Climb The Ladder

Curriculum Goal

Represent and solve problems involving the multiplication of two- or three- digit whole numbers by one-digit whole numbers and by 10, 100 and 1000, using appropriate tools, including arrays.

Students work in groups of two or more.
Students should have prior experience multiplying two-digit numbers by a one-digit number.

In-person version

Letter-sized paper with five “Ladders” containing common multiple numbers (Appendix A)
One deck of cards known as the “Multiples” cards (Appendix B)
One deck of cards numbered one to 10 (Appendix C)
Coloured playing chips, 20 chips of one colour per student (Appendix D)
Pencil (optional)
Paper (optional)

Online version

The goal is to place a chip on each number of one ladder before your opponent(s).
To determine who goes first, students pull one card from the one to ten deck and one card from the multiples deck. The student with the largest product starts.
To start their turn, the student pulls two cards from the one to ten deck and two cards from the multiples deck.
The student has the option to select one of the two cards they pulled from each deck to calculate a product shown on the ladder. If they can successfully create a number on the ladder, they put one chip on that product (e.g. if a student pulls a three and an eight from the first deck and a 30 and a 20 from the second, they can choose to use eight and 20 to create 160 and put a chip down on that spot). All used cards are put to the side and unused cards are added to the bottom of the pile. If students do not make a product found on the ladder or if the only product they can make already has a chip on it, they miss their turn.
Ladder spots can contain only one chip per player.
Encourage students to write equations on paper if it is challenging to solve the problems mentally.
The students go back and forth trying to fill an entire ladder. The student who fills the ladder first wins.
Students play their turns individually. If this is challenging for some students, they can work in pairs.

What strategies do the students implement to calculate the products of the two numbers?
Are students using division to calculate the numbers they need?
What language is being used by the students when discussing what they will need to win? (e.g. All I need is a six and a 60 to get that 360, then I’ll win!)

Make the numbers in the multiples more complex (E.g. Multiplying by 24 instead of 20).
Make the numbers on the one to ten deck double digit numbers.
Deal each player five of the one to ten cards (Appendix C). During each turn, the student must draw one of the “Multiples” cards (Appendix B). They will not draw from the one to 10 pile on their turn because they will use the cards they have just been dealt. This will challenge students to lay their cards strategically because they will need to think about the probability of certain products being available later in the game. The winner will be the first person to fill a ladder or who gets the most chips on one ladder.