^{Figure 1: Left: Average accuracy on 6 mathematical benchmarks. We compare with models fine-tuned on the best, public instruction tuning datasets for mathematical problem-solving: MetaMath (Yu et al., 2024) with 395K examples, MMIQC (Liu et al., 2024a) with 2.3 million examples, as well as vanilla rejection tuning (VRT) with 590K examples. Both DART-Math (Uniform) and DART-Math (Prop2Diff) use 590K training examples. Right: Number of responses for each query descending by difficulty across 3 synthesis strategies. Queries are from the MATH training split (Hendrycks et al., 2021). VRT is the baseline biased towards easy queries, while Uniform and Prop2Diff are proposed in this work to balance and bias towards difficult queries respectively. Points are slightly shifted and downsampled for clarity.}