It is acknowledged that the whole number multiplication and division operation sequence should be completed, or almost completed, in the Montessori Lower Elementary classroom. However, it is also acknowledged that more students are moving into the Upper Elementary classroom not having achieved abstraction in multiplication and therefore have no introduction to the whole number division sequence. In addition, students are weak in their multiplication facts (6s, 7s, 8s, and 9s) thereby inhibiting the more advanced multiplication presentations.

This is problematic since the mathematical sequence for both the advanced fractions and decimals assumes mastery of all whole number operations. Providing developmentally appropriate, scaffolded presentations to advance studentsâ€™ understanding in whole number operations at the Upper Elementary level necessitates making choices about what to present and what to leave out. It also implies that the amount of time dedicated to masteryâ€™ is also drastically shortened.

While it is preferable that the complete sequence be adhered to at the developmentally appropriate level, a viable sequence to move students forward is offered. The task cards also provide opportunities for multiplication fact acquisition, while filling in pertinent mathematical comprehension of what happens when multiplying by factors of ten.

Below are some basic assumptions that will allow the teacher to facilitate these presentations:

- Checkerboard and Flat Bead Frame are the salient presentations for multiplication
- Students must complete the multiplication problems at a Passage/Level 3, therefore recording the partial products and abstractly adding the partial products to calculate the total product.
- Higher multiplication facts are purposely chosen to reinforce these facts. If students need assistance in retrieving the products, allow them to use multiplication finger Chart 1.
- Teachers need to introduce, reinforce, and require students to use the appropriate mathematical nomenclature.
- Take opportunities to supplement students understanding by asking questions and making connections between what is shown with the materials, and what is transpiring in the algorithm.

Anticipate that the Transition Card sequence should take between 5 - 7 weeks to complete.

#### As with all our materials this set of task cards meets appropriate math standards.

- 4.oA.A.1: Interpret a multiplication equation as a comparison..
- 4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison
- 4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations.
- 4.OA.B.4: Find all factor pairs for a whole number. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is a multiple of a given one-digit number.
- 4.OA.C.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
- 4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
- 4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, +, and < symbols to record the results of comparison.
- 4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations.
- 4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation.

#### Transition Math Task Cards

#### Level 9-12

A set of task cards providing a bridge that allows students to connect mathematical facts and skills between lower and upper elementary

Credits:

"Wooded Bridge in the port between sunrise" - Tope007; All other images copyright ETC Montessori