Division Practice

Multiplication, run backwards — and asked twenty-six ways.

110 pages · 76 practice sets · 2,174 problems - every one with its answer in the full printed key, the four Check Yourself pages worked through at the back, and Division Words last: every term with the page that practices it.

Division is where the times tables pay off, and this book makes the connection explicit: the first pages draw the rows and groups the ÷ sign is talking about, then every fact in Stage 1 is a multiplication fact read backwards, so a child who knows 6 x 7 already knows 42 ÷ 7. From there a ladder of 74 short sets climbs through the fact family, the missing number, the sign and the undo, patterns, dividing by 10, 100 and 1,000, factors and multiples, money and two-step stories, remainders as real leftovers - and what a story does with them - to long division in the classic bus-stop frame, taught as the five-move loop it actually is: divide, multiply, subtract, compare, bring down.

Is it right? Two pages print a worked division in full, carrying one slip or none, and the child names the step that went wrong or writes correct - the error-analysis page the tests use.

The steps fade. The first long-division frames print the five moves beside them, the next set prints faint guides where the working goes, then the frame is bare. A worked example shows the whole loop inside the frame, and a page names the zero in the quotient: 416 ÷ 4 is 104, not 14.

The strategies the standard names and most books skip. Estimate first with compatible numbers. Check it by multiplying. Break the number apart and divide the pieces - the partial quotient. Two-digit dividends before three-digit ones; two-digit divisors and four-digit dividends at the top.

A page for the grown-up before each stage. What the stage teaches, the words it uses, a checklist to color as the skills are done, and what to say when a child is stuck. Beside every set number is the skill in plain words, the last page of every skill is marked QUICK CHECK, and on the review pages the key names the page that teaches each item.

Not the same page over and over. Twenty-six kinds of question, the rule on every page, three reference pages, three Looking Back pages, four Puzzle Breaks - follow the path, division chains, remainder riddles with a bingo card, who am I? - and a Ready for Grade 5? page.

No wall of problems. Every page is a handful of small lettered blocks worth 100 points together; every frame has real room to work, and the Check Yourself pages carry a Y/N column to mark against the key.

An answer key you can trust, by construction. Every answer was generated together with its problem and independently re-checked by a separate program before printing - every worked division replayed line by line, the riddles re-solved by search, the path maze walked again from its own labels. The key and the pages agree by construction, not by proofreading.

Inside:

• 76 practice sets and 2,174 problems across four stages: the facts; missing numbers and the rules; remainders; long division
• Rows and groups, fact families, the missing number, the sign and the undo, patterns, true or false, seven kinds of division story, the remainder interpreted, divisibility, factors and multiples, the estimate, the check, the partial quotient, the frame, a zero in the quotient, worked divisions to judge
• The rule on every page, three reference pages, a parent page before each stage, Division Words at the back
• Three Looking Back pages, four Puzzle Breaks and a Ready for Grade 5? page
• Full printed answer key, machine-checked at build time, with the working for every Check Yourself answer
• Start Here placement check with a gallery of the question shapes, badge tracker, personal-best log and a certificate - copy-friendly for one family or one classroom