Arithmetic for schools

Edition 2.0 is the edition for classrooms. It adds Kindergarten, and it gives every grade its own Teacher’s Edition. Each child has a printed book for the grade: in Kindergarten the child writes in it, and from Grade 1 works in a squared notebook beside it. Learning starts with the hands, with sticks, cubes, coins and paper strips, and then moves to pencil and paper. No lesson needs a screen.

The books listed on this site’s home page are the current edition, written for families. Edition 2.0 is written from the same course and replaces them in a classroom. It is being written now and is not yet in print.

Arithmetic is the first course of With Every Reason, a mathematics series from Kindergarten to Grade 12 built on the same principles. Grades 7 to 12 are being planned now. Kindergarten to Grade 6 is a complete course in itself, so a school can adopt it on its own.

What each classroom has

Grade	Each child’s book	The teacher’s books
K	Book K	Teacher’s Edition, Kindergarten
1	Grade 1	Teacher’s Edition, Grade 1
2	Grade 2	Teacher’s Edition, Grade 2
3	Grade 3	Teacher’s Edition, Grade 3
4	Grade 4	Teacher’s Edition, Grade 4
5	Grade 5	Teacher’s Edition, Grade 5, Solutions to Grade 5
6	Grade 6	Teacher’s Edition, Grade 6, Solutions to Grade 6

Beside these: the class materials list, sheets to print (the card sheet, the strips), a Family Page for each unit to send home, and the Guide for Teachers and Parents as an optional reference for the whole argument of the course.

How the course answers an adoption committee’s questions

The teaching of standards

Edition 2.0 is being written to Arizona’s standards, not the Common Core’s: each standard in the grade where Arizona places it, and taught with its reason. Every lesson is being written with the codes of the standards it meets. Each grade’s correlation to Arizona’s standards is generated from the books’ source and sent with that grade’s review materials. How it is made is on Arizona standards.

Explicit instruction

The Teacher’s Edition gives every lesson of the year in order, word for word: what to set on the table, what to say and ask, the sentence to wait for from the children, and the whole reason for the rule, so the teacher needs no other book on the desk. A rule is never handed over as a trick. The children first do it with objects, then see why it works, then practise it.

Scope and sequence

The grades build one idea: a number records a measuring. Each grade’s units, in teaching order, are on Scope and sequence.

Evidence of effectiveness

No class has used edition 2.0 yet, so it has no results. Its main choices follow two practices that the What Works Clearinghouse’s 2021 practice guide on helping children who struggle with mathematics supports with strong evidence: objects, then drawings, then numbers; and word problems solved by drawing how the quantities relate. That is a reason to expect it to work, not a result. The research, the two places the course knowingly departs from it, and how we join a district’s pilot are on Approach and evidence.

Assessments

Every lesson ends by listening for one sentence that shows the day’s idea, and each chapter ends with a short check. The teacher keeps a record of each unit against its standards, and each grade will have a year-end assessment. The child is never shown a score, only whether an idea is heard or not yet heard. The practice later in the day is never marked.

Variety of resources

Each grade has the child’s book, the Teacher’s Edition, hands-on materials from a list, sheets to print, Family Pages, and in Grades 5 and 6 a book of worked solutions. Every child’s book is illustrated by the quantities themselves, drawn plainly, so that a child who is still learning to read can follow a problem from its picture.

Differentiation

• A marked core in every lesson, designed so that a child who works half again as slowly can finish it in the lesson’s minutes. For a child slower still, the Teacher’s Edition marks a smaller core by a rule printed in advance, and no reason or proof is left out of it.
• Problems at three levels in every chapter, marked with stars, so that a child at one level always sees the next on the same page.
• A math circle every other week, in Grades 2 to 6 in a period of its own, with problems that need an idea rather than a method; in Grade 1 it is played as a game.
• For a child who finds it hard: more short sittings, never longer ones; the objects kept longer; a smaller step in every lesson; and a lesson tried again, with a change, on the unit’s open day. What the child has not reached is moved, never cut, and never sent home.
• For a child who joins late, a short bridge into the grade.

Ease of use

One plan for the year, with the minutes of each day. Grade 1: a 45-minute lesson. Grades 2, 3 and 4: a lesson of 50, 60 and 60 minutes, and a second practice later in the day of about 23, 17 and 45 minutes, which is part of the course, not an extra. Grades 5 and 6: a 50-minute lesson, with written practice at home. The practice days and the review weeks are in the calendar first, and the lessons fill the rest. No lesson needs a device, a login or an internet connection.

Review materials, prices and ordering

• Review materials of edition 2.0 for an adoption committee, on request: the Teacher’s Edition lessons of Kindergarten and Grade 1, and each later grade’s as it is finished, with that grade’s correlation to Arizona’s standards.
• A one-page note on the research behind the design, and where the course departs from it, on request.
• Our terms for a pilot, in writing, on request.
• Prices for a school, quoted on request: each child’s book per student per year of the book’s life, and the Teacher’s Edition with a class set.
• A presentation to your committee, in person or online, on request.

Contact and publisher

To ask for review materials, a presentation to your committee, a pilot or a quotation, write to sales@witheveryreason.org.

The books are published by With Every Reason, an imprint of Kagu, LLC, in Scottsdale, Arizona. The author is Igor J. Barani.