 2

Patterns and Relations (Patterns), Specific Outcome 3:

Ø Sort a set of objects, using two attributes, and explain the sorting rule.

[C, CN, R, V]

Grade 3

Patterns and Relations (Patterns), Specific Outcome 3:

Ø Sort objects or numbers, using one or more than one attribute.

[C, CN, R, V]

Materials

· numerous Band-Aids of various sizes, colours, textures, materials

· Band-Aid boxes to sort Band-Aids into; e.g.,

– photocopy the Band-Aid box sorting mat on p. 86

– bring in empty boxes for students to put Band-Aids into

– photocopy the Band-Aid box sorting mat and paste it to a pocket/envelope (cut a
slit where the box opens so that the Band-Aids could be placed inside the cut with Band-Aids sticking out

Activity

Bring in a variety of Band-Aids. Empty numerous boxes of Band-Aids into a bin. Have students work with a partner to sort the Band-Aids, based on a sorting rule determined by them. Have students use a Band-Aid box to sort Band-Aids by size, colour, texture and material. Students can use more than one box if they have more than one sorting rule. Have them share their sorting rule with another set of partners. The second set of partners could also try to figure out what sorting rule was used.

How Many Band-Aids Do I Need to…?

Curriculum Correlation

Grade 1

Shape and Space (Measurement), Specific Outcome 1:

Ø Demonstrate an understanding of measurement as a
process of comparing by:

· identifying attributes that can be compared

· ordering objects

· making statements of comparison

· filling, covering or matching.

[C, CN, PS, R, V]

Materials

· Band-Aids (real ones for the reference chart, photocopied or laminated Band-Aids for the activity

· paper

· writing tools

· chart for recording estimates and actual measures

Activity

Using Band-Aids, create a reference chart with students to show how much space is used by one, two, three, four, five or six Band-Aids. Have a student choose a body part, of the teacher, that might require one or more Band-Aids; e.g., a foot.

Demonstrate to students how to work together with a partner to trace the body part on a piece of paper. Ask students for estimates of how many Band-Aids would be needed to cover the entire body part. They could refer to the chart to make their estimate or to help explain their reasoning.

Working as partners, have students select 2–3 body parts to estimate, trace and cover with Band-Aids. In preparing for this activity, you could photocopy Band-Aids on paper or laminate Band-Aids of various sizes. Students could use the paper/laminated
Band-Aids to cover their body parts and check their estimates.

Counting and Comparing Band-Aids

Curriculum Correlation

Kindergarten

Number, Specific Outcome 4:

Ø Represent and describe numbers 2 to 10, concretely and pictorially.

[C, CN, ME, R, V]

Number, Specific Outcome 5:

Ø Compare quantities 1 to 10, using one-to-one correspondence.

[C, CN, V]

Grade 1

Number, Specific Outcome 3:

Ø Demonstrate an understanding of counting by:

· indicating that the last number said identifies “how many”

· showing that any set has only one count

· using the counting-on strategy

· using parts or equal groups to count sets.

[C, CN, ME, R, V]

Number, Specific Outcome 4:

Ø Represent and describe numbers to 20, concretely, pictorially and symbolically.

[C, CN, V]

Number, Specific Outcome 5:

Ø Compare sets containing up to 20 elements, using:

· referents

· one-to-one correspondence

to solve problems.

[C, CN, ME, PS, R, V]

Materials

· Band-Aids

· cards with one number (2–10) written on each

Activity

Have students draw a number card and stick the appropriate number of Band-Aids on the empty half of the card. Cut the cards apart. Place the Band-Aid cards face up on the table. Draw a number card. Have students try to match the number card to the Band-Aid card.

Place the Band-Aid cards face down on the table. Set the number cards off to the side. Draw two Band-Aid cards. Have students estimate which card has more. Keep the card that has more and place the card with less face down on the table. Have students repeat these steps until they have only one card left on the table.

Band-Aid Box Sorting Map

The Shopping Basket by John Burningham.6

Annotation: Steven’s mom sends him to the store to get groceries but a number of animals along the way distract Steven.

Patterns, Patterns

Curriculum Correlation

Kindergarten

Patterns and Relations (Patterns), Specific Outcome 1:

Ø Demonstrate an understanding of repeating patterns (two or three elements) by:

· identifying

· reproducing

· extending

· creating

patterns using manipulatives, sounds and actions.

[C, CN, PS, V]

Grade 1

Patterns and Relations (Patterns), Specific Outcome 1:

Ø Demonstrate an understanding of repeating patterns (two to four elements) by:

· describing

· reproducing

· extending

· creating

patterns using manipulatives, diagrams, sounds and actions.

[C, PS, R, V]

Grade 2

Patterns and Relations (Patterns), Specific Outcome 1:

Ø Demonstrate an understanding of repeating patterns (three to five elements) by:

· describing

· extending

· comparing

· creating

patterns using manipulatives, diagrams, sounds and actions.

[C, CN, PS, R, V]

6. John Burningham, The Shopping Basket (London, UK: Red Fox: Random House, 1992).

Patterns and Relations (Patterns), Specific Outcome 2:

Ø Demonstrate an understanding of increasing patterns by:

· describing

· reproducing

· extending

· creating

numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.

[C, CN, PS, R, V]

Materials

· physical objects or paper cutouts of the groceries Steven bought

· bags

· counter top or table

Activity

Working with a partner, students take on acting roles—one student is Steven, the other is the grocery clerk. In this activity, Steven creates patterns and the grocery clerk identifies and extends the pattern.

As Steven’s groceries go through the checkout, he lines them up in a pattern on the counter for the grocery clerk (the pattern should repeat at least twice). Steven should have a remainder of groceries that are not placed on the counter. As the grocery clerk rings the groceries into the cash register, he or she states what the item is and puts it in a bag, all the while analyzing the pattern. When all the groceries from the counter are placed in the bag, the grocery clerk must ask Steven for the next item in the pattern. If the pattern was identified correctly and the grocery clerk asks for the proper item, Steven gives it to him or her. This process is repeated until all groceries are in the bag. Students then reverse roles and the activity can be repeated.

Packing Groceries

Curriculum Correlation

Kindergarten

Patterns and Relations (Patterns), Specific Outcome 2:

Ø Sort a set of objects based on a single attribute, and explain the sorting rule.

[C, CN, PS, R, V]

Shape and Space (Measurement), Specific Outcome 1:

Ø Use direct comparison to compare two objects based on a single attribute, such as length (height), mass (weight) and volume (capacity).

[C, CN, PS, R, V]

Shape and Space (3-D Objects and 2-D Shapes), Specific Outcome 2:

Ø Sort 3-D objects, using a single attribute.

[C, CN, PS, R, V]

Grade 1

Patterns and Relations (Patterns), Specific Outcome 3:

Ø Sort objects, using one attribute, and explain the sorting rule.

[C, CN, R, V]

Shape and Space (Measurement), Specific Outcome 1:

Ø Demonstrate an understanding of measurement as a process of comparing by:

· identifying attributes that can be compared

· ordering objects

· making statements of comparison

· filling, covering or matching.

[C, CN, PS, R, V]

Shape and Space (3-D Objects and 2-D Shapes), Specific Outcome 2:

Ø Sort 3-D objects and 2-D shapes, using one attribute, and explain the sorting rule.

[C, CN, R, V]

Grade 2

Shape and Space (Measurement), Specific Outcome 3:

Ø Compare and order objects by length, height, distance around and mass (weight), using nonstandard units, and make statements of comparison.

[C, CN, ME, R, V]

Shape and Space (3-D Objects and 2-D Shapes), Specific Outcome 6:

Ø Sort 2-D shapes and 3-D objects, using two attributes, and explain the sorting rule.

[C, CN, R, V]

Grade 3

Number, Specific Outcome 12:

Ø Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 × 5) by:

· representing and explaining division using equal sharing and equal grouping

· creating and solving problems in context that involve equal sharing and equal grouping

· modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically

· relating division to repeated subtraction

· relating division to multiplication.

[C, CN, PS, R]

Shape and Space (Measurement), Specific Outcome 4:

Ø Demonstrate an understanding of measuring mass (g, kg) by:

· selecting and justifying referents for the units g and kg

· modelling and describing the relationship between the units g and kg

· estimating mass, using referents

· measuring and recording mass.

[C, CN, ME, PS, R, V]

Materials

· balance scale

· empty containers that will fit on the balance scale

· samples of the foods that Steven was shopping for (real or created)

· bags for groceries

Activity

Students are faced with a few problems to solve as they help Steven bag the items he purchased.

Most baggage clerks put the heaviest items in the bag first, so as not to squish or crush the other groceries. Have students order groceries from heaviest to lightest and put them in bags accordingly.

At the grocery store, students indicate to the cashier how many bags they would like. Suppose Steven asked for 2 bags. Have students try to divide the groceries evenly between the 2 bags. Have them try this again for 3, 4 or 5 bags.

Steven’s groceries were put into 4 bags that all weighed close to the same to make Steven’s walk home easier. Have students try to arrange the objects into 4 bags (containers) so they have a similar weight.

Have students sort the groceries into bags, based on a student-selected sorting rule. Have students see if another student can identify the sorting rule.

Sharing Groceries

Curriculum Correlation

Grade 2

Number, Specific Outcome 2:

Ø Demonstrate if a number (up to 100) is even or odd.

[C, CN, PS, R]

Activity

Suppose that Steven decided to share his groceries with each animal as he met them. By acting out each scene, students can determine which grocery amounts are odd and which are even. Have students say which ones could be shared evenly. Have them say which ones they would not want to share with any of the animals.

Give Me One, Please!

Curriculum Correlation

Grade 2

Statistics and Probability (Data Analysis), Specific Outcome 1:

Ø Gather and record data about self and others to answer questions.

[C, CN, PS, V]

Statistics and Probability (Data Analysis), Specific Outcome 2:

Ø Construct and interpret concrete graphs and pictographs to solve problems.

[C, CN, PS, R, V]