Multiplication with Bead Bars
Materials:
Yellow felt underlay the size of the table
Box with 10 compartments
50 of each bead bar 1 – 10
Purposes:
To memorize the essential multiplication combinations
The geometric form of multiplication is useful to show that:
The multiplier is not a quantity but only an indicator of how many times a quantity is taken
A succession of lines creates a surface
Indirect preparation for exercises in algebra, geometry, and division
Age: 5
Preparation: The child has done multiplication with the Stamp Game
Presentation 1: Introduction
Invite the child to get the underlay and then the box of beads.
Remind the child she has seen these beads before and now we will use them for multiplication.
Example for 7: Place one 7 bead place horizontally on the left side of the mat. “Seven taken one time.” Have the child count the bar.
Remove another 7 and place it vertically under the seven on the mat. “Seven one times is seven.”
Remove two and set them horizontally to the right of the first. “Seven taken two times”
Have the child count each bead.
The child will build 14 vertically under the two sevens. “Seven taken 2 times is 14”
Repeat all the way to seven taken 9 times gradually transferring it completely to the child.
Note: Halfway through if you feel the child will understand counting on, show them. (Start counting at the end of the last answer)
Summarize the combinations verbally: seven taken one time is seven, seven taken two times if fourteen, etc.
Ask the child which number they would like to find all the multiples for, probably not tens because they will run out but the others will be fine.
Presentation 2: Commutative Law
Ask the child to pick a number 3, 4, 5, 6, 7.
Example: Child picks 5
You pick a number. Example: 3
Have the child take five 3 times and lay them horizontally.
You take three 5 and times lay them vertically next to or beside the five beads
Note how their shapes are similar
Have the child count the fives. Review, “Five taken 3 times is 15.”
Have the child count the threes. Review, “Three taken 5 times is 15.”
Explain that they are commutative pairs, they are sets that equal each other.
Repeat for another pair. Example: Six 4 times and then Four taken 6 times.
Child counts each and the guide summarizes.
Invite the child to fill up the entire underlay with commutative pairs
Presentation 3: How Many Ways
Chose a number that will have several factors like 12, 16, 18, 24, 32
Example: 24.
Because all numbers can be made with one, start with the two bead. Line them up downward, horizontally oriented, counting aloud, until you get to 24.
Start the child finding ways to make 24 with the three beads by taking out the first three, oriented the same, counting aloud.
Continue with the four beads in the same way.
Have the child start with the fives. They will see that aren’t even so they will go back in the box.
Continue until all the ways to make 24 with multiples have been found.
Once the child has finished, verbally summarize each group.
Control of Error: None
Pedagogical Notes:
Start with 7’s because there are no repetitive answers
You can stitch or draw a line on the underlay to guide the child in the layout of the beads.
Where has the child seen this layout before? Verification 2 in the Addition Snake Game!